5.7: Common Forces
- Define normal and tension forces
- Distinguish between real and fictitious forces
- Apply Newton’s laws of motion to solve problems involving a variety of forces
Forces are given many names, such as push, pull, thrust, and weight. Traditionally, forces have been grouped into several categories and given names relating to their source, how they are transmitted, or their effects. Several of these categories are discussed in this section, together with some interesting applications. Further examples of forces are discussed later in this text.
A Catalog of Forces: Normal, Tension, and Other Examples of Forces
A catalog of forces will be useful for reference as we solve various problems involving force and motion. These forces include normal force, tension, friction, and spring force.
Normal force
Weight (also called the force of gravity) is a pervasive force that acts at all times and must be counteracted to keep an object from falling. You must support the weight of a heavy object by pushing up on it when you hold it stationary, as illustrated in Figure \(\PageIndex{1}\)(a). But how do inanimate objects like a table support the weight of a mass placed on them, such as shown in Figure \(\PageIndex{1}\)(b)? When the bag of dog food is placed on the table, the table sags slightly under the load. This would be noticeable if the load were placed on a card table, but even a sturdy oak table deforms when a force is applied to it. Unless an object is deformed beyond its limit, it will exert a restoring force much like a deformed spring (or a trampoline or diving board). The greater the deformation, the greater the restoring force. Thus, when the load is placed on the table, the table sags until the restoring force becomes as large as the weight of the load. At this point, the net external force on the load is zero. That is the situation when the load is stationary on the table. The table sags quickly and the sag is slight, so we do not notice it. But it is similar to the sagging of a trampoline when you climb onto it.
We must conclude that whatever supports a load, be it animate or not, must supply an upward force equal to the weight of the load, as we assumed in a few of the previous examples. If the force supporting the weight of an object, or a load, is perpendicular to the surface of contact between the load and its support, this force is defined as a normal force and here is given by the symbol \(\vec{N}\). (This is not the newton unit for force, or N.) The word normal means perpendicular to a surface. This means that the normal force experienced by an object resting on a horizontal surface can be expressed in vector form as follows:
\[\vec{N} = -m \vec{g} \ldotp \tag{5.11}\nonumber \]
In scalar form, this becomes
\[N = mg \ldotp \tag{5.12}\nonumber \]
The normal force can be less than the object’s weight if the object is on an incline.
Consider the skier on the slope in Figure \(\PageIndex{2}\). Her mass including equipment is 60.0 kg. (a) What is her acceleration if friction is negligible? (b) What is her acceleration if friction is 45.0 N?
Strategy
This is a two-dimensional problem, since not all forces on the skier (the system of interest) are parallel. The approach we have used in two-dimensional kinematics also works well here. Choose a convenient coordinate system and project the vectors onto its axes, creating two one-dimensional problems to solve. The most convenient coordinate system for motion on an incline is one that has one coordinate parallel to the slope and one perpendicular to the slope. (Motions along mutually perpendicular axes are independent.) We use x and y for the parallel and perpendicular directions, respectively. This choice of axes simplifies this type of problem, because there is no motion perpendicular to the slope and the acceleration is downslope. Regarding the forces, friction is drawn in opposition to motion (friction always opposes forward motion) and is always parallel to the slope, w x is drawn parallel to the slope and downslope (it causes the motion of the skier down the slope), and w y is drawn as the component of weight perpendicular to the slope. Then, we can consider the separate problems of forces parallel to the slope and forces perpendicular to the slope.
Solution
The magnitude of the component of weight parallel to the slope is
\[w_{x} = w \sin 25^{o} = mg \sin 25^{o},\nonumber \]
and the magnitude of the component of the weight perpendicular to the slope is
\[w_{y} = w \cos 25^{o} = mg \cos 25^{o} \ldotp\nonumber \]
- Neglect friction. Since the acceleration is parallel to the slope, we need only consider forces parallel to the slope. (Forces perpendicular to the slope add to zero, since there is no acceleration in that direction.) The forces parallel to the slope are the component of the skier’s weight parallel to slope w x and friction f. Using Newton’s second law, with subscripts to denote quantities parallel to the slope, $$a_{x} = \frac{F_{net\; x}}{m}$$where F net x = w x - mg sin 25°, assuming no friction for this part. Therefore, $$a_{x} = \frac{F_{net\; x}}{m} = \frac{mg \sin 25^{o}}{m} = g \sin 25^{o}$$ $$(9.80\; m/s^{2})(0.4226) = 4.14\; m/s^{2}$$is the acceleration.
- Include friction. We have a given value for friction, and we know its direction is parallel to the slope and it opposes motion between surfaces in contact. So the net external force is $$F_{net\; x} = w_{x} - f \ldotp$$Substituting this into Newton’s second law, \(a_x = \frac{F_{net\; x}}{m}\), gives $$a_{x} = \frac{F_{net\; x}}{m} = \frac{w_{x} - f}{m} = \frac{mg \sin 25^{o} - f}{m} \ldotp$$ We substitute known values to obtain $$a_{x} = \frac{(60.0\; kg)(9.80\; m/s^{2})(0.4226) - 45.0\; N}{60.0\; kg} \ldotp$$This give us $$a_{x} = 3.39\; m/s^{2},$$ which is the acceleration parallel to the incline when there is 45.0 N of opposing friction.
Significance
Since friction always opposes motion between surfaces, the acceleration is smaller when there is friction than when there is none. It is a general result that if friction on an incline is negligible, then the acceleration down the incline is a = g sin \(\theta\), regardless of mass. As discussed previously, all objects fall with the same acceleration in the absence of air resistance. Similarly, all objects, regardless of mass, slide down a frictionless incline with the same acceleration (if the angle is the same).
When an object rests on an incline that makes an angle \(\theta\) with the horizontal, the force of gravity acting on the object is divided into two components: a force acting perpendicular to the plane, wy , and a force acting parallel to the plane, wx (Figure \(\PageIndex{3}\)). The normal force \(\vec{N}\) is typically equal in magnitude and opposite in direction to the perpendicular component of the weight w y . The force acting parallel to the plane, w x , causes the object to accelerate down the incline.
Be careful when resolving the weight of the object into components. If the incline is at an angle θ to the horizontal, then the magnitudes of the weight components are
\[w_{x} = w \sin \theta = mg \sin \theta\nonumber \]
and
\[w_{y} = w \cos \theta = mg \cos \theta\nonumber \]
We use the second equation to write the normal force experienced by an object resting on an inclined plane:
\[N = mg \cos \theta \ldotp \tag{5.13}\nonumber \]
Instead of memorizing these equations, it is helpful to be able to determine them from reason. To do this, we draw the right angle formed by the three weight vectors. The angle \(\theta\) of the incline is the same as the angle formed between w and w y . Knowing this property, we can use trigonometry to determine the magnitude of the weight components:
\[\cos \theta = \frac{w_{y}}{w},\quad w_{y} = w \cos \theta = mg \cos \theta\nonumber \]
\[\sin \theta = \frac{w_{x}}{w},\quad w_{x} = w \sin\theta = mg \sin \theta\nonumber \]
A force of 1150 N acts parallel to a ramp to push a 250-kg gun safe into a moving van. The ramp is frictionless and inclined at 17°. (a) What is the acceleration of the safe up the ramp? (b) If we consider friction in this problem, with a friction force of 120 N, what is the acceleration of the safe?
Tension
A tension is a force along the length of a medium; in particular, it is a pulling force that acts along a stretched flexible connector, such as a rope or cable. The word “tension” comes from a Latin word meaning “to stretch.” Not coincidentally, the flexible cords that carry muscle forces to other parts of the body are called tendons. Any flexible connector, such as a string, rope, chain, wire, or cable, can only exert a pull parallel to its length; thus, a force carried by a flexible connector is a tension with a direction parallel to the connector. Tension is a pull in a connector. Consider the phrase: “You can’t push a rope.” Instead, tension force pulls outward along the two ends of a rope. Consider a person holding a mass on a rope, as shown in Figure \(\PageIndex{4}\). If the 5.00-kg mass in the figure is stationary, then its acceleration is zero and the net force is zero. The only external forces acting on the mass are its weight and the tension supplied by the rope. Thus,
\[F_{net} = T - w = 0,\nonumber \]
where T and w are the magnitudes of the tension and weight, respectively, and their signs indicate direction, with up being positive. As we proved using Newton’s second law, the tension equals the weight of the supported mass:
\[T = w = mg \ldotp \tag{5.14}\nonumber \]
Thus, for a 5.00-kg mass (neglecting the mass of the rope), we see that
\[T = mg = (5.00\; kg)(9.80\; m/s^{2}) = 49.0\; N \ldotp\nonumber \]
If we cut the rope and insert a spring, the spring would extend a length corresponding to a force of 49.0 N, providing a direct observation and measure of the tension force in the rope.
Flexible connectors are often used to transmit forces around corners, such as in a hospital traction system, a tendon, or a bicycle brake cable. If there is no friction, the tension transmission is undiminished; only its direction changes, and it is always parallel to the flexible connector, as shown in Figure \(\PageIndex{5}\).
Calculate the tension in the wire supporting the 70.0-kg tightrope walker shown in Figure \(\PageIndex{6}\).
