4.5: Elastic Collisions in One Dimension
Learning Objectives
- Describe an elastic collision of two objects in one dimension.
- Determine the final velocities in an elastic collision given masses and initial velocities.
Let us consider various types of two-object collisions. These collisions are the easiest to analyze, and they illustrate many of the physical principles involved in collisions. The conservation of momentum principle is very useful here, and it can be used whenever the net external force on a system is zero.
We start with the elastic collision of two objects moving along the same line—a one-dimensional problem. An elastic collision is one that also conserves total kinetic energy, in addition to the total momentum. Figure \(\PageIndex{1}\) illustrates an elastic collision in which kinetic energy and momentum are conserved.
Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic—some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. One macroscopic collision that is nearly elastic is that of two steel blocks on ice. Another nearly elastic collision is that between two carts with spring bumpers on an air track. Icy surfaces and air tracks are nearly frictionless, more readily allowing nearly elastic collisions on them.
Definition: ELASTIC COLLISION
An elastic collision is one that conserves total kinetic energy.
Now, to solve problems involving one-dimensional elastic collisions between two objects we can use the equations for conservation of momentum and conservation of internal kinetic energy. First, the equation for conservation of momentum for two objects in a one-dimensional collision is
\[p_{1}+p_{2}=p_{1}^{\prime}+p_{2}^{\prime} \quad\left(F_{\text {net }}=0\right) \nonumber \]
or
\[m_{1} v_{1}+m_{2} v_{2}=m_{1} v_{1}^{\prime}+m_{2} v_{2}^{\prime} \quad\left(F_{\mathrm{net}}=0\right), \nonumber \]
where the primes (') indicate values after the collision. By definition, an elastic collision conserves total kinetic energy, and so the sum of kinetic energies before the collision equals the sum after the collision. Thus,
\[\frac{1}{2} m_{1} v_{1}^{2}+\frac{1}{2} m_{2} v_{2}^{2}=\frac{1}{2} m_{1} v_{1}^{\prime 2}+\frac{1}{2} m_{2} v_{2}^{\prime}{ }^{2} \text { (two-object elastic collision) } \nonumber \]
expresses the equation for conservation of total kinetic energy in a one-dimensional collision.
Example \(\PageIndex{1}\): Calculating Velocities Following an Elastic Collision
Calculate the velocities of two objects following an elastic collision, given that
\[m_{1}=0.500 \mathrm{~kg}, m_{2}=3.50 \mathrm{~kg}, v_{1}=4.00 \mathrm{~m} / \mathrm{s}, \text { and } v_{2}=0. \nonumber\]
Strategy and Concept
First, visualize what the initial conditions mean—a small object strikes a larger object that is initially at rest. This situation is slightly simpler than the situation shown in Figure \(\PageIndex{1}\) where both objects are initially moving. We are asked to find two unknowns (the final velocities \(v_{1}^{\prime}\) and \(v_{2}^{\prime}\)). To find two unknowns, we must use two independent equations. Because this collision is elastic, we can use the above two equations. Both can be simplified by the fact that object 2 is initially at rest, and thus \(v_{2}=0\). Once we simplify these equations, we combine them algebraically to solve for the unknowns.
