7: Food and Choice
Sometimes Environmental History can be a frustrating or even a depressing topic of study. Many of the interactions between people and their environments we have explored in this course have been stories of tragedy and disaster, and the environmental future we and our children face will probably be challenging. In this final chapter, we are going to ask whether individuals can do anything to influence American society’s relationship with its environment for the better. Specifically, we will examine food.
The exact relationship between history and the present is something not all historians agree about. Just because things turned out the way they did, we are not compelled to believe this outcome was inevitable. And although most historians try to avoid using overly simplistic “lessons” from history to argue about what we should do in the present, most would also agree that we study the past to learn about our present circumstances and about how to choose the best future. Over the years I have spoken with many teachers of Environmental History and they have usually expressed two interests. First, trying to end the semester on a positive or at least on a hopeful note. And second, trying to turn all the information we’ve covered in Environmental History toward the question, “Okay, here we are, so what should we do now?
Here are some examples. In April 2014, a Supreme Court decision called McCutcheon v. FEC (Federal Elections Commission) effectively eliminated limits of campaign contributions. In other words, the the new law says more money you have, the more influence you should have in the political process. Whether that actually changes anything or simply acknowledges a reality that has existed for some time remains to be seen, but either way McCutcheon shows how little impact individuals have in our current political system. The Supreme Court Decision is particularly bad news for the environment. The plaintiff in the case, Sean McCutcheon, is CEO of an Alabama-based corporation called Coalmont Electrical Development. As the name suggests, McCutcheon’s company is a contractor working primarily with mining and utility companies. McCutcheon brought the suit because he opposed the $117,000 limit on aggregate contributions in a national campaign cycle. The coal-based energy industry had a lot of money to spend opposing what they called “President Obama’s War on Coal” and they desperately wanted to pack the government with people who would support their coal mining and their coal-fired power plant agendas. Since the 2016 election, the coal industry has had allies in the highest national offices. We’ll see if that saves the coal industry or just delays its end.
One place where actual voters seem to have a little bit more power is California, which has a ballot proposition system that allows proposed laws to be submitted directly to the people for a vote. In the 2012 election there were eleven propositions on the California ballot and in 2016 there were eighteen statewide initiatives ranging from marijuana legalization and gun control to tobacco taxes and educational bonding. In 2016 twelve of the sixteen propositions passed; in 2012 only five passed and six failed. One of the failed 2012 initiatives was Proposition 37, which called for GMO (Genetically Modified Organism) food labeling. GMO labeling was supported by a few food-related companies like Whole Foods, Organic Valley, and Annies (at the time a publicly-traded corporation making organic macaroni and cheese, bought out by General Mills in 2014). Advocates for Prop. 37 raised $8.7 million to use in their media campaign supporting labeling. Their basic message was not that GMOs should be banned, but simply that people had the right to know what was in their food. Opponents of the labeling law raised $46.5 million, the biggest contributor being Monsanto whose $8 million contribution was nearly equal to all the money raised by proponents. The list of companies that contributed more than $150,000 to block GMO labeling is a who’s-who of food manufacturers and chemical companies. At the top of the list, below Monsanto, was DuPont ($5.4 million), Pepsico ($2.1 million), The Grocery Manufacturers Association, DOW Agrisciences, Bayer Cropscience, BASF, and Syngenta (all contributing $2 million). Kraft Foods, Coca-Cola, Nestle, Conagra, General Mills, Kellogg, Smithfield, Del Monte, Campbell’s Soup, and Heinz all contributed between a half million and two million dollars to defeat GMO labeling. Even Ocean Spray Cranberries threw in $387,000.
All these companies believed GMO labeling would be bad for their bottom line, and that a California law might lead to more labeling laws across America. So it is fair to assume they all use GMOs to some extent, and that they would prefer for their customers not to know the actual extent of their GMO use. It is unclear, of course, exactly what effects foods containing GMOs actually have on nutrition and on the health of the people who eat them. But in a large part, that mystery is due to a lack of research at universities and regulatory organizations that rely on the industry for most of their grant funding and personnel. However, we should note that in spite of being outspent 5 to 1 by labeling opponents, Prop. 37’s advocates garnered over six million votes or 48.6% of the final tally. Nearly half of California voters wanted to know what was in their food. The proposition almost passed — but if a GMO labeling law can’t pass in California, what hope is there for a legislative solution anywhere else?
The good news is that California consumers and their allies in other states now have a detailed list of the few food companies that supported and the many that opposed labeling, which they can use to make decisions about what to buy. Even if some GMOs turn out to be harmless, the corporations that opposed labeling have identified themselves with the cause of reducing transparency and making it harder for their customers to make informed purchase decisions. The California election results suggested to many activists that if people are going to change the food system in today’s political environment, it won’t be through government action. Luckily, no one is actually holding a gun to our heads forcing us to eat Smithfield meat, General Mills Cheerios, or Del Monte canned beans. Everybody eats, but somehow most of us have forgotten we can vote with our food dollars. Partly this is because the food industry has been seducing us for decades with inexpensive, tasty treats. But if six million Californians stopped drinking Coke and Pepsi products or eating Kraft’s Mac & Cheese, Lunchables, and Velveeta, would that be a more effective method of voting for change than Prop. 37?
Humans are hard-wired by evolution to crave fat, sweets, and salt because those were the essential nutrients that were scarcest in our diets. Nowadays, they’re just cheap ingredients for food manufacturers. And as anyone who has been to cooking school will tell you, the easiest way to make anything taste good is to add fat. Even bland water chestnuts can become tasty hors d’ouevres if you wrap them in bacon.  Have you noticed the recent explosion of “sweet and salty” and “barbecue” flavors that add sugar, on top of the already wide assortment of “nacho cheese” and “sour cream and onion” flavored chips on supermarket and convenience store shelves?
An element of the food puzzle that causes a lot of disagreement is meat. Americans eat about 270 pounds of meat every year per capita. That’s more than anyone else except Australians and, oddly, citizens of Luxembourg. Our consumption of beef peaked in the mid-1970s and since then chicken has steadily increased until it finally overtook beef in the last few years. For a while food experts claimed that a chicken dinner was actually healthier than a burger or a steak. But most of the chicken consumed in America today is eaten in the form of nuggets, buckets, and wild wings. And in terms of farming practices and environmental impact, chicken and beef are very similar. Both are raised in large-scale confinement facilities (CAFOs) where the animals are fed a diet of corn and antibiotics. Then they, along with pigs and turkeys, are shipped to processing factories that are increasingly owned by just a couple of global corporations such as Tyson, JBS of Brazil, and the Shuanghui Group of China, which recently bought US meat processor Smithfield Foods’s pork operation for $4.7 billion (JBS bought Smithfield’s beef operation in 2009).
We examined the growth of the meat-packing industry in Chapter 7 and noticed that a major factor in the success of the Chicago industry was the introduction of USDA inspection. The government is still responsible for inspecting food products at taxpayer expense, but the agencies given the task of insuring food safety don’t have the budgets or manpower to do the job very effectively. Most problems with food are discovered only when someone becomes sick. The US Food and Drug Administration (FDA) maintains an online list of product recalls and safety alerts. Most of the food products on the bulletin either contain an unlisted ingredient like milk or peanuts that might be dangerous to consumers with allergies, or they are contaminated. The most common contaminants are salmonella and listeria. The USDA maintains its own list, and most of the food products it recalls either contain unlisted allergens or contain salmonella or E. coli. It’s important to note that when the USDA and FDA recall a food product, on the average 63% of the product recalled is not recovered from store shelves, and is sold through to consumers.
The Escherichia coli 0157:H7 variety that is found in many meat products is an enterohemorrhagic strain that causes bloody diarrhea and kidney failure, and can be fatal. Recent research discovered that this strain can bind to plant surfaces (like the skins of fresh fruit and vegetables) and can colonize the roots of lettuces and spinach plants in commercial operations. In 2001 a two-year old boy named Kevin Kowalcyk died of hemolytic uremic syndrome after eating an E. coli-infected hamburger. Legislation called Kevin’s Law designed to strengthen the USDA’s ability to shut down packing plants that have multiple health violations was defeated a couple of years later by the meat industry. But some of the elements of Kevin’s Law were included in an FDA Food Safety Modernization Act that finally passed in 2011. Unfortunately, according to Barbara Kowalcyk (who has a Ph.D. in Epidemiology and Biostatistics and is also the dead boy’s mother who founded the Center for Foodborne Illness Research and Prevention), “The FDA does not currently have sufficient resources to implement the new provisions.”
In addition to the danger of contamination, meat has been criticized by some food activists as a ridiculous waste of resources. According to The Journal of Animal Science, a quarter-pound hamburger takes 6.7 pounds of feed and over 50 gallons of water to produce. Multiply that by the “billions and billions” served by just one major fast food chain, and you begin to see the magnitude of the issue. Most critics of meat estimate that the ratio is about 10 to 1. Ten people, they claim, could be fed plant products using the resources used to feed one person meat. The 10:1 ratio argument has been embraced by Vegans as proof that their diet is the only way to feed all the people of the world. But is this an argument against meat per se, or against meat produced the way we make it now?
In a recent book called Meat: A Benign Extravagance, British author Simon Fairlie coined the term “default livestock” to describe animals raised in a more traditional and, he argued, more sustainable way. Animals, Fairlie observed, have historically been fed things that humans either could not eat or chose not to eat. Ruminants such as goats, sheep, and cattle, grazed on pastures that were either fallow fields in a crop rotation system or hillsides and rangelands unfit for planting. Pigs and chickens ate leftovers and byproducts like peelings and the mash left after a batch of beer or wine was made. Or they ate foods like acorns and fallen fruit that humans could consume but usually can’t be bothered with. If meat production was taken out of CAFOs and returned to this historic “default,” Fairlie argued, people could still enjoy a diet including some meat. The portions would be a bit smaller, but they would be healthier and they’d be sustainable.
As we’ve already seen, CAFOs and corn-fed livestock are the results of subsidies that make it cheaper for a farmer to buy feed than to grow it. But they are also a result of consumer decisions. When we buy a Smithfield pork tenderloin at the Walmart to grill, Americans generally do not think about how the animals were raised and slaughtered. We are unaware of the conditions in the packing plant, where workers who are often illegal aliens working for low wages are judged on speed and on the number of animals they can put through the system in a day. According to a recent book, an animal was killed every 12 seconds at the head of the “disassembly line” where the author was stationed. We are not even aware that the profits from that Smithfield pork loin are going to end up in the Brazilian bank accounts of JBS S.A. rather than in the hands of the American farmer or processors who made the product.