Strategy
As you can see in Figure \(\PageIndex{6}\), the wire is bent under the person’s weight. Thus, the tension on either side of the person has an upward component that can support his weight. As usual, forces are vectors represented pictorially by arrows that have the same direction as the forces and lengths proportional to their magnitudes. The system is the tightrope walker, and the only external forces acting on him are his weight \(\vec{w}\) and the two tensions \(\vec{T}_{L}\) (left tension) and \(\vec{T}_{R}\) (right tension). It is reasonable to neglect the weight of the wire. The net external force is zero, because the system is static. We can use trigonometry to find the tensions. One conclusion is possible at the outset—we can see from Figure \(\PageIndex{6}\)(b) that the magnitudes of the tensions T L and T R must be equal. We know this because there is no horizontal acceleration in the rope and the only forces acting to the left and right are T L and T R . Thus, the magnitude of those horizontal components of the forces must be equal so that they cancel each other out.
Whenever we have two-dimensional vector problems in which no two vectors are parallel, the easiest method of solution is to pick a convenient coordinate system and project the vectors onto its axes. In this case, the best coordinate system has one horizontal axis (x) and one vertical axis (y).
Solution
First, we need to resolve the tension vectors into their horizontal and vertical components. It helps to look at a new free-body diagram showing all horizontal and vertical components of each force acting on the system (Figure \(\PageIndex{7}\)).
Consider the horizontal components of the forces (denoted with a subscript x):
\[F_{net x} = T_{Rx} − T_{Lx} \ldotp\nonumber \]
The net external horizontal force F net x = 0, since the person is stationary. Thus,
\[F_{net x} = 0 = T_{Rx} − T_{Lx} \ldotp\nonumber \]
\[T_{Lx} = T_{Rx} \ldotp\nonumber \]
Now observe Figure \(\PageIndex{7}\). You can use trigonometry to determine the magnitude of T L and T R :
\[\cos 5.0^{o} = \frac{T_{Lx}}{T_{L}}, \quad T_{Lx} = T_{L} \cos 5.0^{o}\nonumber \]
\[\cos 5.0^{o} = \frac{T_{Rx}}{T_{R}}, \quad T_{Rx} = T_{R} \cos 5.0^{o} \ldotp\nonumber \]
Equating T Lx and T Rx :
\[T_{L} \cos 5.0^{o} = T_{R} \cos 5.0^{o} \ldotp\nonumber \]
Thus,
\[T_{L} = T_{R} = T,\nonumber \]
as predicted. Now, considering the vertical components (denoted by a subscript y), we can solve for T. Again, since the person is stationary, Newton’s second law implies that F net y = 0. Thus, as illustrated in the free-body diagram,
\[F_{net y} = T_{Ly} + T_{Ry} - w = 0 \ldotp\nonumber \]
We can use trigonometry to determine the relationships among T Ly , T Ry , and T. As we determined from the analysis in the horizontal direction, T L = T R = T:
\[\sin 5.0^{o} = \frac{T_{Ly}}{T_{L}}, \quad T_{Ly} = T_{L} \sin 5.0^{o} = T \sin 5.0^{o}\nonumber \]
\[\sin 5.0^{o} = \frac{T_{Ry}}{T_{R}}, \quad T_{Ry} = T_{R} \sin 5.0^{o} = T \sin 5.0^{o} \ldotp\nonumber \]
Now we can substitute the vales for T Ly and T Ry , into the net force equation in the vertical direction:
\[F_{net y} = T_{Ly} + T_{Ry} - w = 0\nonumber \]
\[F_{net y} = 0 = T \sin 5.0^{o} + T \sin 5.0^{o} - w = 0\nonumber \]
\[2T \sin 5.0^{o} - w = 0\nonumber \]
\[2T \sin 5.0^{o} = w\nonumber \]
and
\[T = \frac{w}{2 \sin 5.0^{o}} = \frac{mg}{2 \sin 5.0^{o}},\nonumber \]
so
\[T = \frac{(70.0\; kg)(9.80\; m/s^{2})}{2(0.0872)},\nonumber \]
and the tension is
\[T = 3930\; N \ldotp\nonumber \]
Significance
The vertical tension in the wire acts as a force that supports the weight of the tightrope walker. The tension is almost six times the 686-N weight of the tightrope walker. Since the wire is nearly horizontal, the vertical component of its tension is only a fraction of the tension in the wire. The large horizontal components are in opposite directions and cancel, so most of the tension in the wire is not used to support the weight of the tightrope walker.
If we wish to create a large tension, all we have to do is exert a force perpendicular to a taut flexible connector, as illustrated in Figure \(\PageIndex{6}\). As we saw in Example 5.13, the weight of the tightrope walker acts as a force perpendicular to the rope. We saw that the tension in the rope is related to the weight of the tightrope walker in the following way:
\[T = \frac{w}{2 \sin \theta} \ldotp\nonumber \]
We can extend this expression to describe the tension T created when a perpendicular force (F \(\perp\) ) is exerted at the middle of a flexible connector:
\[T = \frac{F_{\perp}}{2 \sin \theta} \ldotp\nonumber \]
The angle between the horizontal and the bent connector is represented by \(\theta\). In this case, T becomes large as \(\theta\) approaches zero. Even the relatively small weight of any flexible connector will cause it to sag, since an infinite tension would result if it were horizontal (i.e., \(\theta\) = 0 and sin \(\theta\) = 0). For example, Figure \(\PageIndex{8}\) shows a situation where we wish to pull a car out of the mud when no tow truck is available. Each time the car moves forward, the chain is tightened to keep it as straight as possible. The tension in the chain is given by T = \(\frac{F_{\perp}}{2 \sin \theta}\), and since \(\theta\) is small, T is large. This situation is analogous to the tightrope walker, except that the tensions shown here are those transmitted to the car and the tree rather than those acting at the point where F \(\perp\) is applied.
One end of a 3.0-m rope is tied to a tree; the other end is tied to a car stuck in the mud. The motorist pulls sideways on the midpoint of the rope, displacing it a distance of 0.25 m. If he exerts a force of 200.0 N under these conditions, determine the force exerted on the car.
In Applications of Newton’s Laws , we extend the discussion on tension in a cable to include cases in which the angles shown are not equal.
Friction
Friction is a resistive force opposing motion or its tendency. Imagine an object at rest on a horizontal surface. The net force acting on the object must be zero, leading to equality of the weight and the normal force, which act in opposite directions. If the surface is tilted, the normal force balances the component of the weight perpendicular to the surface. If the object does not slide downward, the component of the weight parallel to the inclined plane is balanced by friction. Friction is discussed in greater detail in the next chapter.
Spring force
A spring is a special medium with a specific atomic structure that has the ability to restore its shape, if deformed. To restore its shape, a spring exerts a restoring force that is proportional to and in the opposite direction in which it is stretched or compressed. This is the statement of a law known as Hooke’s law, which has the mathematical form
\[\vec{F} = -k \vec{x} \ldotp\nonumber \]
The constant of proportionality k is a measure of the spring’s stiffness. The line of action of this force is parallel to the spring axis, and the sense of the force is in the opposite direction of the displacement vector (Figure \(\PageIndex{9}\)). The displacement must be measured from the relaxed position; x = 0 when the spring is relaxed.
Real Forces and Inertial Frames
There is another distinction among forces: Some forces are real, whereas others are not. Real forces have some physical origin, such as a gravitational pull. In contrast, fictitious forces arise simply because an observer is in an accelerating or noninertial frame of reference, such as one that rotates (like a merry-go-round) or undergoes linear acceleration (like a car slowing down). For example, if a satellite is heading due north above Earth’s Northern Hemisphere, then to an observer on Earth, it will appear to experience a force to the west that has no physical origin. Instead, Earth is rotating toward the east and moves east under the satellite. In Earth’s frame, this looks like a westward force on the satellite, or it can be interpreted as a violation of Newton’s first law (the law of inertia). We can identify a fictitious force by asking the question, “What is the reaction force?” If we cannot name the reaction force, then the force we are considering is fictitious. In the example of the satellite, the reaction force would have to be an eastward force on Earth. Recall that an inertial frame of reference is one in which all forces are real and, equivalently, one in which Newton’s laws have the simple forms given in this chapter.
Earth’s rotation is slow enough that Earth is nearly an inertial frame. You ordinarily must perform precise experiments to observe fictitious forces and the slight departures from Newton’s laws, such as the effect just described. On a large scale, such as for the rotation of weather systems and ocean currents, the effects can be easily observed (Figure \(\PageIndex{10}\)).
The crucial factor in determining whether a frame of reference is inertial is whether it accelerates or rotates relative to a known inertial frame. Unless stated otherwise, all phenomena discussed in this text are in inertial frames.
The forces discussed in this section are real forces, but they are not the only real forces. Lift and thrust, for example, are more specialized real forces. In the long list of forces, are some more basic than others? Are some different manifestations of the same underlying force? The answer to both questions is yes, as you will see in the treatment of modern physics later in the text
Explore forces and motion in this interactive simulation as you push household objects up and down a ramp. Lower and raise the ramp to see how the angle of inclination affects the parallel forces. Graphs show forces, energy, and work.
Stretch and compress springs in this activity to explore the relationships among force, spring constant, and displacement. Investigate what happens when two springs are connected in series and in parallel.


10: Hypothesis Testing with Two Samples
You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. The general procedure is still the same, just expanded. To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs. Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportions.
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- 10.1: Prelude to Hypothesis Testing with Two Samples
- This chapter deals with the following hypothesis tests: Independent groups (samples are independent) Test of two population means. Test of two population proportions. Matched or paired samples (samples are dependent) Test of the two population proportions by testing one population mean of differences.