Solution
For this problem, note that \(v_{2}=0\) and use conservation of momentum. Thus,
\[p_{1}=p_{1}^{\prime}+p_{2}^{\prime} \nonumber\]
or
\[m_{1} v_{1}=m_{1} v_{1}^{\prime}+m_{2} v_{2}^{\prime}. \nonumber\]
Using conservation of internal kinetic energy and that \(v_{2}=0\),
\[\frac{1}{2} m_{1} v_{1}^{2}=\frac{1}{2} m_{1} v_{1}^{\prime 2}+\frac{1}{2} m_{2} v_{2}^{\prime 2}. \nonumber\]
Solving the first equation (momentum equation) for \(v_{2}^{\prime}\), we obtain
\[v_{2}^{\prime}=\frac{m_{1}}{m_{2}}\left(v_{1}-v_{1}^{\prime}\right). \nonumber\]
Substituting this expression into the second equation (internal kinetic energy equation) eliminates the variable \(v_{2}^{\prime}\), leaving only \(v_{1}^{\prime}\) as an unknown (the algebra is left as an exercise for the reader). There are two solutions to any quadratic equation; in this example, they are
\[v_{1}^{\prime}=4.00 \mathrm{~m} / \mathrm{s} \nonumber\]
and
\[v_{1}^{\prime}=-3.00 \mathrm{~m} / \mathrm{s}. \nonumber\]
As noted when quadratic equations were encountered in earlier chapters, both solutions may or may not be meaningful. In this case, the first solution is the same as the initial condition. The first solution thus represents the situation before the collision and is discarded. The second solution (\(v_{1}^{\prime}=-3.00 \mathrm{~m} / \mathrm{s}\)) is negative, meaning that the first object bounces backward. When this negative value of \(v_{1}^{\prime}\) is used to find the velocity of the second object after the collision, we get
\[v_{2}^{\prime}=\frac{m_{1}}{m_{2}}\left(v_{1}-v_{1}^{\prime}\right)=\frac{0.500 \mathrm{~kg}}{3.50 \mathrm{~kg}}[4.00-(-3.00)] \mathrm{m} / \mathrm{s} \nonumber\]
or
\[v_{2}^{\prime}=1.00 \mathrm{~m} / \mathrm{s}. \nonumber\]
Discussion
The result of this example is intuitively reasonable. A small object strikes a larger one at rest and bounces backward. The larger one is knocked forward, but with a low speed. (This is like a compact car bouncing backward off a full-size SUV that is initially at rest.) As a check, try calculating the internal kinetic energy before and after the collision. You will see that the internal kinetic energy is unchanged at 4.00 J. Also check the total momentum before and after the collision; you will find it, too, is unchanged.
The equations for conservation of momentum and internal kinetic energy as written above can be used to describe any one-dimensional elastic collision of two objects. These equations can be extended to more objects if needed.
MAKING CONNECTIONS: TAKE-HOME INVESTIGATION—ICE CUBES AND ELASTIC COLLISION
Find a few ice cubes which are about the same size and a smooth kitchen tabletop or a table with a glass top. Place the ice cubes on the surface several centimeters away from each other. Flick one ice cube toward a stationary ice cube and observe the path and velocities of the ice cubes after the collision. Try to avoid edge-on collisions and collisions with rotating ice cubes. Have you created approximately elastic collisions? Explain the speeds and directions of the ice cubes using momentum.
Section Summary
- An elastic collision is one that conserves total kinetic energy.
- Conservation of kinetic energy and momentum together allow the final velocities to be calculated in terms of initial velocities and masses in one dimensional two-body collisions.
Glossary
- elastic collision
- a collision that also conserves total kinetic energy, in addition to the total momentum


22.10: Arthur Gordon Pym, Cannibal of Nantucket
What makes us human? What separates us from wild animals? Is it what we will do or won’t do to survive?
The part about cannibalism really disturbed me. It is scary to me how they are able to apply human reasoning to justify the death and consumption of someone whose survival they were trying to ensure during the storm. The worst part wasn’t the killing-and-eating-another-human-being, it was the simple matter-of-fact way it was described.
“He made no resistance whatever, and was stabbed in the back by Peters, when he fell instantly dead…having in some measure appeased the raging thirst which consumed us by the blood of the victim and having by common consent taken off the hands, feet, and head, throwing them together with the entrails, into the sea, we devoured the rest of the body, piecemeal, during the four ever memorable days ”(81).
Parker ceases to live. He becomes a thing, a resource, a meal to be divided among them. But he ceases to be human before that.  The four of them begin to de-evolve at that moment, when they are hungry enough to think they would do anything , eat anything to survive. But the devolution from humanity is a process. As Pym himself stated, he had considered cannibalism as a means to survive. They were all thinking about it. When Parker first brings up the idea that eating each other might be the only option, they continue to de-evolve. If he were to jump straight from human to beast, he would have killed and eaten Pym without a pause. But he didn’t. He consented to the drawing of straws. This was the next step backwards. Picking straws doesn’t make murder civilized.