A growing number of Americans, however, are visiting farmers markets and buying shares in CSAs (Community Supported Agriculture). They are taking the opportunity to eat more fresh vegetables and locally produced meat,and eggs. In some cases they are even getting raw milk, although the food safety laws that were designed to protect the public from distant, anonymous food processors now sometimes prevent people from buying food from their neighbors unless those products have gone through a similar regime of of processing and inspection. One of the big barriers preventing more people from selling farm products locally is the time and expense involved in obeying all the rules and laws written to regulate global corporations. Another barrier is the cost of land and equipment. An acre of farmland that is anywhere near an American city is usually priced like a suburban house lot, because the alternative to planting it is building a new subdivision. And when starting as a commercial chicken farmer means that you have to build a confinement building to the specifications of the company that sends you a couple hundred thousand day-old chicks, often the only way to get going is to become what amounts to an indentured servant of a poultry company like Tyson. As a result, the average age of the American farmer is now well over 60.
With these costs in mind, farmers like Virginian author Joel Salatin are beginning to design systems that can be started at a reasonable commercial scale without much capital investment, and that are portable. Salatin’s chicken and turkey “tractors” can be hitched to a pickup truck and hauled to pastures where the farmer is going to raise the birds. This scheme allows a farmer to grow thousands of premium-priced free range birds on rented land. Salatin himself inherited a 500-acre farm in Virginia’s Shenandoah Valley, but to his credit he understands that’s not the way a new generation of sustainable farmers is going to be created. Salatin says that the electric mesh fence and battery-based fence charger he uses may be the most important agricultural innovations in decades (I use them too, and I agree). The fence controllers use microchips to pulse the electrical charge in millisecond increments, preventing the lightweight fence material from melting and allowing fences to be powered by 12-volt rechargeable batteries. This means fences can be set up quickly and moved easily. Animals can be contained and protected from predators far from permanent electrical sources, and can be rotated through fields with unprecedented flexibility. Salatin has designed a grazing rotation using cattle and chickens that he believes could be scaled up to a level where it could actually feed the world.
Scalability is an important issue in this new style of local farming. Critics have argued for decades that farmers markets and CSAs are elite institutions that appeal only to affluent liberals who can afford to spend more than necessary to support local farming for political reasons — but are irrelevant in the “real world” where we have to feed everybody. Feeding the world a diet equivalent to that of a typical American, they say, would take 90% of the available land area. The key, of course, is that feeding everyone like a typical American isn’t what locavores have in mind. Advocates of local solutions believe everyone’s diet needs to change. Fairlie’s idea of default livestock and Salatin’s claim that his grassfed cattle and chicken operation could be scaled up are at least a starting point for discussing a new food system. Sustainable food advocates like Michael Pollan are quick to point out that changing our eating habits produces immediate health benefits as well as long-term social benefits. “Eat food. Not too much. Mostly plants.” is the motto of Pollan’s 2008 bestseller, In Defense of Food. Pollan argues that the food system is going to change, because it is unsustainable. As fossil fuel costs rise, fertilizer production, farm-equipment operation, food processing, and transportation will all become more expensive. The average American’s food travels over 5,000 miles from farm to fork. The typical grocery cart is filled with out-of-season fruits and vegetables, many of which cross the equator on their way to the supermarket. Millions of pounds of perishable produce are actually shipped by jet because they would never make it to market before spoiling if they went by container ship. So jet fuel is actually part of the social cost and the carbon footprint of the pint of strawberries I might buy in Minnesota in January.
A lot of time and energy go into subsistence farming, and we have come a long way since the days when nearly everyone was a farmer in Early American society. Very few people want to give up their careers and their interests and live like the pioneers did in the eighteenth and nineteenth centuries. Although many Americans may decide to supplement their diets with vegetables from a garden or with eggs and meat from a backyard henhouse, the food industry will likely be where the most significant changes are made (or not made) in the future. So the question is, can consumers influence the food industry in ways that will lead to healthier food choices and increased sustainability?
For some people, lifestyle is politics. Conspicuous consumption makes as statement, as does living out of dumpsters. Between these two extremes are a lot of alternatives, and they have changed over time. “Baseball, hot-dogs, apple pie, and Chevrolet” was once a popular advertising slogan. Since then, the old fashioned conservative value of “Buy American” has gone so far out of style (in reality, if not always in rhetoric) that no one would seriously consider running a national advertising campaign in which the product’s American-ness was its most important attribute. In recent years, an organization called Adbusters has sponsored an annual, national anti-consumerism boycott, calling on people to buy nothing on “Black Friday,” the day after Thanksgiving. Buy Nothing Day was an event for several years, and is still observed by some critics of consumerism. Perhaps “sustainable” might be a better concept for people to build a movement around, rather than GMO-free. The science is still unresolved regarding GMOs, as mentioned earlier. But for many people, the issue with GMOs isn’t really genetic modification per se, as much as the idea that global corporations like Syngenta and Monsanto should not be patenting genomes and manipulating them behind a veil of secrecy and government protection that destroys transparency and makes people paranoid.
Organic is another difficult concept. Given the choice between a certified organic bag of chips and a regular one, what are we actually choosing? Which bag of chips is better for the environment, if the regular chips are local and the certified organic ones had to be shipped all the way from a factory in California? And in any case, are either of the bags of chips actually any good for us? Sustainability, as a concept, has the additional advantage that it may actually be measurable and we may be able to ask questions based on those measurements about how our choices affect sustainability at both a personal and societal level. How do my personal choices about food, or about which car to drive, or about how to heat my house influence my ability to sustain my family’s lifestyle? Does our social choice to subsidize corn increase or decrease the sustainability of our food system? If nothing else, discussions about sustainability would tend to focus our attention on the long term and on those economic externalities we usually fail to see.
I’m not sure how much of an answer that is. But for my part, I’m going to continue planting a garden and raising chickens so I know where the meat I feed my family comes from. I may also stop buying from those companies on the list of corporations that opposed labeling in California. If a lot of people did that, it might be a more effective way to change their behavior than through a government that is pretty much owned by those corporations. Now all I have to do is convince a few million of my fellow consumers to join me! But seriously, maybe that’s easier these days than representative democracy. Maybe the moral of the story really is that talk is cheap, but everything we actually do is political.
Further Reading
- Simon Fairlie, Meat: A Benign Extravagance, 2011
- Michael Pollan, In Defense of Food: An Eater’s Manifesto, 2008
- Joel Salatin, Folks, This Ain’t Normal: A Farmer’s Advice for Happier Hens, Healthier People, and a Better World, 2011


11.10: Sample problems and solutions
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Exercise \(\PageIndex{1}\)
Calculate the moment of inertia of a uniform disk of mass \(M\) and radius \(R\) , rotated about an axis that goes through its center and is perpendicular to the disk.
- Answer
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We need to split up the disk into mass elements, \(dm\) , that we can sum together to obtain the moment of inertia of the disk. We can choose a ring of radius \(r\) and radial thickness \(dr\) for the shape of our mass element, as depicted in Figure \(\PageIndex{1}\).
We can define a surface mass density, \(\sigma\) , equal to the mass per unit area of the disk:
\[\begin{aligned} \sigma = \frac{M}{\pi R^2}\end{aligned}\]
The mass of the ring shaped element is thus given by:
\[\begin{aligned} dm = \sigma 2\pi r dr\end{aligned}\]
where \(2\pi r dr\) is the area of the mass element. You can imagine unfolding the mass element into a rectangle of height \(dr\) and of length \(2\pi r\) to obtain its area. Now that we have expressed the mass element in terms of \(r\) , we can proceed to calculate the moment of inertia of the disk.
We know from Example 11.6.1 , that the infinitesimal moment of inertia, \(dI\) , of a ring of radius \(r\) and infinitesimal mass, \(dm\) , about its axis of symmetry is given by:
\[\begin{aligned} dI = dm r^2\end{aligned}\]
The moment of inertia of the disk, is found by summing the moments of inertia of the infinitesimal rings:
\[\begin{aligned} I &=\int dI = \int dm r^2 = \int_0^R \sigma 2\pi r dr r^2 =2\pi \sigma \int_0^R r^3 dr \\[4pt] &=2 \pi \sigma \frac{1}{4}R^4 = 2\pi \left( \frac{M}{\pi R^2} \right) \frac{1}{4}R^4\\[4pt] &=\frac{1}{2}MR^2\end{aligned}\]
where we removed the surface mass density by expressing it in term of the total mass and radius of the disk.
Discussion
The moment of inertia of a disk of mass \(M\) and radius \(R\) is half of that of a ring of radius \(R\) and mass \(M\) . It is thus easier to rotate the disk than the ring.
Exercise \(\PageIndex{2}\)
A sign holder is built by attaching a bar of mass \(M\) and length \(L\) to a wall using a hinge that allows the bar to rotate in the vertical plane. The sign of mass \(m\) is attached to the end of the bar that is opposite from the wall. The bar is held up by a rope that is attached to the wall on one end and to the bar on the other end, two thirds of the length of the bar from the wall, as illustrated in Figure \(\PageIndex{2}\). The rope makes an angle \(θ\) with respect to the horizontal bar. Find the tension in the rope and the magnitude of the force exerted by the hinge onto the bar.
- Answer
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The whole system does not move and so it is in static equilibrium. In order to determine the forces exerted on the bar by the rope and the hinge, we model the bar as being in static equilibrium. The forces exerted on the bar are:
- \(\vec F_g\) , the weight of the bar, with magnitude \(Mg\) , exerted at the bar’s center of mass.
- \(\vec F_m\) , a downwards forced exerted by the sign at the end of the bar, with magnitude \(mg\) .
- \(\vec T\) , a force of tension exerted by the rope at a distance \(2/3 L\) from the wall.
- \(\vec R\) , a force exerted by the hinge on the bar at the end next to the wall 1 . We expect that the force from the hinge will have both a horizontal component, \(R_x\) , and a vertical component, \(R_y\) , in order for the net force on the bar to be zero.
The forces are illustrated in Figure \(\PageIndex{3}\) along with our choice of coordinate system (and the \(z\) axis, not shown, points out of the page).