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- 10.2: Two Population Means with Unknown Standard Deviations
- The comparison of two population means is very common. A difference between the two samples depends on both the means and the standard deviations. Very different means can occur by chance if there is great variation among the individual samples.
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- 10.4: Comparing Two Independent Population Proportions
- Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions.
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- 10.5: Matched or Paired Samples
- When using a hypothesis test for matched or paired samples, the following characteristics should be present: Simple random sampling is used. Sample sizes are often small. Two measurements (samples) are drawn from the same pair of individuals or objects. Differences are calculated from the matched or paired samples. The differences form the sample that is used for the hypothesis test. Either the matched pairs have differences that come from a population that is normal or the number of difference
Contributors and Attributions
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Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


And like the Golden Rule, the fiats to “love thy neighbor as thyself” and to “love, and do as you will,” are neither specific nor helpful, and may be wrong or harmful in many cases where good intentions lead to bad results.  Love, in terms of feelings or concern alone, does not insure right conduct toward the loved one or toward anyone. Rather than love’s being a guide to ethics, I have been arguing that ethics — right behavior — is a part of love (as well as an important part of other relationships). If you do not treat people right, they, regardless of what they feel for you (even if it is some kind of attraction), cannot have love for you. And if others do not treat you right, whatever you feel for them (even if it is some kind of attraction) cannot be love. But loving someone does not imply you will treat them right. And I think it does not necessarily even imply that you will try to, let alone that you will succeed. However, you do have responsibilities and obligations to try to do what is best for your family members and for friends, people with whom you have grown interdependent, who depend on you and help you out at times with some sacrifice to themselves, children who are in your care. This is an ethical obligation or responsibility, not one dependent on love or something as uncertain, unpredictable, and possibly ephemeral as feelings. Such responsibilities and obligations might be overridden by higher obligations, but they ought not be dismissed for no good reason or just because one is simply no longer “in love” (for example, “magically attracted”) or no longer feels like fulfilling them.
Responsibility and Neglect of Obligation
In one of my classes someone made the point that (in the book of Job God was not responsible for Job’s misfortune — the devil was. God only let the devil do it. However, on both models or concepts of responsibility described earlier in the section on free will, God was still responsible in that He could have prevented the catastrophe had He chosen to (and He could have chosen to). Likewise the doctor who could perform either a successful abortion or a successful delivery. He is responsible for whatever he chooses, since he could have done either, and he could choose either. In this sense he is playing God either way, not just when he acts “actively” to perform the abortion. He is responsible either way. And it is no good answer in ethics to say in such cases we should do the “natural thing” or just let nature take its course; since if we did natural things we would still be living in the jungles, still be eating with our fingers, still be doing without diapers and toilet training for our children, and without toilets for ourselves. We would not be using vaccines to prevent disease or antibiotics to cure it. Since probably most of what we do and think right is not natural, it is hard to argue in certain difficult or controversial cases that the natural thing is therefore the right or obligatory thing simply because it is natural.
The modern way to try to shirk responsibility is through deference to rules, company policy, regulations, the law, or through supposed delegation of responsibility to a committee or to another person, group, or department. Actually one can only pretend to avoid responsibility these ways because the point remains that if you have the capability to change the outcome or to control or even to influence the committee or the other people, you have the responsibility to try, or to have a good reason not to have to try. You cannot simply say, it is not in your hands, because that is not true. Saying something is not your responsibility does not make it true. And having something not be part of your job description does not alone prevent it from being your moral responsibility.
Goodness of Persons vs. Rightness of Acts
This is an important distinction. People can try to do right without succeeding, and they may be responsible in various ways for omitting to do something that ought to be done, without in either cases thereby being evil or morally bad. I am not sure I know all the things that make a person a good one (for whatever instance or amount of time is in question) but some qualities that come to mind are their being conscientious, responsible, trying to do right things, trying to figure out what things are right, being concerned about and considerate of other people’s feelings, etc. I don’t know whether being loving in terms of feelings would count. I doubt it. Seems more a character trait or psychological trait rather than strictly a moral trait. Anyway, good people can do, and often in fact do, wrong things when they are trying to do right; and bad people can do right things (though this is probably rarer) even though they are trying to be selfish, vindictive, or spiteful at the time. Since it is necessary to know a person’s rationale, motives, and intentions to determine whether he is good or bad or not, it is wise to exercise extreme caution in making such judgments, since these are usually harder to know than just whether his action is right or wrong. It is usually easier to judge the rightness of acts, since the act can be seen, than to judge the goodness and badness of persons. You can hold that someone is being wrong without accusing him of being a bad person; and this can often help you get your point across without his becoming too defensive to see it. In some cases, there will be clear-cut malevolence intended, but in most cases in life among civilized people it will be difficult to tell whether the perpetrator of wrong acts is malevolent or incompetent or simply misguided, myopic, or incidentally ignorant, though well-intentioned. Until you can prove otherwise, it is often better to assume mistake rather than malevolent intent. It is generally better — because more tactful and more effective at least to begin pointing out a problem by saying something like “I don’t think this is the right thing to do because….” than to say something like, “How could you be so selfish (mean, stupid, or whatever)….”
The Ethics of Caring
In line with the preceding paragraph, it seems to me that an “ethics of caring”, which is something of a recent theory of ethics advocated by some, does not necessarily point out the right thing to do. It is a good thing to care about people, but it is also a good thing to care about doing what is right for people whether you care about them — i.e., have any personal feelings for them over and above humane feelings you would have for anyone – or not. In some cases, one’s feelings for another can even override one’s judgment in a harmful way. It may be that having personal feelings toward another person will make one work harder to try to figure out what is right and to try to do it, but it is not clear that is more likely to lead to knowledge about what is right than will simply caring about doing the right thing. It is probably true that caring about people whether in a special way or even just in a humane way, along with treating them right is better than just treating them right. But it is not clear that caring will help one know the right acts to do; and if the choice were between being treated right by someone who didn’t care and being treated wrong by someone who did care but was mistaken, I think I would prefer to be treated right without compassion than wrong with it. Of course, in a situation where no one can actually solve your problems or help you, then compassion will be preferable than lack of it, but compassion by itself is not a guide to determining what is right in a given situation. It may only help you be more diligent in seeking what is right, but is no guarantee you will find it.
“Virtue Ethics”
Usually attributed to Aristotle (I believe mistakenly), “virtue ethics” is the view that there are certain virtues, such as loyalty, integrity, truthfulness, etc. that let us act rightly. Aristotle did point out that ethics consisted of doing what is right and not just knowing what is right to do, and that without the proper cultivation and practice of virtuous behavior, people might not do what they know in their minds they should. But Aristotle thought that the virtues to be developed were those which one discovered through reason, and once one discovered them, then one should cultivate or practice them so that they became easier to do when necessary. The modern theory however seems to assume that there are certain virtues which are the right way to behave under all circumstances; e.g., never lie, always be loyal, etc. Aristotle would, I am pretty sure disagree with that, and think that such a principle led to extremes rather than to the golden mean, that he thought most virtues represented. For example, undercover police agents need to lie to do their work. Similarly spies. But I think it is also okay to lie when doing so will cause only good but telling the truth will do only harm. Particularly in cases where one is trying to build confidence in, say, a child, and the lie will help that but the truth will undermine it. So, for example, one might tell a child s/he looks good in some outfit that is not all that attractive on him/her, but is not so bad that others will poke fun and prove you to have lied. That is particularly true if your child’s confidence will help him/her actually seem more attractive to others than would a better outfit that the child does not feel confident wearing. Or, in teaching children to ride a bicycle, I lie to them about not letting go because otherwise they will not even let me help them learn to ride. I don’t let go until I know they can balance the bike, and I have them ride on grass at the time I do let go.  But when I point out how far they got on their own after I had let go, and tell them they can ride their bicycle now by themselves, they immediately get over their anger and want to ride by themselves again. So I think lying about not letting go is a good lie that is right to tell. Or consider loyalty. Clearly blind loyalty to someone like Hitler or to someone out to make money at any cost to others is not a good kind of loyalty and is not right to have. I would argue that the only thing that makes something a virtue is that it is right to do, not that any act is right because it fits into a category that is simply considered to be a virtue. While truth telling and loyalty are often right ways to behave, that does not mean they are always the right thing to do. And if a normally virtuous behavior would in some particular instance only cause significant harm and its opposite behavior would instead achieve much good, then it seems pretty clear to me that it is not the right thing to do in that particular case, and is not a “virtue” then.
Conscience
The problems with principles which rely on conscience telling you or anyone what is right are that (1) conscience can be wrong — conscience usually has more to do with good intentions and is satisfied with them than with whether acts really are right or not. Also (2), some people’s consciences are more easily satisfied than others and then they ought to be. Many former Nazis had, and many still have, clear consciences about their acts. This is not to say that people who follow principles cannot be wrong; it just does not make their wrong be right. As I mentioned earlier, principles should not say a right act is one that you think does the greatest good, keeps a promise, or whatever; principles should say a right act is one that in fact does the greatest good, keeps a promise, or whatever. Otherwise for an act to be right, a person only has to think he is doing the right thing; he would not have to actually be doing the right thing. In the case of conscience, this translates into the only requirement for an act’s being right is for the person performing it to have a clear conscience, for whatever reason, about it. You could never then say anything, without being contradictory, like “I know you think that was the right thing and I know your conscience is clear about what you did, but what you did was wrong.” Any principle or theory which makes that kind of statement contradictory is a flawed one.