The actual killing and consumption are the final steps in their de-evolution. Parker is reduced to an object of sustenance, but Pym, Peters, and Augustus are no longer fully human. They have become a more primitive kind of hunter.
The saddest part is that Parker’s death wasn’t necessary. The next page describes Pym remembering the existence of the axe and with it cutting through to the store room. And frankly, they treat the tortoise better than Parker.


19.3: Displaying Array Members
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Overview
To
display
all
array members
, visit each element using a
for
loop and output the element using index notation and the loop control variable.
Discussion
Accessing Array Members
Assume an integer array named ages with five values of 49, 48, 26, 19, and 16, respectively. In pseudocode, this might be written as:
Declare Integer Array ages[5]
Assign ages = [49, 48, 26, 19, 16]
To display all elements of the array in order, we might write:
Output ages[0]
Output ages[1]
Output ages[2]
Output ages[3]
Output ages[4]
While this works for short arrays, it is not very efficient, and quickly becomes overwhelming for longer arrays. One of the principles of software development is don’t repeat yourself (DRY) . Violations of the DRY principle are typically referred to as WET solutions, which is commonly taken to stand for either “write everything twice”, “we enjoy typing” or “waste everyone’s time”. [1]
Rather than repeating ourselves, we can use a for loop to visit each element of the array and use the loop control variable as the array index. Consider the following pseudocode:
Declare Integer Array ages[5] Declare Integer index Assign ages = [49, 48, 26, 19, 16] For index = 0 to 4 Output ages[index] End
This approach is much more efficient from a programming perspective, and also results in a smaller program. But there is still one more opportunity for improvement. Most programming languages support a built-in method for determining the size of an array. To reduce potential errors and required maintenance, the loop control should be based on the size of the array rather than a hard-coded value. Consider:
Declare Integer Array ages[5] Declare Integer index Assign ages = [49, 48, 26, 19, 16] For index = 0 to Size(ages) - 1 Output ages[index] End
This method allows for flexible coding . By writing the for loop in this fashion, we can change the declaration of the array by adding or subtracting members and we don’t need to change our for loop code.
Key Terms
- don’t repeat yourself
- A principle of software development aimed at reducing repetition of software patterns, replacing it with abstractions, or repetition of the same data, using data normalization to avoid redundancy. [2]


3.1E: Functions and Function Notation (Exercises)
For the following exercises, determine whether the relation is a function.
1. \(\{(a, b),(c, d),(e, d)\}\)
2. \{(5,2),(6,1),(6,2),(4,8)\}\)
3. \(y^{2}+4=x,\) for \(x\) the independent variable and \(y\) the dependent variable
4. Is the graph in Figure 1 a function?
For the following exercises, evaluate the function at the indicated values:
\[\begin{array}{lllll} f(-3) ; & f(2) ; & f(-a) ; & -f(a) ; & f(a+h) .\end{array} \nonumber\]
5. \(f(x)=-2 x^{2}+3 x\)
6. \(f(x)=2|3 x-1|\)
For the following exercises, determine whether the functions are one-to-one.
7. \(f(x)=-3 x+5\)
8. \(f(x)=\mid x-3\)
For the following exercises, use the vertical line test to determine if the relation whose graph is provided is a function.
9.
10.
11.
For the following exercises, graph the functions.
12. \(f(x)=\mid x+1\)
13. \(f(x)=x^{2}-2\)
For the following exercises, use Figure 2 to approximate the values.
14. \(f(2)\)
15. \(f(-2)\)
16. If \(f(x)=-2,\) then solve for \(x\).
17. If \(f(x)=1,\) then solve for \(x\).
For the following exercises, use the function \(h(t)=-16 t^{2}+80 t\) to find the values in simplest form.
18. \(\frac{h(2)-h(1)}{2-1}\)
19. \(\frac{h(a)-h(1)}{a-1}\)


9.9: Pretérito e Imperfecto II
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Learning Objectives
- Distinguish the use of imperfect for ongoing actions and preterit for interrupting actions in the past.