We start by writing out the \(x\) and \(y\) components of Newton’s Second Law (with zero acceleration):
\[\begin{aligned} \sum F_x &= R_x - T\cos\theta =0\\[4pt] \sum F_y &= R_y + T\sin\theta - Mg - mg=0\end{aligned}\]
We can choose the axis about which to calculate the torques. Since all of the forces are in the \(xy\) plane, we choose to calculate the torques about an axis parallel to the \(z\) axis that goes through the hinge on the wall. The force from the hinge, \(\vec R\) , will thus result in a torque of zero (since it has a lever arm of zero). The torque from each force about the hinge is given by:
\[\begin{aligned} \vec \tau_M &= \vec r_M \times \vec F_g = \left(\frac{L}{2}\hat x\right) \times (-Mg \hat y) =-Mg\frac{L}{2} \hat z\\[4pt] \vec \tau_T &= \vec r_T \times \vec T = \left(\frac{L}{3}\hat x\right) \times (-T\cos\theta \hat x + T\sin\theta \hat y) =T\sin\theta\frac{L}{3} \hat z\\[4pt] \vec \tau_m &= \vec r_m \times \vec F_m = (L\hat x) \times (-mg \hat y) =-mgL\hat z\\[4pt]\end{aligned}\]
The sum of the torques in the \(z\) direction must be zero for static equilibrium, which allows us to determine the magnitude of the force of tension:
\[\begin{aligned} \sum \tau_z = \tau_{Mz} + \tau_{Tz}+ \tau_{mz} &=0\\[4pt] -Mg\frac{L}{2} + T\sin\theta\frac{L}{3} -mgL &=0\\[4pt] -Mg\frac{1}{2} + T\sin\theta\frac{1}{3} -mg &=0\\[4pt] \therefore T&= \frac{3g}{\sin\theta} \left( m + \frac{M}{2}\right)\end{aligned}\]
Using the \(x\) and \(y\) components of Newton’s Second Law, we can now use the tension to determine the \(x\) and \(y\) components of the force exerted by the hinge:
\[\begin{aligned} R_x &= T\cos\theta = \frac{3g}{\tan\theta} \left( m + \frac{M}{2}\right)\\[4pt] R_y &= (M+m)g - T\sin\theta = (M+m)g - 3g \left( m + \frac{M}{2}\right)= -\left( 2m + \frac{M}{2}\right)g\end{aligned}\]
We find that the \(y\) component of the force from the hinge is in the negative \(y\) direction, so our diagram in Figure \(\PageIndex{3}\) is wrong ! If you removed the hinge on the wall and instead held that end of the bar with your hand, you would feel that the end of the bar is trying to go into the wall and upwards, as the bar tries to rotate with the opposite end moving downwards due to the weight of the sign. You would have to push in the positive \(x\) and negative \(y\) direction to keep the bar from moving.
Discussion
In this example, we saw that we needed to use both the sum of the forces and the sum of the torques in order to determine the forces on the bar.
Footnotes
1. We chose the letter R for “Reaction”, as this is the force of reaction from the hinge as the bar pushes against the hinge.


8.5: Skills to Support Confirming Communication Climates
Receiving and Giving Feedback
How we respond to negative feedback, criticism, and corrections can reveal a lot about who we are. Do we respond defensively, or do we receive criticism and feedback graciously and with an open mind? Responding negatively to feedback communicates that we are closed-minded and unwilling to learn and change. On the other hand, thoughtfully receiving feedback shows a willingness to adapt, change, and grow.
In this section, we’re going to learn how to respond non-defensively to feedback and criticism, how to manage frustration while remaining professional, and how to provide positive feedback as well.
Responding Non-defensively to Feedback and Criticism
We need to reflect on how we react to criticism from others and develop our skills in responding in a constructive way. That requires us to take the time and make the effort to process the feedback that others give us in different situations. According to an article titled “The Right Way to Respond to Negative Feedback” (Eurich, 2018):
We can’t act on feedback until we truly understand it. Especially when we hear something new, it’s usually a good idea to ask a few trustworthy sources whether they’ve noticed the same behavior. Not only does this give us more detail about what we are doing to create a certain impression, it helps us avoid overcorrecting based on one person’s opinion. After all, as Roman philosopher Marcus Aurelius stated, “Everything we hear is an opinion, not a fact.”
First off, set your defenses aside and engage your active listening and empathy skills. For empathy, keep in mind that it may be just as difficult for the person giving the feedback as it is for you to receive it. Active listening is important to prevent you from jumping to conclusions and becoming defensive. Additionally, putting defensiveness aside, you may learn something helpful and constructive. Upon receiving feedback, whether in person or in writing, here are some helpful strategies to help you react and acknowledge the feedback.
Use the Feedback WALLET
Consider turning those potentially negative initial reactions to feedback into an opportunity for reflection, planning, and future action. Keep the acronym WALLET in mind, and pull out these helpful suggestions from your “feedback WALLET” to use: W ait, A void attacking back, L isten, L earn, E ngage in planning, and T ake control:
- Wait . Take a moment to digest the information before making any response or decision. Give yourself some time to hear, review, and contemplate the information that is being shared with you. Giving yourself some time to think about and reflect on the feedback can help you avoid jumping to conclusions. This is possibly one of the most important tips to take out of your “feedback WALLET” to use.
- Avoid attacking back . It’s human nature to become defensive when engaged with something unpleasant, like receiving feedback. Listen with an open mind and resist the urge to rebut every point of “criticism” from your communicating partner.
- Listen . Focus your attention and energy on actively listening to the feedback. Identify the key points being made. Ask for clarification and/or examples to help you better understand the messages being shared with you.
- Learn . Reframe the feedback and criticism as an opportunity to learn and grow. Even if you don’t agree with the feedback, there is always something to be learned from how others perceive you.
- Engage in planning . Don’t make excuses. Make a plan instead! Start making a plan of action to correct the issue or work towards a solution. This shows your initiative for problem-solving.
- Take control . “Responsibility” is not the same as “fault.” It’s easy for us to place blame on others or external circumstances. Taking responsibility means taking control of your behavior and responses. Ask yourself, “What can I do differently to get the desired response/results?” By doing this, your perception changes to one of action and looking for opportunities, rather than self-pity and playing the blame game.
Stay Clear of Negative Responses
- Don’t take it personally. Reframe the feedback and criticism as an opportunity to learn and grow. Even if you don’t agree with the feedback, there is always something to be learned from how others perceive you. For example, portray yourself as a gracious recipient of feedback by responding with, “Thank you for taking the time to notice my work and share your thoughts with me.”
- Don’t react right away. It’s human nature to become defensive when engaged with something unpleasant, like receiving feedback. Listen with an open mind and resist the urge to rebut every point of “criticism” from your communicating partner. Ask for time to process and digest the feedback when necessary.
- Don’t argue back. Take this opportunity to listen and learn. Sometimes receiving feedback that seems to conflict with our self-image can make us feel threatened. In this case, rather than respond with something like, “You’re out of your mind! I don’t do that!” It's quite ok for you to use an “I-message”: “I feel surprised that you see my work rushed and sloppy. What can you suggest to help me improve on this?”
- Don’t point fingers and blame others. Remember “responsibility” is not the same as “fault.” It’s easy for us to place blame on others or external circumstances. Taking responsibility means taking control of our behavior and responses. Ask yourself, “What can I do differently to get the desired response/results?” By doing this, your perception changes to one of action and looking for opportunities, rather than self-pity and playing the blame game.
- Don’t make excuses. Start making a plan of action to correct the issue or work towards a solution. This shows your initiative for problem-solving.
Practice P ositive Responses
- Be grateful. Simply thank your communication partner for taking the time to offer their feedback.
- Ask questions. It’s OK to ask for clarification if you don’t understand what’s going on or why/how the negative feedback came about.
- Paraphrase and restate what you understood to have heard to ensure that you interpreted the feedback correctly.
- Ask for help. Ask for one or two simple steps that can nudge you towards improvement.
- Aim for mutual satisfaction. Are the proposed corrections mutually agreed upon? As we know from experience, if one side is not happy with something, that side will not follow through.
- Follow-up to follow-through. Hold yourself accountable and schedule a follow-up. That shows your communicating partner your willingness to learn and improve. But don’t wait too long to schedule that follow-up or you’ll lose your momentum.
Managing Frustration while Remaining Professional
No one likes to deal with a Negative Nellie (or Neil). So how do we remain professional when we're feeling frustrated? The definition of professionalism varies, but it generally boils down to being good at what you know and do, maintaining a positive attitude, treating the people you work with respectfully, maintaining a professional appearance, and meeting your professional obligations promptly. However, all of us, at one time or another, have had our professionalism tested by a co-worker, a superior, a client/customer, or an unanticipated situation. How we handle ourselves in these situations directly impacts the communication climate, either positively or negatively. Here are some suggestions:
- Take a deep breath. Pause and give yourself some time to think about how you want to respond. We often end up regretting those “in the heat of the moment” responses. Research indicates that different emotions are linked to different types of breathing (Philippot et al., 2002). For example, when we are feeling stressed or anxious, our breathing tends to be short, shallow, fast, and irregular. On the other hand, deep, slow, and regular breaths are associated with feelings of joy. This study suggests that when we take the time to mindfully breathe deeply and slowly we will begin to associate the corresponding emotions of calm and joy.
- Look for the positives. There is always something to be learned from every situation. According to the Mayo Clinic (2022), positive thinking leads to positive health benefits. While researchers are still not certain why positive thoughts lead to better health, one theory believes that having a positive outlook allows us to handle stressful situations better, thus reducing the harmful effects stress can have on our bodies. Accordingly, focusing on our strengths and not weaknesses will not only help to energize us but will help build on a positive outlook.
- Reframe how you look at the feedback and use it as motivation. Stacey Finkelstein and Ayelet Fishbach (2012) point out that our experience level dictates the kinds of feedback that motivates us. Novices look for encouragement and positive feedback. Experts prefer more critical feedback that could help develop weaker skills. Therefore, put the negative energy and frustration to work for you to find ways you can turn the obstacle into an opportunity. Set new goals and focus your energy on achieving your new goals.
- Remember that you are in control. Don’t forget that you are in charge of your life and what you need to do to be happy and successful. Choose to use the feedback that you decide is useful and lose the feedback that is not helpful or relevant. It is important to “remember that you don't have to use every bit of feedback that comes to you. You have the power” (Furlan & Schneider, 2021).