Doing Right When It Is Not In Your Own Self Interest
Why do the right thing when it is not in your own self-interest? Why make sacrifices you can never regain? The initial answer is because it is in someone else’s interest; because it brings about the greatest good for the greatest number of deserving people, because it keeps a promise; because it … — any of the reasons that justify the act in the first place. Some then ask, but why do it anyway? Why be moral? This is a moral question that seems to require a non-moral answer, since the moral answer will have then already been given. I do not know that a good nonmoral answer to this question can or needs to be given. If a morally blind or insensitive person wants to know what the point is in being moral, how can you show him? Is it not like a blind person’s asking to be explained the difference between blue and red? It cannot be explained to him; not because there is no explanation, but because he cannot “see” it or understand it. The difference between blue and red is a difference in color, and you can only perceive and understand that difference if you can see different colors. If the blind person then asks for the difference besides that or beyond that, there is no satisfactory answer; and there need not be one. Perhaps to explain the point of morality or of being moral (whether it is in our own self-interest or not) we can only answer with Batman’s tautology in one comic that “Good is better than evil, Robin.”
I have lately come to believe there is another answer that can also be given, which is that by doing the right thing, even when it is not in your own best interest, you make yourself a more “deserving” person — a person more deserving of having good happen to you. Now, just being deserving does not, of course, mean that good will actually happen to you, but it means it should. And just as in some metaphysical sense “good is better than evil”, it is also, in some metaphysical way, better to be a deserving person than not to be one. Deserving people are better in some way than undeserving people. And it is better to be deserving even if you are not necessarily then better off — meaning even if you do not benefit in the way you deserve.
In one of my ethics classes one time, the students felt that it was right to keep money that you found instead of giving it back to the person who had lost it. One woman even remarked that she had found a purse with cash in it once and returned it all intact to the person who had lost it, and that she felt guilty about that because she thought she should have kept the money. I disagreed with them and we argued periodically about it throughout the term. They also held a view that seemed to me to be oddly inconsistent with their view about keeping found money, though they saw no inconsistency. They believed that if someone they did not know was about to accidentally leave their purse or wallet when they left a restaurant or library or any such place, that they should tell the person so that they did not lose it. They believed they were entitled to keep lost money, but they had an obligation to help people who were still within sight not lose their money. So they had an obligation to prevent money from being lost, even though it could be theirs the second it was lost, but they had no obligation to return lost money to anyone.
The last point I made that term was that if they held the view they did about not having to return lost money, they could then neither expect nor demand that anyone should return any money they themselves might lose. I said that I thought that if they were not willing to return found money, then they did not deserve to have any money they lost returned to them. I also pointed out that I thought that it was just not as good to live in a community where people did not unselfishly help each other as it was to live in a community where people did help each other, even if that meant you were the one who often helped others but did not necessarily need or receive help in return. That was about as far as I could take this then, and now, except to point to a story that was once on either Twilight Zone or Alfred Hitchcock or a series like those.
In that story a stranger comes one evening to the door of a married couple, bringing with him a briefcase that contains a fortune in cash (at the time of the show, it was a million dollars, but with inflation would today be much more). He will leave the briefcase with them for 24 hours, returning to pick it up tomorrow, and they may keep the money or give it back to him when he comes. He will take back the briefcase either empty or still full of the money, whichever they decide; it does not matter to him. The only catch is that if they keep the money, someone they do not know, somewhere in the world will die who would not otherwise have died that day.
The couple falls to arguing about what they should do, and most of the episode is taken up with their arguments. They finally decide to keep the money, since, they figure, one more death among the thousands of people who die every day throughout the world will be of no real consequence, and since it is not as though that person would live forever otherwise anyway.
The man returns to pick up the, now empty, briefcase, and as he is about to leave they ask him why he wants it, since the value of the case is insignificant compared to the value of the money. Why bother coming back for the briefcase? He responds that he needs it back because he is going to put another million dollars in it and take it to someone who does not know them.
Two Closing Thoughts About Ethics
1) I think ethics takes precedent or should take precedent over all other things in life. Business, political, governmental, military, or whatever considerations should (and actually do) all come secondary to ethical considerations. You cannot suspend acting ethically for any of these things or for any reason though you may try or may pretend to or may think you can. Of course, certain choices may be difficult and have compelling reasons or obligations on both sides. There can often be disagreement among good, intelligent, well-meaning people. But the point is that you must try to determine what the morally correct answer is, and not just ignore that in order to “follow orders”, “obey rules”, “abide by the decision of the committee”, “do [your] job”, or “not make waves.” These kinds of reasons may be overriding or sufficient justifications in some cases, but they are not necessarily always or automatically so.
I think all our choices have a moral component or character, though not all our deliberations or decisions recognize this. We do not always take morality into account in making our choices. Not thinking at all; being blind to all but one side; peer pressure; habit; fashion; fad; social, governmental, or employer pressure; tradition; parental guidance; religious prescriptions, etc., particularly when they are not perceived as influencing our decisions, often make us choose things without considering whether they are really right or not. This is often very unfortunate.
(2) Do ethics. Do it as Socrates did; discuss, analyze, question, explain, try to guide others to see what you see and try to remain open to seeing what they do. Help others show you what they know if they are not as good at explaining their views and their insights as you might be. Help draw out of them what they really think, so that you both can analyze it and scrutinize it to see whether it holds up. This way both of you can learn what is right and what is not, and why. As with Socrates, even if you only find out what you do not know, you will be the wiser for it; for it is better to know what you do not know than to believe untruths.
But do it, as did Socrates, tactfully and nicely and in honest search for truth, not contemptuously, abusively, or arrogantly. Even then, you will not be universally loved. Socrates made enemies and was ultimately condemned to death essentially for practicing philosophical inquiry. And even in supposedly civilized places today, people do not always take kindly to being questioned or to having someone disagree with them on ethical grounds. (People seem to feel they are all expert enough in moral matters and do not like to have their expertise challenged. Or perhaps they misconstrue challenge of the rightness of their ideas as challenge of their own goodness or good intentions.) They are not likely to put you to death for it anymore, but often they can make your life miserable for it. You need to be circumspect with many people and only to discuss or disagree about important issues with them. With others it is safe to discuss all kinds of ideas about ethics. The more you can do it with different people, the more your knowledge of ethics can grow and the better morally you can become.
 What should you do and/or say in response? and why?
What if they had said instead that you must choose and kill one of your friends or they will kill all of them (or all of you) and that the choice and responsibility for everyone’s’ lives is yours? What should you do and/or say in response? and why? Explain and justify your answer.
I believe my answer, to these questions, along with some of the points I make in “ The Flaw of Legalism in Society and Education ” show there is a problem with the way utilitarianism is often stated1, and with my own ethical principle, which contains some utilitarian aspects, though with many restrictions or qualifying conditions2.
My Answer
I would say this to the captors in both cases, and the justification for saying it is given in the answer itself:
A person who would give me such a choice is so evil as not to be trusted to tell the truth.
You can say I am responsible for the choice, but that is not true, since it is an artificial responsibility imposed by you and that is within your control and responsibility.  These people are all innocent and do not deserve to be murdered. It is better to die an innocent and deserving person than to be someone who kills them and who is thus neither innocent nor deserving. Do what you wish; choose whatever kind of person you wish to be, and become that kind of person. The choice is yours to be decent and civilized or to be even more reprehensible and evil than you were in giving me this choice.
 If you have not killed or forced a killing like this before, you do not need to start now. The choice is not mine; it is yours.
 Or if we take a slightly different case – you are asked by the Nazi SS if you know where a Jew is hiding, and you do, should you risk being killed by the SS or should you turn in the Jew that is hiding? Even if turning in the Jew protects you and your family, it seems incorrect to say it would be morally right to turn in the Jew. It may be expedient; it may be necessary to protect yourself and your family, it may be understandable and perhaps even excusable, but it hardly seems right or the appropriate terminology to refer to it as being the morally right thing to do.3
Or take the case of standing up for an unpopular cause and risking ostracism and all the ills, social and economic, that may accompany it. Even if it is understandable that one might back away from defending the cause, that does not seem to make doing so right, and it would not make it wrong to defend the cause even if you and your family suffer for it.
In the previously mentioned essay about legalism I quote the following from President George
Washington’s Farewell Address:
“Let it simply be asked: Where is the security for property, for reputation, for life, if the sense of religious obligation desert the oaths which are the instruments of investigation in courts of justice? And let us with caution indulge the supposition that morality can be maintained without religion. Whatever may be conceded to the influence of refined education on minds of peculiar structure, reason and experience both forbid us to expect that national morality can prevail in exclusion of religious principle.”
And I then say:
“ And I suspect, but cannot prove, that what Washington had in mind here is that there needs to be some role involving belief in punishment (by God), or else some people at least will not do what is right.” (The idea is that although people may escape legal punishment here on earth, they cannot escape punishment by a perfectly knowing and just God when they die; and those who do not receive rewards they deserve on earth will receive those rewards when they die.)
That essay goes on to make other points, but in light of what I have written above — i.e., that punishment of you and your loved ones for doing a right act does not make your act wrong, and that avoidance of punishment through one’s actions do not make those actions right – it cannot be that the right act always brings about the most good (on earth), and it cannot be that even in my principle it does, if the harm avoided is undeserved or unfair punishment or the good achieved is undeserved or unfair favor.
In short, the problem is this: some cases of doing the greatest balance of good for the most deserving people seem to be right and others seem not to be – particularly in the case of avoiding unfair punishment. Utilitarianism cannot account for this distinction, and I don’t think that even my principle as stated above accounts properly for it.