Depending on how you combine the preterit and the imperfect together you are expressing a different meaning, because the tenses themselves have different relations to time. In English, these distinctions have to be expressed by means of adverbs or prepositional phrases, but in Spanish the choice of preterit or imperfect expresses not just that the action happened in the past, but also * how * the action happened.
-
A combination of imperfect with imperfect:
When you want to convey that two actions were ongoing at the same time in the past, you use the imperfect tense. You will often see the words “mientras” ( while ) and “y” to show that these actions were in progress simultaneously.
Examples: -
A combination of preterit with preterit:
When you want to convey a series of completed actions in the past, you use the preterit tense for each of them. It is very important that the events are stated in order of what happened first.
Examples:- Mi tía se levantó a bailar, el tacón de su zapato se rompió y ella se cayó. ( My aunt got up to dance, the heel of her shoe broke off, and she fell. )
- Mi tío la salvó antes de tocar el piso, la levantó y la hizo girar por un momento. ( My uncle caught her before she touched the floor, he lifted her up and twirled her for a moment. )
-
A combination of imperfect with preterit:
When you want to show that an action was in progress when another action began, you use the imperfect for the continuous action and the preterit for the interrupting action.
Examples:- Nuestra prima bailaba con mi hermano cuando su novio llegó a la fiesta. ( Our cousin was dancing with my brother when her boyfriend arrived at the party. )
- El novio se estaba poniendo celoso hasta que yo le expliqué la situación. ( The boyfriend was getting jealous until I explained the situation. )


2.5: Some Basic Biochemistry- Carbon, Monomers, Polymers and the Synthesis and Degradation of Macromolecules
Like evolution, the origin of life involved some prebiotic ‘natural selection’ of chemicals in the environment. As with evolution, this chemical selection would favor expanding possibility and diversity. In simple terms, atoms that could interact with a maximal number of other atoms to form the largest number of stable molecules would have been most likely to accumulate in the environment. The tetravalent C atom met these criteria for chemical selection, proving perfect for building an organic chemistry set.
At the same time, water turned out to be the perfect place to launch prebiotic chemical selection experiments. Water persists as the life’s universal solvent, which by way, is why evidence of water in places beyond our earth gets us all excited!
A. Isomerism in Organic Molecules and the Diversity of Shape
The carbon skeleton is a perfect platform of organic molecule diversity. The differences in arrangement of atoms and functional chemical groups around C atom result in isomerism . Isomers of an organic molecule have the same chemical formula but different shapes (and so, potentially different chemical properties and biochemical function). The larger the carbon skeleton of an organic molecule, the greater the diversity of molecular shapes available for chemical selection.
Look at the examples of structural isomers and geometric isomers below.
It is easy to see that the structural isomers of C4H10 (above left and right) have different shapes. You cannot convert one structural isomer to the other without breaking covalent bonds. In the geometric isomers of C4H8 in the lower panel, the H atoms on the double-bonded C atoms can be on the same (cis) or opposite (trans) side of the planar double bond. Geometric isomers too, cannot be interconverted without breaking chemical bonds. Optical isomers are yet a third kind of isomer. They exist around optically active ( asymmetric , or chiral ) carbons. A chiral C is one that is covalently linked to four different atoms and/or molecular groups. The principle of chirality is illustrated below.
Optical isomers (also called enantiomers ) also differ in shape , and just like structural and geometric isomers, they can’t be converted from one to the other without breaking and re-making covalent bonds. We say that optical isomers are optically active because they bend, or rotate light in opposite directions in a polarimeter . Light passing through a solution of one optical isomer is rotated in one direction while light passing through the other isomer is rotated in the opposite direction. These directions are referred to as l, or levo (meaning left) and d or dextro (meaning right). If a molecule has more than one chiral C (glucose for example has four chiral carbons), its behavior in a polarimeter will be based on the sum of optical activities of all the chiral carbons. The common isomer of glucose in our diet is d-glucose . The d- and l- isomers of glucose are illustrated below (showing chiral carbons in red).