Giving Constructive Feedback
Providing constructive feedback is a key factor to support a positive and productive environment. Constructive feedback involves providing individuals with timely and meaningful information regarding strengths and weaknesses in their interpersonal interactions as well as concrete steps for improving any areas of weakness thus fostering personal and professional growth. You may think that simply giving feedback is helping the recipient improve. But giving good, positive, and constructive feedback is not an easy task. Here are some things to consider:
- Are you in a position to comment or provide feedback?
- Is the recipient ready to receive your feedback? If not, you’re walking into a negative communication climate that’s not going to get any better. Timing is important.
- Does the other person want your feedback? If the response is no, you’ll have to come up with another way to deal with the problem at hand.
If all the stars align and the recipient is open and ready to engage in a feedback discussion, be sure to keep these three things in mind as you craft your feedback:
- Be positive. Especially when you know the feedback will include criticism, start and end with positives. Sandwiching the criticisms and corrections between the good points and what they are doing right will help your message be received more positively. See Figure \(\PageIndex{3}\) for a diagram of the "Feedback Sandwich" (an accessible text version is linked in the figure caption).
- Avoid using absolutes or negative words. Absolutes include words like always, never, or don’t. Avoiding using absolutes communicates you are open to different interpretations, solutions, and entertaining the “gray” areas. Psychology research has shown that as humans, we tend to focus more on the negatives to try and make sense of our world. Knowing that, try to replace negative words and phrases with positive ones.
- Avoid comparison. According to social comparison theory, it’s natural that we want to compare ourselves to others. But these comparisons also tend to result in resentment and frustration when the comparisons portray us as less than. Stop comparing people and situations.
- Be specific. Avoid using evaluative adjectives and remember to try and use descriptive words that are precise and straightforward. Address specific issues, behavior, or attitudes that can be improved upon and/or changed. If you are suggesting improvements/changes, specify what you expect and how to achieve it.
All in all, for feedback to be positive, it needs to:
- be given and received at the right time and right place;
- be given with positive points and a specific plan of action;
- be based on facts and information directed at working towards a solution.
Jackson Bird presents “constructive feedback” to his audience about interacting with people who identify as transgender. Through his TED Talk on transgender experiences, he discusses topics such as pronouns, bathroom usage, and more, all while bringing humor, empathy, and transparency to the conversation in an effort to bring awareness and acceptance. Watch the TED Talk or read the transcript and then complete the reflection questions.
Reflection Questions
- How does aspects of your identity (race, religion, nation, age, sex, and so forth) shape your understanding of gender?
- After receiving this “feedback” from Jackson, reflect on your own reactions when first meeting someone who identifies as transgender. For example, can you relate to what Jackson talks about in terms of people’s curiosity regarding transgender bathroom use and their sex lives? How do you keep that curiosity in check so as not to offend your communication partner?
- What tips do you find most useful from the TED Talk?
- Based on the information in this chapter on confirming and disconfirming messages, how can you apply the information to improving the way you talk and listen to transgender people?


6.3: Art and Dominant Culture
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- Elizabeth B. Pearce, Jessica N. Hampton, Hannah Morelos, & Katie Niemeyer
- Linn-Benton Community College via OpenOregon
Art has been a part of history and daily lives for centuries, however many individuals face a place of discrimination and underrepresentation based on their gender, race, sexuality, or other social characteristic. Even in the 20th century we see the perceived differences between men and women’s art in the way that artists are often described. Why is a woman referred to as a “female artist”? A person of color as a “Black photographer”? Or a “Latinx sculptor”? In contrast, when created by a White man, race and gender are often not mentioned.
The topic of whiteness as the dominant culture can be an uncomfortable topic for many, while seeming quite obvious to others. When we describe whiteness, we are using the term to describe a particular system, particularly one that tends to give power to a particular group of people, and oppression to another group of people, otherwise known as White privilege. “White washed art” can be described as giving privilege to a group of people based on their social characteristics and perpetuating a system that favors Euro-Americans (mostly White people).
When we talk about whiteness in art, it allows us the opportunity to peel back a layer of denial. Western expansion and dominance of Indigenous communities is one reason that there is a preference for White and westernized art and institutions. It is interesting to note that implicit bias, “the attitudes and stereotypes that affect our actions that we aren’t aware of, can affect how and what we feel and think about the word art when we hear it.” [1]
What do you think of when you think of “art”? An example of implicit bias would be when an individual from Western culture is asked about art, it is a relatively common bias to think about art in the context of dominant social characteristics. For example, social characteristics such as being “male” or being “White” are dominant in Western culture, especially in the United States. The David statue, created by one of the most famous and revered artists of the 14th century, possibly ever, Michelangelo Buonarroti of Florence Italy, is commonly recognized and is one of the most famous sculptures in the world. The David sculpture is created by individuals possessing dominant social characteristics have made the arts, by association, a practice that is dominantly White and male. We learn early on as children in the U.S through our experience with social institutions.
Social institutions are complex systems that influence its members and present opportunities for members to influence them as well. For example, schools and museums are examples of places that children enter and participate in where they are exposed to art that is, for the most part, majorly White and male dominated. Examples within this chapter show both the built in biases and the ways in which artistic expression helps us move beyond the socially constructed ideas and expand our definitions of art and beauty.
Art, Race, Ethnicity, and Culture
Ken Monkman is a North American artist well known for his paintings that reexamines the past. He frames his work by noting that these past experiences significantly influence the present. Monkman describes his use of visual art to examine the experience of Indigenous people in North America, both during the period of colonization and the effects on the present day families. His paintings depict the violence that European settlers acted upon Indiginous people, and the cultural beliefs that have been silenced. He creates works of art that tell the story from the perspective on those who were harmed and emphasizes the heroism of Indigenous families, the nonbinary aspect of gender they expressed, and other cultural aspects.
Monkman describes his use of visual art to examine the experience of Indigenous people in North America, both during the period of colonization and the continued effects on the present day families in the video below.
A YouTube element has been excluded from this version of the text. You can view it online here: https://openoregon.pressbooks.pub/families/?p=149
Kehinde Wiley is another artist known for using his work to expose hypocrisies in the framing of European history, such as the Age of Reason, or Enlightenment period which is known for its progress in liberty, universalism, separation of church and state, and freedom. This same time period is known for the colonialism of many indigenous people and people of color, including Napolean Bonaparte himself who reinstituted slavery in the French colonies a year after the famous Jacques-Louis David painting “Bonaparte Crossing the Alps” was painted.
Wiley’s re-interpretation of this painting, “Napoleon Leading the Army Over the Alps,” pictures a young Black man in the same pose, but in a way that questions the heroism and softens the military masculinity portrayed in the original. He confronts and critiques the portrayal of Black people in art.
The paintings hang side-by-side in the Brooklyn Museum, through May 2020.
Art, Sex, and Gender
Art, reflective of society, has been work dominated by men. Their work was more likely to be sponsored, commissioned, featured, publicized and preserved. Women artists have often been seen as secondary. The well-known artist Frida Kahlo was a Mexican painter who was inspired by artifacts of her culture and used a folk art style. She explored themes of identity, postcolonialism, class, race, and gender. A prime example of marginalization taking place in Frida Kahlo’s lifetime was when she lived in Detroit married to a male artist named Diego Rivera. In Detroit Frida Kahlo never showed her portraits in any exhibitions however, she did get the opportunity to be interviewed. Although she was interviewed and was praised for her work through this opportunity, when the article came out it was titled “Wife of the Master Mural Painter Gleefully Dabbles in Works of Art”.
Through this lens, Frida Kahlo was publicly known to her peers and the world as “Diego Rivera’s wife” and not as an artist. But Kahlo’s work surpassed Rivera’s in terms of artistic and social recognition.Kahlo died in 1954 at age 47, and her work became best known between the 1970’s and 1990’s. She is regarded as an icon of Chicanos (civil rights movement), feminism, and the LGBTQ+ movement.
Many paintings considered classic representations of ancient myths and events were painted by men. Carmen McCormack, a 2019 graduate of Oregon State University’s Bachelor of Fine Arts program, has recreated some works from a female, feminist and/or lesbian perspective. For example, she has reinterpreted Francois Boucher’s painting “ Leda and the Swan” from 1741 which tells the story of the seduction or rape of Leda by Zeus in the form of a swan.
“I wanted to reinterpret that as a feminist, as a woman and as a contemporary painter,” McCormack said in an interview with the Corvallis Gazette-Times.“In the original (the women) were smiling, which is interesting for a male painter because it reinterprets the story of sexual violence — it’s not a happy thing.” McCormack’s version shows a dark stormy background, and the women’s facial expressions and body language suggest more fear and resistance than does the original.
Centuries ago, genders were oppressed and underrepresented in their creative aspects. We can acknowledge that although there has been an improvement there are still groups, genders, and individuals who face underrepresentation, discrimination, and oppression. New York is known as the hub of art and yet it is estimated that 76% to 96% of the art showcased in art galleries is by male artists. We can see that to this day there is a gender gap in the art industry that continues in the 21st century.
Film
Film, another visual medium, is a part of many family’s daily lives. Mainstream movies are accessible to Americans via many formats. Although women and people of color are represented in audiences in greater percentages than their population base, they are vastly underrepresented in lead roles both on and off screen. In 2018 only one female, Greta Gerwig, and one person of color, Jordan Peele, were nominated for Best Director in the Oscars competition. And in an analysis of speaking roles for women in the 900 most popular films from 2007 to 2016, fewer than one third of the roles went to women. Representation is worse for nonbinary people and when intersectionality of color and gender are examined. [2]
When a child goes into the movies, they are exposed to a variety of people. What most of these actors and actresses have in common is that they are White. As of 2017, only 20% of all lead actors and actresses on screen were people of color. [3] To the children watching these movies, this is the majority demographic being represented. When they do see a prominent character that looks like them, it shows them that they can fit into societal roles.