Before I go on to discuss this further and to try to resolve it, let me contrast it with a different problem that seems possibly similar in a morally relevant way. I don’t know who first raised this problem, but it contrasts the following two scenarios: 1) a train is out of control and is headed to a fork where you have to either send it one way or another – if you send it one way, it will kill some innocent person that will be in its path on the track, but if you send it the other way, it will kill twenty people who are in its path on the track. What should you do (assuming no special knowledge of the supposed value of any of the lives involved, or assuming that all the lives are of equal moral value)? Utilitarianism and my principle both will say the right thing to do is to divert the train to run over the one person in order to save the twenty, not vice versa. 2) a train is traveling along a track and the engineer does not know that twenty people are stuck on that track ahead and will be killed unless the train is stopped. The only way to stop the train is by getting the engineers attention by throwing someone onto the track in front of the train, sacrificing that person. Utilitarianism demands throwing the person onto the track, but I don’t think my principle allows that, so I do not believe this problem is quite the same as the one of the Nazis or the captors of you and your friends or of undeserved punishment in general, in which I stand by the answer I gave above to the captors’ case. The people on the track have either put themselves in harm’s way or have been unluckily put there by others. Once that has happened, nothing can be done by anyone to save everyone (all 21 people), and you should save the most you can. However, in the second scenario, while it may be unfortunate that the twenty will die, there is not a person already in harm’s way who is in the same boat they are. You would have to sacrifice someone innocent who is not in harm’s way until you put him there. That would be wrong for you to do to him. At best you could in a saintly way sacrifice yourself to save the twenty, but you are not obligated to do that and you do not have the right to sacrifice the person who has done nothing to be in harm’s way. Even if someone else were to want to throw that person onto the track and you had the power to stop him from doing so, I think you have the obligation to stop him because it would violate that innocent person’s right to be sacrificed. The person already on the track is not “innocent” in the same way if he put himself in harm’s way, or at least is already in harm’s way in a manner that is not your fault and is beyond your control.
In the Nazi or truthful captors’ cases, utilitarianism says to sacrifice someone to save the greater number of others, but I am afraid my principle also does that too if it were to be interpreted normally in the way it is expressed. I don’t know any easy way to amend it other than to say that punishment and reward (or perhaps unfair punishment and unfair reward) should not count as a consideration in calculating the amount of harm avoided or the amount of good accomplished. That is, the harm suffered due to unfair punishment does not turn an otherwise right act into a wrong one. The only goods and harms that should count are ones that are in some sense a natural or unavoidable, intrinsic consequence of the act, not extrinsic ones which result from choices made by others in response to the act. That is why I write in The Abortion Debate that insofar as people want to minimize or end abortions, they should minimize or eliminate as much as possible the reasons and causes women choose to have them, rather than making punishment for them so Draconian that the woman’s best choice for herself is to cause a baby to be born if it in fact it really should not be because it will needlessly suffer in unredeemable and unjustifiably horrible ways. The point is to make having a baby be right for the sake of the baby, not make having it be right for the sake of the mother’s avoiding punishment if that is not really in the best interest of the baby or is not fair to the mother (as in making women have a baby that endangers their lives or that was conceived by rape for which they are not responsible).
Now normally, of course, we think that punishment is justified if it helps make someone do what is the right act in the first place. We thus threaten punishment in order to try to deter wrongdoing. But that only deters those who are egoists seeking their own best interests, not those who know they are actually seeking to do what is right but which we mistakenly think is wrong. I am not opposed to punishment, as I explain in “Justification of Punishment” but punishment needs to be either a deterrent or a penalty for doing acts that are wrong apart from the punishment, not for making right acts be or seem to be wrong. Similarly, rewards need to be an incentive for doing what is right apart from the reward, not an additional good consequence that makes a wrong act be or seem to be right.
So it seems to me that my general ethical principle needs to be amended to the following: An act is right if and only if, of any act open to the agent to do, its intrinsic or natural consequences, apart from any extrinsic unfair rewards or punishments, bring about the greatest good (or the least evil, or the greatest balance of good over evil) for the greatest number of deserving people, most reasonably and fairly distributed, as long as no rights or incurred obligations are violated, as long as the act does not try to inflict needless harm on undeserving people, as long as the act does not needlessly risk harm in a reckless, negligent, heedless, or irresponsible manner, and as long as the act and its consequences are fair or reasonable to expect of the agent.* Rights have to be justified or explained or demonstrated; not just anything called a right is actually a right.
scenario 4
Let us take into consideration that the most effective non-permanent methods of birth control usually say on the labels that they are 99% effective. If this means such methods as condoms fail to contain semen 1 out of 100 times, that if you use them with intercourse twice a week, they will fail once a year. Of course, the woman might not be fertile during those failures, except, 25% of the time, might result in an unwanted pregnancy on average once every four years with condoms; more frequently if sex is more frequent or at least more frequent during fertile times. Now suppose, that abortion is used as the backup means of birth control, and suppose that whenever abortion is used for that purpose, on average once in every 400 times that people all over the world had sex using 99% effective birth control, some innocent living adult died in his/her sleep who otherwise would not have died. Should sex of this sort, which is thus only for pleasure, be considered morally acceptable? Why or why not? Use the general ethical principle to support your response . ***NOTE***The question is NOT about whether abortion is right, but whether it is right to have sex or not if you would have an abortion for any resulting pregnancy as a means of birth control.
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Further, the amount of goodness created or evil prevented may, in some cases, be significant enough to legitimately override a right or incurred obligation that a lesser amount of good created or evil prevented may not. Overriding a right or incurred obligation is not the same as violating it.
*What is fair and reasonable to expect of an agent:
It is fair or reasonable for people to do things at little risk or cost to themselves that bring great benefit, prevent great harm, or create a much greater balance of benefit over harm, to others. Apart from cases where an agent has some special higher obligation that he has assumed or incurred, as the risk or cost to the agent increases and/or the benefit to others decreases, an agent is less obligated to perform the act. At some point along these scales, the obligation ceases altogether, though the act may be commendable or “saintly” to voluntarily perform (that is, it may be “over and above the call of duty”). At other points, the act may be so unfair to the agent — may be so self-sacrificing for the agent to perform, even if voluntary, and/or of so little benefit to deserving others, that it would be wrong. (Not every act of sacrifice or martyrdom is all right or acceptable.)
Key Takeaways
- Right acts consider many elements: best consequences, fairest and most reasonable distribution of burdens and benefits among deserving people affected, risk and severity of potential harm, intended harm (even if failed) to innocent people, what is fair and reasonable to expect of an agent, specially incurred obligations, rights and what they are and the difference between overriding both them and specially incurred obligations versus violating either. When these elements all point to the same act or option being right, there is little problem with ethical choices. Only when in a given situation the different elements give conflicting answers does it have to be decided which ones should prevail and how to weigh the importance of one element against the other(s).
Key Terms
- Consequentialist (also called ‘teleological’) principles and theories of ethics are those which hold that the overall good or harm of consequences are what make acts right or wrong.
- Non-consequentialist (also called deontological) principles and theories of ethics are those which hold that things other than consequences are what make acts right or wrong.
- Ethical Egoism is the principle that everyone should act in their own best interest
- Psychological Egoism is the view that everyone does act in their own perceived best interest and cannot do otherwise.
- Ethical hedonism is the principle that everyone should seek their own greatest happiness, satisfaction, pleasure, contentment.
- Psychological hedonism is the view that everyone does act to maximize their own greatest happiness and cannot do otherwise.
- Utilitarianism is the principle that all acts should do what causes the greatest good for the greatest number of people.
- Act utilitarianism is the form of utilitarianism that says right acts are those which individually do the greatest good for the greatest number.
- Rule utilitarianism is the form of utilitarianism that says right acts are those which conform to the rules that do the greatest good for the greatest number even if the individual act does not do the most good for the most people.
Review Questions
- Question : What are ethical egoism and ethical egoistic hedonism? And what are psychological egoism and psychological hedonism?
- Question : What is Utilitarianism?
- Question: Should the Golden Rule apply to personal relationship and love? Why or why not? Or if so, in what way; if not, in what way? Does the Golden Rule let you know what is right to do? Why or why not?


10.29: Reading- Product Marketing in the Marketing Mix
The Role of Product Marketing
Product marketing is the function of understanding the target customer’s needs, and promoting and selling the product to the target customer. In many organizations this is a different function from product management, which is responsible for defining the product that the company will build. Obviously the two functions must interact closely, but each has a different primary focus.
The product marketer is focused on the market. This includes analyzing and understanding the market, and presenting the product to the market. In other words, product marketers must bring information in and get it out. These activities are summarized in the table below:
| Inputs to the company | Outputs to the market |
|---|---|
| Define market needs or problems that the product should address | Define key messages to the communicate product benefits to the target market |
| Complete a competitive analysis to understand other offerings in the market | Create marketing materials about the product |
| Identify which market segments the product will target | Define the sales approach |
| Define market requirements for the product | Create lead generation plans |
| Create buyer persona documents that describe the personality, behavior, and desires of buyer types | Develop sales materials such as Web site content, brochures, presentations, and product demonstrations |
| Determine price | Provide training and support to distribution channel partners |
The product management function will use the inputs from product marketing to define detailed product requirements and oversee the development of products that meet those requirements. We will discuss the complexity of this process further when we delve into new-product development.