When movies such as Home, Black Panther, or Crazy Rich Asians came out, people of color flocked to see them. These are movies where there are not obvious stereotypes and there are people of color playing leading roles. Movies with successful people of color are important because, without them, they are pushed to the back of the mind and this reinforces the dominant culture of White as the norm. Especially with the movie Home, parents brought their children to see the main character with the same skin color or hair type as their own. The main character,
Tip, is a young African American girl with natural hair that helps save the day and gets her mom back home. Having a strong young child of color is important because when reading fairy tales to preschoolers, it was found when they were told to draw the main character, most of the students drew a figure with blonde hair and light skin. This implies that these children, even the children of color, saw that White skin meant a happy ending. [4] In their mind, only this type of character was allowed to save the day and be a star.
Representation in movies also pertains to how the characters are portrayed. Do they follow common, sometimes derogatory, stereotypes? Are they seen as the villain? Are they the first to be killed? While a film may have a more diverse cast, if people of color are being represented through stereotypes or type casting- when a person is repeatedly cast for the same type of character, usually based on looks- it sheds a negative light on those people.
In March 2020 the Washington Post Magazine initiated a project in which they asked actors of minoritized groups what kind of roles they typically were cast in, and what kind of roles they would like to play. [5] The article emphasizes the experience of non-White actors in Hollywood. The pictorial essay is linked here, and this is one example from the essay.
The picture on the left shows the role that Nanji is typically cast in; the picture on the right shows a role she would like to play.
Typecasting people contributes to the reinforcement of stereotypes of people of color and other minoritized groups; it emphasizes the centrality of White people both as the norm and as the keepers of interesting plot lines and life stories.
Representation of People of Color
How are people of color represented in visual mediums? And which people of color are prominent? Notice that when leading roles are cast in visual mediums they are often people of lighter colored skin. This is called “colorism” and is distinct from racism in that it shows a preference for the visual look, as opposed to implying that there is inferiority based on race. [6] A recent example is the prominence of Jennifer Lopez (J-Lo) and Shakira in the 2020 Super-Bowl half-time show. While both women are Latina, many people of color do not feel represented by lighter-skinned people who have dyed their hair blonde.
Understanding “isms”
Another way that film can help us to understand the world is to view how an “ism” affects a group that we are not a part of, such as understanding how women experience sexism, or Black people experience racism. But how do we identify which movies can help us really understand what really happens, what the effects are and what “isms” feel like? One of the best ways is to listen to a member of the group that experiences it. Podcasts such as the 1A Movie Club’s program “‘The Help’ Doesn’t Help” in June 2020 helps to explain how White-centered stories about racism fail to expose and teach realistically and deeply. White-centered refers to stories which are told primarily from the White person’s point-of-view, with a lead or leads who are White, and sometimes feature what is called the “white saviour” meaning that it takes someone who is White to solve the problem, save the day, or otherwise fix some aspect of racism. Instead the the podcast hosts and guests recommend the following movies amongst others:
- “13th” (2016)
- “Blackkklansman” (2018)
- “Get Out” (2017)
- “I Am Not Your Negro” (2016)
- “Just Mercy” (2019)
- “When They See Us” (2019)
To listen to the 1A Movie Club lively discussion and debate about movies, Rotten Tomatoes and other movie rating systems, racism, health care, the racial empathy gap, history and current events, listen here.
https://the1a.org/segments/the-1a-movie-club-why-the-help-doesnt-help/
Employment
While our discussion has focused on representation and on the effects that lack of representation has on families, it is important to mention employment. An obvious outcome of fewer people of color or other minoritized groups in media means people in these groups have fewer employment opportunities. A person who has multiple intersectional characteristics has even fewer options. Rosie Perez, in this one minute video talks about the intersectionality of being a woman of color, weight, hotness, ethnicity and age whose job is to act.
A YouTube element has been excluded from this version of the text. You can view it online here: openoregon.pressbooks.pub/families/?p=149
Rosie Perez’ descriptions are supported by research. Family films made between 2006 and 2009 in the United States and Canada were studied specifically for gender bias, but also included appearance and age in the assessment. Beautiful women, with unrealistic body types, exposed skin, and waists so tiny that they would leave “little room for a womb or any other internal organs” are featured in these films with 14-24% possessing these features.In addition, it is most common for women to be under the age of 39 years (about 74%) with a higher percentage of men over the age of 40 years. [7]
Licenses and Attributions
Open Content, Shared Previously
Figure 8.15. “Napoleon Crossing the Alps” by Jacques-Louis David. Public domain.
Figure 8.16. “Poster – Frida Kahlo” by Vagner Borges . License: CC BY-NC-ND 4.0 .
Figure 8.17. “ Leda and the Swan ” by François Boucher. Public domain.
Figure 8.19. “ Adam Driver, John David Washington, and Director Spike Lee at the 2019 Critics’ Choice Awards ” by Chris Miksanek. License: CC BY-SA 4.0 .
All Rights Reserved Content
Figure 8.15. “Napoleon Leading the Army over the Alps” (c) Kehinde Wiley . Image used under fair use.
Figure 8.16. “ Coconuts ” by Frida Kahlo (c) Banco de México Diego Rivera & Frida Kahlo Museums Trust. Image used under fair use.
Figure 8.17. “Leda and the Swan” (c) Carmen McCormack . Image used under fair use.
Figure 8.18. “Tasneem Nanji: Typecast role: Hijabi. Ideal role: Punk rocker” by Haruka Sakaguchi & Griselda San Martin . Images used under fair use.
“ Shame and Prejudice: Artist Kent Monkman’s story of resilience ” (c) University of Toronto. License Terms: Standard Youtube license.
“ Rosie Perez on Roles for Women of Color ” (c) PBS. License Terms: Standard YouTube license.
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The Kirwan Institute for the Study of Race and Ethnicity (2015). Understanding implicit bias. Retrieved February 18, 2020, from
http://kirwaninstitute.osu.edu/resea...implicit-bias/
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Tan, S. (2018, February 28). This year's Oscar nominees are more diverse, but has Hollywood really changed? Washington Post.
https://www.washingtonpost.com/graph...sity-in-films/
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Statista. (2020, February 17). • Ethnicity of lead actors in movies in the U.S. 2019. Retrieved February 28, 2020, from
https://www.statista.com/statistics/...lms-ethnicity/
↵
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Hurley, D. L. (2005). Seeing white: Children of color and the Disney fairy tale princess. The Journal of Negro Education, 74(3), 221–232. ↵
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Sakaguchi, H. & San Martin, G. (2020, March 4). How Hollywood sees me ... and how I want to be seen. Washington Post Magazine. www.washingtonpost.com/magaz...roles-instead/ ↵
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Farrow, K. (2019, January 10). How the camera sees color. National Museum of African American History & Culture. Retrieved March 9, 2020, from
https://nmaahc.si.edu/explore/storie...era-sees-color
↵
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Smith, S.L. & Choueiti, M. (n.d.). Gender disparity on Screen and behind the camera in family films. Geena Davis Institute on Gender in Media. Retrieved June 2, 2020, from
https://seejane.org/wp-content/uploa...y-films-v2.pdf
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13.6: Pregnancy
The Placenta And Foetal Membranes
As the embryo increases in size, the placenta , umbilical cord and foetal membranes (often known collectively as the placenta ) develop to provide it with nutrients and remove waste products (see diagram 13.12). In later stages of development the embryo becomes known as a foetus .
The placenta is the organ that attaches the foetus to the wall of the uterus. In it the blood of the foetus and mother flow close to each other but never mix (see diagram 13.13). The closeness of the maternal and foetal blood systems allows diffusion between them. Oxygen and nutrients diffuse from the mother’s blood into that of the foetus and carbon dioxide and excretory products diffuse in the other direction. Most maternal hormones (except adrenaline), antibodies, almost all drugs (including alcohol), lead and DDT also pass across the placenta. However, it protects the foetus from infection with bacteria and most viruses.
Diagram 13.11 - Development and implantation of the embryo
Diagram 13.12. The foetus and placenta
The foetus is attached to the placenta by the umbilical cord . It contains arteries that carry blood to the placenta and a vein that returns blood to the foetus. The developing foetus becomes surrounded by membranes. These enclose the amniotic fluid that protects the foetus from knocks and other trauma (see diagram 13.12).
Diagram 13.13 - Maternal and foetal blood flow in the placenta
Hormones During Pregnancy
The corpus luteum continues to secrete progesterone and oestrogen during pregnancy. These maintain the lining of the uterus and prepare the mammary glands for milk secretion. Later in the pregnancy the placenta itself takes over the secretion of these hormones.
Chorionic gonadotrophin is another hormone secreted by the placenta and placental membranes. It prevents uterine contractions before labour and prepares the mammary glands for lactation. Towards the end of pregnancy the placenta and ovaries secrete relaxin , a hormone that eases the joint between the two parts of the pelvis and helps dilate the cervix ready for birth.
Pregnancy Testing
The easiest method of pregnancy detection is ultrasound which is noninvasive and very reliable Later in gestation pregnancy can be detected by taking x-rays.
In dogs and cats a blood test can be used to detect the hormone relaxin .
In mares and cows palpation of the uterus via the rectum is the classic way to determine pregnancy. It can also be done by detecting the hormones progesterone or equine chorionic gonagotrophin ( eCG ) in the urine. A new sensitive test measures the amount of the hormone, oestrone sulphate , present in a sample of faeces. The hormone is produced by the foal and placenta, and is only present when there is a living foal.
In most animals, once pregnancy is advanced, there is a window of time during which an experienced veterinarian can determine pregnancy by feeling the abdomen.
Gestation Period
The young of many animals (e.g. pigs, horses and elephants) are born at an advanced state of development, able to stand and even run to escape predators soon after they are born. These animals have a relatively long gestation period that varies with their size e.g. from 114 days in the pig to 640 days in the elephant.
In contrast, cats, dogs, mice, rabbits and higher primates are relatively immature when born and totally dependent on their parents for survival. Their gestation period is shorter and varies from 25 days in the mouse to 31 days in rabbits and 258 days in the gorilla.
The babies of marsupials are born at an extremely immature stage and migrate to the pouch where they attach to a teat to complete their development. Kangaroo joeys, for example, are born 33 days after conception and opossums after only 8 days.


28.0: Prelude to Invertebrates
A brief look at any magazine pertaining to our natural world, such as National Geographic , would show a rich variety of vertebrates, especially mammals and birds. To most people, these are the animals that attract our attention. Concentrating on vertebrates, however, gives us a rather biased and limited view of biodiversity, because it ignores nearly 97 percent of the animal kingdom, namely the invertebrates. Invertebrate animals are those without a cranium and defined vertebral column or spine. In addition to lacking a spine, most invertebrates also lack an endoskeleton. A large number of invertebrates are aquatic animals, and scientific research suggests that many of the world’s species are aquatic invertebrates that have not yet been documented.


18.2B: Elastic Arteries
An elastic or conducting artery has a large number of collagen and elastin filaments in the tunica media.
- Distinguish the elastic artery from the muscular artery
Key Points
- Elastic arteries include the largest arteries in the body, those closest to the heart. They give rise to medium-sized vessels known as muscular, or distributing, arteries.
- Elastic arteries differ from muscular arteries both in size and in the relative amount of elastic tissue contained within the tunica media.
- Arterial elasticity gives rise to the Windkessel effect, which helps to maintain a relatively constant pressure in the arteries despite the pulsating nature of blood flow.
Key Terms
- elastic arteries : An artery with a large number of collagen and elastin filaments, giving it the ability to stretch in response to each pulse.
- tunica media : The middle layer of a vein wall with bands of thin smooth muscle.
Elastic arteries contain larger numbers of collagen and elastin filaments in their tunica media than muscular arteries do, giving them the ability to stretch in response to each pulse.
Elastic arteries include the largest arteries in the body, those closest to the heart, and give rise to the smaller muscular arteries. The pulmonary arteries, the aorta, and its branches together comprise the body’s system of elastic arteries. In these large arteries, the amount of elastic tissue is considerable and the smooth muscle fiber cells are arranged in 5 to 7 layers in both circular and longitudinal directions.
Anatomy of the Arterial Wall : Arterial wall layers including the tunica intima and the tunica media. In elastic arteries, the tunica media is rich with elastic and connective tissue.
The aorta : The aorta makes up most of the elastic arteries in the body.
Arterial elasticity gives rise to the Windkessel effect, which through passive contraction after expansion helps to maintain a relatively constant pressure in the arteries despite the pulsating nature of the blood flow from the heart.
The Aorta
Due to position as the first part of the systemic circulatory system closest to the heart and the resultant high pressures it will experience, the aorta is perhaps the most elastic artery, featuring an incredibly thick tunica media rich in elastic filaments. The aorta is so thick that it requires its own capillary network to supply it with sufficient oxygen and nutrients to function, the vasa vasorum.
When the left ventricle contracts to force blood into the aorta, the aorta expands. This stretching generates the potential energy that will help maintain blood pressure during diastole, when the aorta contracts passively. Additionally, the elastic recoil helps conserve the energy from the pumping heart and smooth the flow of blood around the body through the Windkessel effect.


5.4: Decimals- Scientific Notation
Learning Outcomes
- Convert from scientific notation to decimal notation and back.
In this section, we will look at how to read scientific notation. A very common error that statistics students make is not noticing that the calculator is giving an answer in scientific notation.
Scientific Notation
When a calculator presents a number in scientific notation, we must pay attention to what this represents. The standard way of writing a number in scientific notation is writing the number as a product of a number greater than or equal 1 but less than 10 followed by a power of 10. For example:
\[ 602,000,000,000,000,000,000,000 = 6.02 \times 10^{23} \nonumber\]
The main purpose of scientific notation is to allow us to write very large numbers or very small numbers close to 0 without having to use so many digits. Most calculators and computers use a different notation for scientific notation, most likely because the superscript is difficult to render on a screen. For example, with a calculator:
\[0.00000032 = 3.2E-7 \nonumber\]
Notice that to arrive at 3.2, the decimal needed to be moved 7 places to the right. The "E" represents "times 10 raised to the power of."
Example \(\PageIndex{1}\)
A calculator displays:
\[2.0541E6 \nonumber\]
Write this number in decimal form.
Solution
Notice that the number following E is 6. This means move the decimal over 6 places to the right. The first 4 moves is natural, but for the last 2 moves, there are no numbers to move the decimal place past. We can always add extra zeros after the last number to the right of the decimal place:
\[2.0541E6 = 2.054100E6 \nonumber\]
Now we can move the decimal place to the right 6 places to get
\[2.0541E6 = 2.054100E6 = 2,054,100 \nonumber \]
Example \(\PageIndex{2}\)
If you use a calculator or computer to find the probability of flipping a coin 27 times and getting all heads, then it will display:
\[ 7.45E−9 \nonumber\]
Write this number in decimal form.
Solution
Many students will forget to look for the "E" and just write that the probability is 7.45, but probabilities can never be bigger than 1. You can not have a 745% chance of it occurring. Notice that the number following E is −9. Since the power is negative, this means move the decimal to the left, and in particular 9 places to the left. There is only one digit to the left of the decimal place, so we need to insert 8 zeros:
\[ 7.45E−9 = 000000007.45E−9 \nonumber\]
Now we can move the decimal place to the right 9 places to the left to get
\[ 7.45E−9 = 000000007.45E−9 = 0.00000000745 \nonumber\]
This is a very small probability and essentially rounds to 0.


1.6: Hyperbolic Functions
The hyperbolic functions are important functions defined in terms of exponentials: \[\begin{align} \sinh(x) &= \frac{1}{2}\left(e^{x} - e^{-x}\right) \\ \cosh(x) &= \frac{1}{2}\left(e^{x} + e^{-x}\right) \\ \tanh(x) &= \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\end{align}\] They have properties that are intriguingly similar to the trignometric functions, such as: \[\begin{align} \sinh(x+y) &= \sinh(x)\cosh(y) + \cosh(x)\sinh(y) \\ \cosh(x+y) &= \cosh(x)\cosh(y) + \sinh(x)\sinh(y)\end{align}\] Because of these identities, it is sometimes more convenient to work with hyperbolic functions rather than exponentials. During this course, we will learn about the intricate relationship between the hyperbolic and trigonometric functions.


1.5: Dimensioning
If a drawing is to be complete, so that the object represented by the drawing can be made as intended by the designer, it must tell two complete stories. It tells this with views , which describe the shape of the object, and with dimensions and notes , which gives sizes and other information needed to make the object.
Therefore, your next step is to learn the basics of dimensioning. In that way you will understand not only how to interpret a drawing to get the information you need, but also how to dimension your sketches so that they can be used to communicate size information to others.
Numerals
It may seem a bit basic, but a few exercises with the shapes of numbers comes before dimensioning. The reason for such review is simply that incorrectly or carelessly made numbers on a drawing or sketch can easily be misinterpreted by someone on the job. That can be costly.
Therefore, the study of numbers forms is justified.
The number forms presented here have been determined to be the most legible, and are used by industry nationwide. The United States standardized 1/8” vertical numbers are correctly formed as follows:
Dimension Lines
The dimension line is a fine, dark, solid line with arrowheads on each end. It indicates direction and extent of a dimension. In machine sketches and drawings, in which fractions and decimals are used for dimensions, the dimension line is usually broken near the middle to provide open space for the dimension numerals. In architectural and structural sketches and drawings, the numerals are usually above an unbroken dimension line.
In either case, the dimension line which is closest to the object should be placed approximately
1/2″ away. The other dimensions beyond the first dimension (if any) should be approximately 3/8″ apart. You do not necessarily have to remember this, but you should remember not to crowd your dimension lines and to keep them a uniform distance apart.
The most important thing is that the drawing needs to be “clean” and dimensions need to be located in a space where they cannot be confused with a surface they are not intended to be used for.
Here is how dimension lines should be sketched:
Note: Dimensions less than six feet (72 in.) are given in inches. Dimensions over six feet are usually shown in feet and inches. Be sure that it is clear how dimensions are called out. When calling out dimensions that are over 12”, make sure ALL of dimensions are called out in total inches or feet inches throughout the entire drawing. Either 4’-5” or 53”, they both mean the same thing but if there is a mix of dimensioning it can become easy to look at 4’-8” and see 48”.
Extension Lines
Extension lines on a drawing are fine, dark, solid lines that extend outward from a point on a drawing to which a dimension refers. Usually, the dimension line meets the extension line at right angles. There should be a gap of about 1 / 16″ where the extension line would meet the outline of the object, and the extension line should go beyond the outermost arrowhead approximately 1 /8″. Also, there should be not gaps where extension lines cross. Notice in this example the larger dimensions are correctly placed outside, or beyond the shorter dimensions, and that the dimensions are preferably not drawn on the object itself. Sometimes, however, it is necessary to dimension on the object.
It is important to remember to place dimensions on the views, in a two or three view drawing, where they will be the most easily understood. Avoid dimensioning to a hidden line and avoid the duplication of dimensions. Use common sense; keep dimensions as clear and simple as possible. Remember, the person reading your drawing needs to clearly understand, beyond question, how to proceed. Otherwise, costly time and material will be wasted.
There are two basic methods of placing dimensions on a sketch. They may be placed so they read from the bottom of the sketch (unidirectional dimensions) or from the bottom and right side (aligned dimensions). The unidirectional system is usually best, because it is more easily read by workmen.
When dimensions will not fit in a space in the usual way, other methods are used to dimension clearly, when those crowded conditions exist.
Arrowheads
Arrowheads are placed at each end of dimension lines, on leader lines, etc. Correctly made, arrows are about 1/8” to 3/16” in length, and are about three times as long as they are wide. Usually they have a slight barb, much like a fishhook.
To make your drawing look clean, use the same style throughout your drawing or sketch.
Dimension numerals
Numerals used to dimension an object are normally about 1/8” in height.
When a dimension includes a fraction, the fraction is approximately 1 / 4″ in height, making the fractional numbers slightly smaller to allow for space above and below the fractional line.
Again, it is particularly important that the numbers and fractions you may put on a sketch or drawing be legible. Sloppy numbers can cause expensive mistakes.
Notes
Notes are used on drawings to provide supplementary information. They should be brief and carefully worded to avoid being misinterpreted, and located on the sketch in an uncrowded area. The leader lines going to the note should be kept short. Notes are usually added after a sketch has been dimensioned to avoid interference with dimensions.
Quiz
Directions: Dimension the examples as indicated.
Dimension this 3 ¼ x 6 15/32 rectangle unidirectionally on the top and right sides.
With a note, show a 5/16 drilled hole.
Dimension this object. The shorter lines are 3 inches in length.
Dimension this object. Use a ruler or scale to determine the line lengths.
Oblique Dimensioning
Oblique dimensioning is mostly remembering to avoid dimensioning on the object itself (when possible) and the use of common sense dimensioning principles. It is also usually best to have dimensions read from the bottom (unidirectional) as shown here.