Product marketing and product management are both functions that must be managed well, but in different organizations they are managed differently. The specific roles of individuals will vary significantly depending on the company and the types of products. In a very large company there may be teams of individuals in the product marketing function filling very specialized roles. In a very small company, a single individual may fill both the product marketing and product management functions. In general, it is difficult to span both product marketing and product management because the skills needed to understand and translate broad market needs are different from the skills needed to create detailed product requirements.
The Marketing Mix
As you can see from the list of responsibilities, the product marketing function is not confined to only one aspect of the marketing mix. Instead, the product marketing function focuses on a single product or product line across the marketing mix. Let’s look at a specific example of the product marketing role and a corporate marketing role, and see how they each use the marketing mix.
When Apple introduced the Apple Watch, they had a large team responsible for product marketing. The team was following emerging technology, consumer, and societal trends and identifying what would impact customer needs. They became experts in the features and marketing of competitive products. Product marketers defined the target buyer for the watch and identified the key features the buyer would require. They met with distribution partners. The product marketing team developed pricing recommendations. They managed tradeoffs involving features, schedule, cost, and pricing. They also traveled to trade shows, customer briefings, and press visits to talk about the watch. The product marketing team was Apple’s resident expert on the target market for the Apple watch and the marketing strategy for that product.
Prior to the product launch, product marketing worked with Apple’s marketing communications team to develop the press releases, press strategy, and marketing materials for the launch and ongoing sales. Marketing communications is a corporate function that works across all products. They do not try to become experts in each product but look to the product marketing team to bring that expertise. Instead, the marketing communications team are experts in promotion across all of Apple’s products.
Product marketing understands the right message for the Apple watch’s target market. The marketing communications team knows how to get a writer at the New York Times to write a story about that message.
Contributors and Attributions
- Reading: Product Marketing in the Marketing Mix. Provided by : Lumen Learning. License : CC BY: Attribution


1.20: Discussion- What is Success?
For this activity, create your own definition of success. Dictionary.com defines success as “the favorable outcome of something attempted.” For many students in college, success means passing a class, earning an A, or learning something new. Beyond college, some people define success in terms of financial wealth; others measure it by the quality of their relationships with family and friends.
Here is an example of a brief, philosophical definition of success:
Ultimately, before we can know if we are successful, we must first define what success means for ourselves.
STEP 1 : Develop a 200-400 word post defining what success means to you in college and beyond. To help you write this entry, consider some of the following:
- Find a quote (or make one up) that best summarizes your definition of success. Note the author of the quote, and use quotation marks as appropriate.
- Why does this quote best represent your personal definition of success?
- What people do you consider to be successful and why?
- What is your definition of success?
- What will you do to achieve success?
- What is the biggest change you need to make in order to be successful in college?
- How will you know you’ve achieved success?
Note that if you do not feel comfortable sharing personal information, focus your entry on the generic definition of success and someone you view as successful, then write it about them and how and why you consider them to be successful.
STEP 2 : Respond in two separate posts to two classmates (in at least 75 words). Explicitly address their examples and try to extend, complicate, or redirect their points in a substantive, knowledge-demonstrating way. Be sure to cite relevant concepts and key terms from the module.
Example Post
Discussion entry assignments tend to be more flexible than other types of writing assignments in college, and as a result they can be tailored to your own experiences as long as they answer the primary questions asked in the assignment.
One model of a successful entry about this topic can be found below. Feel free to include your own experiences and examples from real life as they pertain to the issue at hand.
Habits for Success Journal Entry
by Sandy Brown
I found this quote online, and I thought it was both funny and true: “Success is often the result of taking a misstep in the right direction” by Al Bernstein. I’m not sure exactly who Mr. Bernstein is, but he hit the nail right on the head. It seems like the best things in my life have come from some initial screw-up or unintended action on my part.
I enrolled in college the first time right after I graduated high school, but it just didn’t work out for me. My dad offered me a job instead, when he saw how miserable I was, since his office manager had just quit. I’d been helping out at his place all my life, but I didn’t know anything about managing the books. I made some silly mistakes, and some sort of serious ones, but I figured things out pretty quickly.
Now that my dad is looking towards retirement, I’m come back to school to get formal recognition of the work I’ve been doing for the past fifteen years. I originally thought I just wanted to get a Payroll Accounting certificate, but my adviser here talked me into pursuing a full AA degree. I’m glad I made that decision, but it’s been hard. I came home everyday the first week too exhausted to speak to my family. Withdrawing from a couple of classes was the right thing for me to do, even if it means I’ll only be a part-time student for now.
For me, success will be getting my first accounting job after I graduate with my degree and pass the certification exam. I want my future employer to recognize not only the years of experience I have but also the formal education I get with my AA. Success is also being a good role model for my daughters. I don’t want them to just settle for “good enough” like I did when I became an adult, and want them to work hard in order to get to a place where they’re comfortable.
Contributors and Attributions
- Revision and Adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
- Defining Success. Authored by : Linda Bruce. Provided by : Lumen Learning. Located at : courses.candelalearning.com/lumencollegesuccess/chapter/defining-success/. License : CC BY: Attribution


8.4: Using Light Energy to Make Organic Molecules
- Describe the Calvin cycle
- Define carbon fixation
- Explain how photosynthesis works in the energy cycle of all living organisms
After the energy from the sun is converted into chemical energy and temporarily stored in ATP and NADPH molecules, the cell has the fuel needed to build carbohydrate molecules for long-term energy storage. The products of the light-dependent reactions, ATP and NADPH, have lifespans in the range of millionths of seconds, whereas the products of the light-independent reactions (carbohydrates and other forms of reduced carbon) can survive for hundreds of millions of years. The carbohydrate molecules made will have a backbone of carbon atoms. Where does the carbon come from? It comes from carbon dioxide, the gas that is a waste product of respiration in microbes, fungi, plants, and animals.
The Calvin Cycle
In plants, carbon dioxide (CO 2 ) enters the leaves through stomata, where it diffuses over short distances through intercellular spaces until it reaches the mesophyll cells. Once in the mesophyll cells, CO 2 diffuses into the stroma of the chloroplast—the site of light-independent reactions of photosynthesis. These reactions actually have several names associated with them. Another term, the Calvin cycle , is named for the man who discovered it, and because these reactions function as a cycle. Others call it the Calvin-Benson cycle to include the name of another scientist involved in its discovery. The most outdated name is dark reactions, because light is not directly required (Figure \(\PageIndex{1}\)). However, the term dark reaction can be misleading because it implies incorrectly that the reaction only occurs at night or is independent of light, which is why most scientists and instructors no longer use it.
The light-independent reactions of the Calvin cycle can be organized into three basic stages: fixation, reduction, and regeneration.
Stage 1: Fixation
In the stroma, in addition to CO 2 ,two other components are present to initiate the light-independent reactions: an enzyme called ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO), and three molecules of ribulose bisphosphate (RuBP), as shown in Figure \(\PageIndex{2}\). RuBP has five atoms of carbon, flanked by two phosphates.
RuBisCO catalyzes a reaction between CO 2 and RuBP. For each CO 2 molecule that reacts with one RuBP, two molecules of another compound (3-PGA) form. PGA has three carbons and one phosphate. Each turn of the cycle involves only one RuBP and one carbon dioxide and forms two molecules of 3-PGA. The number of carbon atoms remains the same, as the atoms move to form new bonds during the reactions (3 atoms from 3CO 2 + 15 atoms from 3RuBP = 18 atoms in 3 atoms of 3-PGA). This process is called carbon fixation , because CO 2 is “fixed” from an inorganic form into organic molecules.
Stage 2: Reduction
ATP and NADPH are used to convert the six molecules of 3-PGA into six molecules of a chemical called glyceraldehyde 3-phosphate (G3P). That is a reduction reaction because it involves the gain of electrons by 3-PGA. Recall that a reduction is the gain of an electron by an atom or molecule. Six molecules of both ATP and NADPH are used. For ATP, energy is released with the loss of the terminal phosphate atom, converting it into ADP; for NADPH, both energy and a hydrogen atom are lost, converting it into NADP + . Both of these molecules return to the nearby light-dependent reactions to be reused and reenergized.
Stage 3: Regeneration
Interestingly, at this point, only one of the G3P molecules leaves the Calvin cycle and is sent to the cytoplasm to contribute to the formation of other compounds needed by the plant. Because the G3P exported from the chloroplast has three carbon atoms, it takes three “turns” of the Calvin cycle to fix enough net carbon to export one G3P. But each turn makes two G3Ps, thus three turns make six G3Ps. One is exported while the remaining five G3P molecules remain in the cycle and are used to regenerate RuBP, which enables the system to prepare for more CO 2 to be fixed. Three more molecules of ATP are used in these regeneration reactions.
Interactive Link
This link leads to an animation of the Calvin cycle . Click stage 1, stage 2, and then stage 3 to see G3P and ATP regenerate to form RuBP.
During the evolution of photosynthesis, a major shift occurred from the bacterial type of photosynthesis that involves only one photosystem and is typically anoxygenic (does not generate oxygen) into modern oxygenic (does generate oxygen) photosynthesis, employing two photosystems. This modern oxygenic photosynthesis is used by many organisms—from giant tropical leaves in the rainforest to tiny cyanobacterial cells—and the process and components of this photosynthesis remain largely the same. Photosystems absorb light and use electron transport chains to convert energy into the chemical energy of ATP and NADH. The subsequent light-independent reactions then assemble carbohydrate molecules with this energy.
Photosynthesis in desert plants has evolved adaptations that conserve water. In the harsh dry heat, every drop of water must be used to survive. Because stomata must open to allow for the uptake of CO 2 , water escapes from the leaf during active photosynthesis. Desert plants have evolved processes to conserve water and deal with harsh conditions. A more efficient use of CO 2 allows plants to adapt to living with less water. Some plants such as cacti (Figure \(\PageIndex{3}\)) can prepare materials for photosynthesis during the night by a temporary carbon fixation/storage process, because opening the stomata at this time conserves water due to cooler temperatures. In addition, cacti have evolved the ability to carry out low levels of photosynthesis without opening stomata at all, an extreme mechanism to face extremely dry periods.
The Energy Cycle
Whether the organism is a bacterium, plant, or animal, all living things access energy by breaking down carbohydrate molecules. But if plants make carbohydrate molecules, why would they need to break them down, especially when it has been shown that the gas organisms release as a “waste product” (CO 2 ) acts as a substrate for the formation of more food in photosynthesis? Remember, living things need energy to perform life functions. In addition, an organism can either make its own food or eat another organism—either way, the food still needs to be broken down. Finally, in the process of breaking down food, called cellular respiration, heterotrophs release needed energy and produce “waste” in the form of CO 2 gas.
In nature, there is no such thing as waste. Every single atom of matter and energy is conserved, recycling over and over infinitely. Substances change form or move from one type of molecule to another, but their constituent atoms never disappear (Figure \(\PageIndex{4}\)).
CO 2 is no more a form of waste than oxygen is wasteful to photosynthesis. Both are byproducts of reactions that move on to other reactions. Photosynthesis absorbs light energy to build carbohydrates in chloroplasts, and aerobic cellular respiration releases energy by using oxygen to metabolize carbohydrates in the cytoplasm and mitochondria. Both processes use electron transport chains to capture the energy necessary to drive other reactions. These two powerhouse processes, photosynthesis and cellular respiration, function in biological, cyclical harmony to allow organisms to access life-sustaining energy that originates millions of miles away in a burning star humans call the sun.
Summary
Using the energy carriers formed in the first steps of photosynthesis, the light-independent reactions, or the Calvin cycle, take in CO 2 from the environment. An enzyme, RuBisCO, catalyzes a reaction with CO 2 and another molecule, RuBP. After three cycles, a three-carbon molecule of G3P leaves the cycle to become part of a carbohydrate molecule. The remaining G3P molecules stay in the cycle to be regenerated into RuBP, which is then ready to react with more CO 2 . Photosynthesis forms an energy cycle with the process of cellular respiration. Plants need both photosynthesis and respiration for their ability to function in both the light and dark, and to be able to interconvert essential metabolites. Therefore, plants contain both chloroplasts and mitochondria.
Review Questions
Which molecule must enter the Calvin cycle continually for the light-independent reactions to take place?
- RuBisCO
- RuBP
- 3-PGA
- CO 2
- Answer
-
Answer: D
Which order of molecular conversions is correct for the Calvin cycle?
- \(\text{RuBP} + \text{G3P} \rightarrow \text{3-PGA} \rightarrow \text{sugar}\)
- \(\text{RuBisCo} \rightarrow \text{CO}_2 \rightarrow \text{RuBP} \rightarrow \text{G3P}\)
- \(\text{RuBP} + \text{CO}_2 \rightarrow \text{[RuBisCo]} \enspace \text{3-PGA} \rightarrow \text{G3P}\)
- \(\text{CO}_2 \rightarrow \text{3-PGA} \rightarrow \text{RuBP} \rightarrow \text{G3P}\)
- Answer
-
Answer: C
Where in eukaryotic cells does the Calvin cycle take place?
- thylakoid membrane
- thylakoid lumen
- chloroplast stroma
- granum
- Answer
-
Answer: C
Which statement correctly describes carbon fixation?
- the conversion of CO 2 into an organic compound
- the use of RuBisCO to form 3-PGA
- the production of carbohydrate molecules from G3P
- the formation of RuBP from G3P molecules
- the use of ATP and NADPH to reduce CO 2
- Answer
-
Answer: A
Free Response
Why is the third stage of the Calvin cycle called the regeneration stage?
- Answer
-
Answer: Because RuBP, the molecule needed at the start of the cycle, is regenerated from G3P.
Which part of the light-independent reactions would be affected if a cell could not produce the enzyme RuBisCO?
- Answer
-
Answer: None of the cycle could take place, because RuBisCO is essential in fixing carbon dioxide. Specifically, RuBisCO catalyzes the reaction between carbon dioxide and RuBP at the start of the cycle.
Why does it take three turns of the Calvin cycle to produce G3P, the initial product of photosynthesis?
- Answer
-
Answer: Because G3P has three carbon atoms, and each turn of the cycle takes in one carbon atom in the form of carbon dioxide.
Art Connections
Figure \(\PageIndex{2}\): Which of the following statements is true?
- In photosynthesis, oxygen, carbon dioxide, ATP, and NADPH are reactants. G3P and water are products.
- In photosynthesis, chlorophyll, water, and carbon dioxide are reactants. G3P and oxygen are products.
- In photosynthesis, water, carbon dioxide, ATP, and NADPH are reactants. RuBP and oxygen are products.
- In photosynthesis, water and carbon dioxide are reactants. G3P and oxygen are products.
- Answer
-
Answer: D
Glossary
- Calvin cycle
- light-independent reactions of photosynthesis that convert carbon dioxide from the atmosphere into carbohydrates using the energy and reducing power of ATP and NADPH
- carbon fixation
- process of converting inorganic CO 2 gas into organic compounds
- reduction
- gain of electron(s) by an atom or molecule
Contributors and Attributions
-
Connie Rye (East Mississippi Community College), Robert Wise (University of Wisconsin, Oshkosh), Vladimir Jurukovski (Suffolk County Community College), Jean DeSaix (University of North Carolina at Chapel Hill), Jung Choi (Georgia Institute of Technology), Yael Avissar (Rhode Island College) among other contributing authors. Original content by OpenStax (CC BY 4.0; Download for free at<EMAIL_ADDRESS>).


1.16.3: Ionic Strength: Ional Concentration
The ionic strength of a salt solution I containing \(\mathrm{i}\)-ionic substances is defined by equation (a); \(\mathrm{m}_{j}\) is the molality of ionic substance-\(j\), charge number \(\mathrm{z}_{j}\) [1].
\[\mathrm{I}=(1 / 2) \, \sum_{\mathrm{j}=\mathrm{i}}^{\mathrm{j}=\mathrm{i}} \mathrm{m}_{\mathrm{j}} \, \mathrm{z}_{\mathrm{j}}^{2} \nonumber \]
The sum is taken over all \(\mathrm{i}\)-ionic substances in the solution. The situation is slightly complicated by the fact some authors use the term ‘ionic strength’ where the concentration \(\mathrm{c}_{j}\) (expressed using the unit, \(\mathrm{mol dm}^{-3}\)) replaces \(\mathrm{m}_{j}\). The substitution is reasonably satisfactory for dilute salt solutions at ambient \(\mathrm{T}\) and \(\mathrm{p}\) where the mass of water, volume \(1 \mathrm{~dm}^{3}\), is approx. \(1 \mathrm{~kg}\).
The ional concentration of a salt solution \(\Gamma\) is defined by equation (b) where \(\mathrm{c}_{j}\) is expressed using the unit, \(\mathrm{mol dm}^{-3}\) [2].
\[\Gamma=\sum_{j=i}^{j=i} c_{j} \, z_{j}^{2} \nonumber \]
Footnotes
[1] An aqueous solution contains \(\mathrm{K}_{2}\mathrm{SO}_{4}\) (\(0.1 \mathrm{~mol}\)) in \(1 \mathrm{~kg}\) of water(\(\ell\)).
\(\mathrm{m}\left(\mathrm{K}_{2} \mathrm{SO}_{4}\right)=0.1 \mathrm{~mol} \mathrm{~kg}^{-1} ; \mathrm{m}\left(\mathrm{K}^{+}\right)=0.2 \mathrm{~mol} \mathrm{~kg}^{-1}\)
and \(\mathrm{m}\left(\mathrm{SO}_{4}{ }^{2-}\right)=0.1 \mathrm{~mol} \mathrm{~kg}^{-1}\)
Hence \(\mathrm{I}=(1 / 2) \,\left[(0.2)+\left(2^{2} \mathrm{X} 0.1\right)\right]=0.3 \mathrm{~mol} \mathrm{~kg}^{-1}\)
[2] H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, , Reinhold, New York, 2nd. revised edn.1950, p.33.


16.3: Checklist for Transdermal, Eye, Ear, Inhalation, and Vaginal Routes Medication Administration
Use the checklist below to review the steps for completion of “Transdermal, Eye, Ear, Inhalation, and Vaginal Routes for Medication Administration.”
Steps
Disclaimer: Always review and follow agency policy regarding this specific skill.
Follow Steps 1 through 12 in 15.4 “ Checklist for Oral Medication Administration .”
-
-
Transdermal Patch:
- Perform hand hygiene and apply clean gloves
- Remove the old patch (if present).
- Clean the skin with mild soap and water. Dry the area completely.
- Assess the skin for any breaks or rashes. Do not use these areas.
- Apply a new patch wearing gloves. Rotate application site based on manufacturer recommendations. Be careful not to touch the medication surface.
- Press firmly to the patient’s skin for about ten seconds.
- Date, time, and initial a piece of tape and place this next to the patch.
- Perform hand hygiene.