Although it is best not to dimension on the view itself, its usually accepted practice to place diameter and radius dimension on the views if space permits.
Sometime space and time is limited and you might have to bend the typical rules of drawing and dimensioning. The most important thing is to keep the drawing clean, concise, try to not a repeat dimensions but give all required ones.
Directions: Complete as indicated.
Dimension this three inch cube.
The shorter section of this rod is 5/8 inches in diameter by 2 1/8 inches long. The longer section is 7/8 inches in diameter by 3 ½ inches long. Dimension the drawing.
Isometric Dimensioning
When dimensioning an isometric sketch, it is important to keep dimensions away from the object itself, and to place the dimension on the same plane as the surface of the object being dimensioned. You will probably find that to dimension well in isometric will take some practice.
Place notes on an isometric drawing without regard to placing them on the same plane, as with dimensions. It is easier to do, and easier to read.
Isometric notes do not have to be on the same plane.
Notice in the example above that part of each leader line to the notes are sketched at an approximate angle of 15, 30, 45, 60 or 75 degrees. This is done to avoid confusion with other lines. Never draw leader lines entirely horizontal or vertical .
Quiz
Directions: complete as indicated.
Dimension this drawing. The dimensions are 3” long, 2 1/8” wide, 1 5/8” high with a 45◦ angle ½” deep. The angle begins as the midpoint of the 3” long dimension.
Dimension this drawing. The base is ½” x 1 ½” square. The cylinder is 1” ∅. x 1-1/8”
long. The drilled through hole is ∅5/8”.
Quiz
Directions: You will be given an object to sketch and dimension.
Orthographic Dimensioning
When you look at the dovetailed object several pages back, it is easy to see that an isometric sketch can quickly become cluttered with dimensions. Because of this, more complicated sketches and drawings are dimensional in orthographic. This method provides the best way to dimension clearly and in detail.
Here are seven general rules to follow when dimensioning.
- Show enough dimensions so that the intended sizes can be determined without having a workman calculate or assume any distances.
- State each dimension clearly, so it is understood in only one way.
- Show dimensions between points, lines or surfaces which have a necessary relationship to each other or which control the location of other components or mating parts.
- Select or arrange dimensions to avoid accumulations of dimensions that may cause unsatisfactory mating of parts. (In other words, provide for a buildup of tolerances, as in the example below.
- Show each dimension only once. (Do not duplicate dimensions).
- Where possible, dimension each feature in the view where it appears most clearly, and where its true shape appears.
- Whenever possible, specify dimensions to make use of readily available materials, parts and tools.
Notice the dimensions are correctly placed between the views, rather than around the outside edges of the drawing.
Quiz
Directions: one a separate piece of paper, make a dimensioned orthographic sketch of this object.
Directions: on a separate piece of paper, make a dimensional orthographic sketch of the object.
Quiz
Directions: You will be given an object to sketch and dimension.


22.13A: Absorption in the Small Intestine
The absorption of nutrients occurs partially by diffusion through the wall of the small intestine.
- Describe the role played by the small intestine in the absorption of nutrients
Key Points
- Digested food is able to pass into the blood vessels in the wall of the small intestine through the process of diffusion.
- The inner wall, or mucosa, of the small intestine is covered in wrinkles or folds called plicae circulares that project microscopic finger-like pieces of tissue called villi, which in turn have finger-like projections known as microvilli.
- The function of the plicae circulares, the villi, and the microvilli is to increase the amount of surface area available for the absorption of nutrients.
- Each villus transports nutrients to a network of capillaries and fine lymphatic vessels called lacteals close to its surface.
Key Terms
- villi : Tiny, finger-like projections that protrude from the epithelial lining of the intestinal wall.
- plicae circulares : These circular folds (known as the valves of Kerckring or the valvulae conniventes) are large, valvular flaps that project into the lumen of the bowel.
- diffusion : The act of diffusing or dispersing something, or the property of being diffused or dispersed; dispersion.
EXAMPLES
Examples of nutrients absorbed by the small intestine include carbohydrates, lipids, proteins, iron, vitamins, and water.
The Small Intestine
The small intestine is the part of the gastrointestinal tract between the stomach and the large intestine where much of the digestion of food takes place. The primary function of the small intestine is the absorption of nutrients and minerals found in food.
Intestinal villus : An image of a simplified structure of the villus. The thin surface layer appear above the capillaries that are connected to a blood vessel. The lacteal is surrounded by the capillaries.
Digested nutrients pass into the blood vessels in the wall of the intestine through a process of diffusion. The inner wall, or mucosa, of the small intestine is lined with simple columnar epithelial tissue.
Structurally, the mucosa is covered in wrinkles or folds called plicae circulares—these are permanent features in the wall of the organ. They are distinct from the rugae, which are non-permanent features that allow for distention and contraction.
From the plicae circulares project microscopic finger-like pieces of tissue called villi (Latin for shaggy hair). The individual epithelial cells also have finger-like projections known as microvilli. The function of the plicae circulares, the villi, and the microvilli is to increase the amount of surface area available for the absorption of nutrients.
Each villus has a network of capillaries and fine lymphatic vessels called lacteals close to its surface. The epithelial cells of the villi transport nutrients from the lumen of the intestine into these capillaries ( amino acids and carbohydrates) and lacteals (lipids).
The absorbed substances are transported via the blood vessels to different organs of the body where they are used to build complex substances, such as the proteins required by our body. The food that remains undigested and unabsorbed passes into the large intestine.
Absorption of the majority of nutrients takes place in the jejunum, with the following notable exceptions:
- Iron is absorbed in the duodenum.
- Vitamin B12 and bile salts are absorbed in the terminal ileum.
- Water and lipids are absorbed by passive diffusion throughout the small intestine.
- Sodium bicarbonate is absorbed by active transport and glucose and amino acid co-transport.
- Fructose is absorbed by facilitated diffusion.
Section of duodenum : Section of duodenum with villi at the top layer.


6.11: Activities
- Write a technical definition for the word car.
 Then do the same for a train.
Note. Do not go back and modify your definition of car ; test the objects transport truck and train against whatever definition you initially came up with in Task a.
- What is the point of this activity?
A square number is an integer which is equal to the square of some integer. An integer is square free if it is not divisible by any square number other than \(1\text{.}\)
- Is \(0\) a square number? Is it square free?
- Does there exist a negative square number?
- Is every negative number square free?
- Is every prime number square free?
- Is every square free number prime?
- Does there exist an integer which is both a square number and square free?
The following statement is a basic (and very useful) fact about real numbers.
Triangle Inequality: For every pair of real numbers \(x\) and \(y\text{,}\) \(\vert x+y \vert \le \vert x \vert + \vert y \vert\text{.}\)
Use the above statement to directly prove the following extended version of the inequality, without resorting to considering cases of positive/negative for any of the variables.
For every triple of real numbers \(x\text{,}\) \(y\text{,}\) and \(z\text{,}\) \(\vert x+y+z \vert \le \vert x \vert + \vert y \vert + \vert z \vert\text{.}\)
Remark. Using the two-number version of the inequality to prove the three-number version is an example of inductive reasoning, something that we will soon investigate further.
Suppose you are analyzing the rules for a complicated table-top game, and you have come to the following realization.
Given any trio of distinct wizards where the first is zapping the second, at least one of the following must also occur: the first is zapping the third or the third is zapping the second.
If you were to approach proving this statement using the advice you read on how to handle statements involving disjunction in Procedure 6.5.1, the first sentence of your proof would be
Assume \(\underline{ }\).
and the last sentence of your proof would be
Therefore \(\underline{ }\).
What is the difference between proving the contrapositive and proof by contradiction ?
- A positive integer that is greater than \(1\) and not prime is called composite.
Write a technical definition for the concept of composite number with a similar level of detail as in the “more complete” definition of prime number given in Example 6.1.1 .
Note. Don't just define it as “not prime.” And make sure that the equality \(7 = 1 \times 7\) can't be used to justify the statement “\(7\) is composite” by your definition (because prime \(7\) is most definitely not composite).
- Prove by proving the contrapositive: If \(2^n - 1\) is prime, then \(n\) is prime.
- Hint
-
You may find the following “difference of powers” factorization formula useful:
\begin{equation*} a^m - b^m = (a-b)(a^{m-1} + a^{m-2}b + a^{m-3}b^2 + \cdots + a^2b^{m-3} + ab^{m-2} + b^{m-1}) \text{.} \end{equation*}
- Write down a technical definition of the term rational number.
- Prove directly: The sum of two rational numbers is a rational number.
- Prove by contradiction: The sum of a rational number and an irrational number is irrational.
- Disprove by counterexample: The sum of two irrational numbers is irrational.
Refer to Activity \(\PageIndex{2}\).
- Prove that a positive number \(n\) is square free if and only if for every factorization \(n = ab\text{,}\) the integers \(a\) and \(b\) do not share a common factor other than \(1\text{.}\)
- Prove that a positive number is square free if and only if it is not divisible by the square of a prime number.
A pair of prime numbers \(p_1,p_2\) is called a twin prime pair if \(p_2 = p_1 + 2\text{.}\) A prime number is called an isolated prime if it is not part of a twin prime pair.
- Determine the first (i.e. smallest) four twin prime pairs.
- Determine the first (i.e. smallest) two isolated primes.
- Prove that if \(p, p+2\) is a twin prime pair with \(p \ge 5\text{,}\) then \(p+1\) is divisible by \(6\text{.}\)
- Prove that if \(p, p+2\) is a twin prime pair, then \(p-2,p\) and \(p+2,p+4\) cannot be twin prime pairs.


5.13: Putting It Together- Workforce Planning
Although workforce planning is often described in simple terms—for example, Korn Ferry’s 5 Rs: right shape, right skills, right size, right site, and right spend—it is deceptively hard to put that framework in place, much less execute on it. Indeed, HR consultancy XpertHR lists “Understanding Workforce Planning” as one of the top 10 HR compliance challenges for 2019. [1]
Their research revealed not only talent acquisition challenges—virtually a universal issue given the current labor market—but also process issues. To put the data in perspective, let’s review the concept of workplace planning. As stated in Business Strategy and Workforce Planning, workforce planning is a complex research and design problem that involves developing a detailed understanding of a role, its requirements, and how that role relates to organizational strategy and to other roles within the organization. Decisions made during this process have implications for virtually every aspect of business, including finance, legal and operations. Decisions made during this process—in particular, job analysis and job design—also have a significant impact on motivation, satisfaction and retention.