-
Eye Drops:
- Perform hand hygiene.
- Clean the eyes from the inner canthus to the outer canthus using water or normal saline.

- Remove the cap and keep inside sterile. Do not touch the dropper.
- Pull the lower conjunctival sac open.
- Squeeze the ordered drops into the conjunctival sac.
- Apply gentle pressure over the inner canthus.
- Repeat in the other eye if ordered.
- Perform hand hygiene.
-
Ear Drops:
- Perform hand hygiene.
- Clean the external ear of debris.
- Tilt the patient’s head so the affected ear is uppermost.
- Remove the cap and keep inside sterile. Do not touch the dropper.
-
Straighten the auditory canal properly for the age of the patient:
- Adult: Pinna pulled up and back
- Child: Pinna pulled straight back
- Infant and child under three: Pinna pulled back and down
- Squeeze the bottle and allow drop(s) to fall on the side of the auditory canal.
- Release the pinna and massage the tragus to help with movement of the drop into the canal.
- Keep the patient in a lying position with the affected ear up for 5 minutes.
- Repeat in the other ear if ordered.
- Perform hand hygiene.
-
Nose Spray:
- Perform hand hygiene.
- Have the patient blow their nose.
- Have the patient tilt their head back.
- Instruct the patient to inhale with administration if necessary.
- Close the opposite nare.
- Place a bottle or dropper in the affected nare.
- Squeeze the bottle or dropper and have the patient inhale.
- Keep the bottle or dropper compressed and remove from the nare.
- Instruct the patient to hold their breath for a few seconds and then breath out through the mouth.
- Repeat in other nare if ordered.
- Clean tip of bottle with tissue or cloth.
- Perform hand hygiene.
-
Vaginal Cream or Suppository:
- Have the patient void prior to medication administration.
- Position the patient on their back with their knees flexed.
- Perform perineal care. Dispose gloves and perform hand hygiene.
- Put on new gloves.
- Fill the vaginal applicator with the correct dose and lubricate the applicator, OR open the suppository and lubricate dominant index finger and suppository.
- With the nondominant hand spread the labia.
- Insert the applicator completely OR insert the suppository along the posterior vaginal wall.
- Instruct the patient to remain in supine position for 5-10 minutes.
- Perform hand hygiene.
-
Metered-Dose Inhaler (MDI):
- Perform hand hygiene.
- Shake the inhaler.
- IF SPACER IS USED: Attach the inhaler opposite to the mouthpiece.

- Push down on inhaler to release medication.
- Instruct the patient to inhale slowly and deeply through the mouthpiece of the spacer.
- IF NO SPACER USED: Patient should exhale out breath and hold the inhaler one to two inches from their mouth and inhale slowly and deeply as they push down on the inhaler to release the medication. The patient will then hold their breath for 5 to 10 seconds and release their breath through pursed lips. This can be repeated for a second puff after 1-5 minutes.
- Instruct the patient to rinse mouth after finishing with the inhaler.
-
Dry Powder Inhaler (DPI):
- Perform hand hygiene.
- Remove the mouthpiece cover and load the medication if necessary.
- Activate the inhaler per manufacturer directions.
- Have the patient exhale out slowly and completely.
- Instruct the patient to place the mouthpiece of the inhaler in their mouth and inhale deeply and forcefully for at least 2-3 seconds.
- Remind the patient to hold their breath for 10 seconds and then breath out through pursed lips.
- Instruct the patient rinse mouth after finishing with the inhaler.
-
Transdermal Patch:
- Assist the patient to a comfortable position, ask if they have any questions, and thank them for their time.
-
Ensure safety measures when leaving the room:
- CALL LIGHT: Within reach
- BED: Low and locked (in lowest position and brakes on)
- SIDE RAILS: Secured
- TABLE: Within reach
- ROOM: Risk-free for falls (scan room and clear any obstacles)
- Perform hand hygiene.
- Document medication administration and related assessment findings. Report any concerns according to agency policy.


15.12: Excel Table from Access Data
Learning Objectives
- Create Excel table from Access Data
There are times when Access contains data you want to analyze in an Excel spreadsheet. This export may take place once or more frequently depending on the situation. For example, let’s say at work you have a monthly report for your department head which pulls monthly customer contact data from Access into an Excel table. Although Access can create reports, your department manager is more comfortable with Excel and wants the data reported in that program. We’ll walk through setting this scenario up and show you the integration capabilities of Access.
Exporting Data to Excel
Open the Access file to be exported and follow these steps to export the customer contact information into Excel.
Step 1
Before exporting data from Access look through the data to identify any errors (e.g. #Error, #Num!, #Name?, etc.). Fix any errors—otherwise errors might multiply as incorrect information may be placed in incorrect Excel cells in a worksheet. Now that the data is ready go to the next step.
Step 2
Select the External Data tab, Excel button and an Export – Excel Spreadsheet command window opens.
Step 3
Fill out the information asked for in the window:
- File name: name for the exported excel file.
- File format: older Excel versions are available as well as the current *.xlsx extension default.
-
Specify export options:
Decide whether to export the data format and layout or not.
- If exporting the format, the next box/choice becomes available whether to open the destination file after the export is complete or not.
- Click the OK button.
Note: To Format or Not To Format?
How should you determine whether to export data with or without formatting?
- With Formatting: Exporting a table or query with formatting allows the export wizard to use the format property settings, have hyperlink fields exported as hyperlinks and have it use the format settings. With rich text fields text is exported without formatting.
- Without Formatting: Exporting a table or query without format means all records and fields are exported with formatting ignored. Only lookup ID values are exported, and hyperlinks are exported as regular text.
Step 4
One more window opens indicating the export is successful and asks if these same export steps should be saved. This option is used if you are frequently exporting this same data often. In this case we leave the box unchecked.
Step 5
Choose the Excel workbook and file format. If you selected the open the file when done exporting an Excel worksheet will open with the exported Access data. Now you can use the data to do anything in Excel you wish to do.
PRactice Questions
This example was using contact information data in Access, but all kinds of data can be exported from Access to Excel. If an error slipped through, you can either fix it in Excel or return to Access and fix the error there and re-export the data into an Excel worksheet.
Note: Export Possibilities
What is and isn’t possible to export to Excel:
- There are a few types that can be exported to Excel; forms, tables, reports, queries or even a few selected records from a datasheet.
- Things that cannot be exported to Excel are modules or macros and if there are subreports, subdatasheet or subforum in the data they are not exported and must repeat the export for each of them if you want them exported to Excel.
- Only one database object can be exported in a single export, but multiple worksheets can be merged in Excel to cobble together one table or report from the individual exports.
Now that you have walked through exporting a table from Access to Excel, watch this short video to see additional ways to export tables, queries and reports from Access to Excel.
You can also view a transcript for the video “Exporting Tables, Queries and Reports” here (opens in new window ).
Contributors and Attributions
- Excel Table from Access Data. Authored by : Sherri Pendleton. Provided by : Lumen Learning. License : CC BY: Attribution
- Exporting Tables, Queries and Reports from Access to Excel in Access 2016. Authored by : Sali Kaceli. Located at : https://www.youtube.com/watch?v=Mn4zwUMi7yc . License : All Rights Reserved . License Terms : Standard YouTube License


10.4: Simulating Birth-Death Trees
We can use the statistical properties of birth-death models to simulate phylogenetic trees through time. We could begin with a single lineage at time 0. However, phylogenetic tree often start with the first speciation event in the clade, so one can also begin the simulation with two lineages at time 0 (this difference relates to the distinction between crown and stem ages of clades; see also Chapter 11).
To simulate our tree, we need to draw waiting times between speciation and extinction events, connect new lineages to the tree, and prune lineages when they go extinct. We also need a stopping criterion, which can have to do with a particular number of taxa or a fixed time interval. We will consider the latter, and leave growing trees to a fixed number of taxa as an exercise for the reader. Our simulation algorithm is as follows.
simulation algorithm
Assume that we have a certain number of “living” lineages in our tree (1 or 2 initially), a current time ( t c = 0 initially), and a stopping time t s t o p .
- Draw a waiting time t i to the next speciation or extinction event. Waiting times are drawn from an exponential distribution with rate parameter N a l i v e * ( λ + μ ) where N a l i v e is the current number of living lineages in the tree.
- Check to see if the simulation ends before the next event. That is, if t c + t i > t s t o p , end the simulation.
- Decide whether the next event is a speciation event [with probability λ /( λ + μ )] or an extinction event [with probability μ /( λ + μ )]. This can be done by drawing a uniform random number u i from the interval [0, 1] and assigning speciation to the event if u i < λ /( λ + μ ) and extinction otherwise.
- If (3) is a speciation event, then choose a random living lineage in the tree. Attach a new branch to the tree at this point, and add one new living lineage to the simulation. Return to step 1.
- If (3) is an extinction event, choose a random living lineage in the tree. That lineage is now dead. As long as there is still at least one living lineage in the tree, return to (1); otherwise, your whole clade has gone extinct, and you can stop the simulation.
This procedure returns a phylogenetic tree that includes both living and dead lineages. One can prune out any extinct taxa to return a birth-death tree of survivors, which is more in line with what we typically study using extant species. It is also worth noting that entire clades can – and often do – go extinct under this protocol before one reaches time t s t o p . Note also that there is a much more efficient way to simulate trees (Stadler 2011) .
We can think about phylogenetic predictions of birth-death models in two ways: by considering tree topology, and by considering tree branch lengths. I will consider each of these two aspects of trees below.