Challenges cited by survey respondents include the following:
- 43% viewed aligning talent retention strategy with business objectives as very or extremely challenging
- 47% were very or extremely challenged by managing performance and providing professional development opportunities
- 52% of respondents were very or extremely challenged by ensuring employees and supervisors have the necessary skill sets now and for future responsibilities
- 50% of respondents were very or extremely challenged by creating a succession plan
- 49% were very or extremely challenged when it came to increasing employee engagement, morale and satisfaction.
Taking a strategic approach to workforce planning can address these challenges. As CalHR noted, “workforce planning informs recruitment, retention, employee development, knowledge transfer and succession planning.” [2]
In a competitive labor market, it is especially critical to assess the internal supply of labor accurately and manage it effectively. As author and educational advisor Sir Kenneth Robinson notes: Human resources are like natural resources…you have to go looking for them.” Assessment or identifying capabilities is only one part of the equation. Other key elements are creating an effective development framework—the workforce development plan—and developing “good jobs,” whether that’s through job analysis, job design or a combination or the two. A more experimental option supported by Dr. Wrzensniewski’s research is actively engaging employees in a job crafting process.
Day & Zimmermann HR SVP Beth Albright’s integrates these ideas in a coherent whole, observing that “fundamentally, people want to come to work, do a good job, feel like they make a difference and be recognized for their efforts.” [3] However, for that to happen, a company needs to have the right infrastructure and processes in place. Albright argues that “if systems prevent people from doing a good job, you must fix them. If people aren’t being developed and trained, they can’t make a difference in the work they do.” A simple, wholistic concept. Complex—but critical—to implement.
- "The Top 10 Compliance Challenges in 2019." Xpert HR. Accessed September 12, 2019. ↵
- " State of California Workforce Planning Model ." California Department of Human Resources. Accessed September 12, 2019. ↵
- Jerant, Frederick. " How to Heal Human Resources ." Forefront Magazine. 2014. Accessed September 12, 2019. ↵
Contributors and Attributions
- Untitled. Authored by : rawpixel. Provided by : pxhere. Located at : pxhere.com/en/photo/1433389. License : CC0: No Rights Reserved
- Laptop Computer. Authored by : rawpixel. Provided by : Pixabay. Located at : pixabay.com/photos/laptop-computer-technology-monitor-3190194/. License : CC0: No Rights Reserved . License Terms : Pixabay License


4.6: Relative Motion in One and Two Dimensions
- Explain the concept of reference frames.
- Write the position and velocity vector equations for relative motion.
- Draw the position and velocity vectors for relative motion.
- Analyze one-dimensional and two-dimensional relative motion problems using the position and velocity vector equations.
Motion does not happen in isolation. If you’re riding in a train moving at 10 m/s east, this velocity is measured relative to the ground on which you’re traveling. However, if another train passes you at 15 m/s east, your velocity relative to this other train is different from your velocity relative to the ground. Your velocity relative to the other train is 5 m/s west. To explore this idea further, we first need to establish some terminology.
Reference Frames
To discuss relative motion in one or more dimensions, we first introduce the concept of reference frames . When we say an object has a certain velocity, we must state it has a velocity with respect to a given reference frame. In most examples we have examined so far, this reference frame has been Earth. If you say a person is sitting in a train moving at 10 m/s east, then you imply the person on the train is moving relative to the surface of Earth at this velocity, and Earth is the reference frame. We can expand our view of the motion of the person on the train and say Earth is spinning in its orbit around the Sun, in which case the motion becomes more complicated. In this case, the solar system is the reference frame. In summary, all discussion of relative motion must define the reference frames involved. We now develop a method to refer to reference frames in relative motion.
Relative Motion in One Dimension
We introduce relative motion in one dimension first, because the velocity vectors simplify to having only two possible directions. Take the example of the person sitting in a train moving east. If we choose east as the positive direction and Earth as the reference frame, then we can write the velocity of the train with respect to the Earth as \(\vec{v}_{TE}\) = 10 m/s \(\hat{i}\) east, where the subscripts TE refer to train and Earth. Let’s now say the person gets up out of /her seat and walks toward the back of the train at 2 m/s. This tells us she has a velocity relative to the reference frame of the train. Since the person is walking west, in the negative direction, we write her velocity with respect to the train as \(\vec{v}_{PT}\) = −2 m/s \(\hat{i}\). We can add the two velocity vectors to find the velocity of the person with respect to Earth. This relative velocity is written as
\[\vec{v}_{PE} = \vec{v}_{PT} + \vec{v}_{TE} \ldotp \label{4.33}\]
Note the ordering of the subscripts for the various reference frames in Equation \ref{4.33}. The subscripts for the coupling reference frame, which is the train, appear consecutively in the right-hand side of the equation. Figure \(\PageIndex{1}\) shows the correct order of subscripts when forming the vector equation.
Adding the vectors, we find \(\vec{v}_{PE}\) = 8 m/s \(\hat{i}\), so the person is moving 8 m/s east with respect to Earth. Graphically, this is shown in Figure \(\PageIndex{2}\).
Relative Velocity in Two Dimensions
We can now apply these concepts to describing motion in two dimensions. Consider a particle P and reference frames S and S′, as shown in Figure \(\PageIndex{3}\). The position of the origin of S′ as measured in S is \(\vec{r}_{S'S}\), the position of P as measured in S′ is \(\vec{r}_{PS'}\), and the position of P as measured in S is \(\vec{r}_{PS}\).
From Figure \(\PageIndex{3}\) we see that
\[\vec{r}_{PS} = \vec{r}_{PS} + \vec{r}_{S'S} \ldotp \label{4.34}\]
The relative velocities are the time derivatives of the position vectors. Therefore,
\[\vec{v}_{PS} = \vec{v}_{PS'} + \vec{v}_{S'S} \ldotp \label{4.35}\]
The velocity of a particle relative to S is equal to its velocity relative to S′ plus the velocity of S′ relative to S.
We can extend Equation \ref{4.35} to any number of reference frames. For particle P with velocities \(\vec{v}_{PA}\), \(\vec{v}_{PB}\), and \(\vec{v}_{PC}\) in frames A, B, and C,
\[\vec{v}_{PC} = \vec{v}_{PA} + \vec{v}_{AB} + \vec{v}_{BC} \ldotp \label{4.36}\]
We can also see how the accelerations are related as observed in two reference frames by differentiating Equation \ref{4.35}:
\[\vec{a}_{PS} = \vec{a}_{PS'} + \vec{a}_{S'S} \ldotp \label{4.37}\]
We see that if the velocity of S′ relative to S is a constant, then \(\vec{a}_{S'S}\) = 0 and
\[\vec{a}_{PS} = \vec{a}_{PS'} \ldotp \label{4.38}\]
This says the acceleration of a particle is the same as measured by two observers moving at a constant velocity relative to each other.
A truck is traveling south at a speed of 70 km/h toward an intersection. A car is traveling east toward the intersection at a speed of 80 km/h (Figure \(\PageIndex{4}\)). What is the velocity of the car relative to the truck?
Strategy
First, we must establish the reference frame common to both vehicles, which is Earth. Then, we write the velocities of each with respect to the reference frame of Earth, which enables us to form a vector equation that links the car, the truck, and Earth to solve for the velocity of the car with respect to the truck.
Solution
The velocity of the car with respect to Earth is \(\vec{v}_{CE}\) = 80 km/h \(\hat{i}\). The velocity of the truck with respect to Earth is \(\vec{v}_{TE}\) = −70 km/h \(\hat{j}\). Using the velocity addition rule, the relative motion equation we are seeking is
\[\vec{v}_{CT} = \vec{v}_{CE} + \vec{v}_{ET} \ldotp \label{ex2}\]
Here, \(\vec{v}_{CT}\) is the velocity of the car with respect to the truck, and Earth is the connecting reference frame. Since we have the velocity of the truck with respect to Earth, the negative of this vector is the velocity of Earth with respect to the truck: \(\vec{v}_{ET} = − \vec{v}_{TE}\). The vector diagram of this equation is shown in Figure \(\PageIndex{5}\).
We can now solve for the velocity of the car with respect to the truck:
\[\big| \vec{v}_{CT} \big| = \sqrt{(80.0\; km/h)^{2} + (70.0\; km/h)^{2}} = 106.\; km/h \nonumber\]
and
\[\theta = \tan^{-1} \left(\dfrac{70.0}{80.0}\right) = 41.2^{o}\; north\; of\; east \ldotp \nonumber\]
Significance
Drawing a vector diagram showing the velocity vectors can help in understanding the relative velocity of the two objects.
A boat heads north in still water at 4.5 m/s directly across a river that is running east at 3.0 m/s. What is the velocity of the boat with respect to Earth?
A pilot must fly his plane due north to reach his destination. The plane can fly at 300 km/h in still air. A wind is blowing out of the northeast at 90 km/h. (a) What is the speed of the plane relative to the ground? (b) In what direction must the pilot head her plane to fly due north?
Strategy
The pilot must point her plane somewhat east of north to compensate for the wind velocity. We need to construct a vector equation that contains the velocity of the plane with respect to the ground, the velocity of the plane with respect to the air, and the velocity of the air with respect to the ground. Since these last two quantities are known, we can solve for the velocity of the plane with respect to the ground. We can graph the vectors and use this diagram to evaluate the magnitude of the plane’s velocity with respect to the ground. The diagram will also tell us the angle the plane’s velocity makes with north with respect to the air, which is the direction the pilot must head her plane.
Solution
The vector equation is \(\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}\), where P = plane, A = air, and G = ground. From the geometry in Figure \(\PageIndex{6}\), we can solve easily for the magnitude of the velocity of the plane with respect to the ground and the angle of the plane’s heading, \(\theta\).
- Known quantities: $$\big| \vec{v}_{PA} \big| = 300\; km/h$$ $$\big| \vec{v}_{AG} \big| = 90\; km/h$$Substituting into the equation of motion, we obtain \(\big| \vec{v}_{PG} \big|\) = 230 km/h.
- The angle \(\theta\) = tan −1 \(\left(\dfrac{63.64}{300}\right)\) = 12° east of north.