Glucose enantiomers are also referred to as D and L respectively. This is a convention based on the configuration of the four different atoms or groups around the last optically active carbon in a molecule ( 5C in glucose). For glucose, d and l in fact correspond to D and L respectively. As we will see for some molecules, the upper case designation of a chiral molecule does not always indicate how it bends light in a polarimeter, while the lower case d and l always do!
Remember that the shape and chemical properties of any molecule dictates its function. Isomerism in organic (carbon-based) molecules increased the diversity of molecular shapes available for chemical selection. An early selection of isomers (and specific optical isomers in particular) during chemical evolution contributed greatly to chemical functions and reactions we recognize in cells… even before there was life on earth. That all life uses the same isomers of glucose in energy reactions and the same isomers of amino acids to build proteins confirms the prebiotic selection of those isomers!
B. Monomers to Polymers and Back: Dehydration Synthesis and Hydrolysis
All living things build and break down polymers (macromolecules) by dehydration synthesis ( condensation reactions) and hydrolysis , respectively. Dehydration synthesis and hydrolysis reactions are essentially the reverse of each other, as illustrated below:
Condensation reactions build macromolecules by removing a water molecule from interacting monomers. The ‘bond’ that forms in a condensation reaction is not a single bond , but a linkage involving several bonds! The linkages form by removing an OH from one monomer and an H group from the other to form a water molecule.
126 Organic Molecules Monomers & Polymers
Repeated condensation reactions such as the one between two amino acids shown below form the peptide linkages that build polypeptides during translation.
Cells perform repeated condensation reactions to build other polymers, including polysaccharides and polynucleotides (the RNA and DNA nucleic acids). Consider the polymerization of glucose monomers into storage or structural polysaccharides for example. Cells use only (d)glucose is used by cells to make polysaccharides. Straight-chain ( d)glucose with four chiral carbons becomes cyclic when dissolved in water, where the cyclic molecule acquires a fifth chiral carbon, shown below.
The fifth pair of enantiomers in solution are called a and b , or more correctly, a(d)glucose and b(d)glucose . Having selected d-glucose for most cellular energy metabolism, life then exploited the additional chiral carbon in cyclic d-glucose to make the different polysaccharide polymers we now find in plants and animals.
The condensation reactions shown below link glucose monomers, forming storage and structural polysaccharides.
The -OH (hydroxyl) groups on the #1 C of a (d)glucose are below the glucose rings. The condensation reaction removes a water molecule, linking the sugars by an a 1,4 glycoside linkage in the dimer, connecting them by their # 1 and # 4 carbons. Other linkages are possible; diverse a -glycoside linkages characterize branched storage polysaccharides like glycogen in animals and the starches in plants. When b(d)glucose enantiomers polymerize, they form rigid structural polysaccharides such as those of cellulose in plant cell walls. A modified b-glucose called N-acetyl glucosamine (not shown) polymerizes to form chitin , the principal component of fungal cell walls and of the tough exoskeleton of arthropods (insects, crustacea). In another chapter, we’ll revisit the linkage of amino acids the in the process of translation to build a polypeptide, using only L amino acids to make their proteins! We’ll also look at the details of replication and transcription that cells use to catalyze condensation reactions to synthesizing DNA and RNA from nucleotide monomers.
To summarize:
- Linkages in these biopolymers are broken and formed daily in our lives!  Then our cells use condensation reactions to complete the job of turning carrot- and cow-derived monomers into you or me!
- Prebiotic chemical evolution has selected only one of the optical isomers (enantiomers) of glucose, amino acid and other monomers with which to build polymers. This is so even though some of the different isomers are available and even used for different purposes. The flexible a(d)glucose polymer was selected to be the storage polysaccharides that we use for energy, a selection probably made by cells themselves. Storage polysaccharides include the plant starches and animal glycogen . Likewise, the rigid inflexibility of b(d)glucose polymers would have been selected to reinforce cell structure and stability. Since all organisms store carbohydrate energy in a(d)glucose polymers and since b(d)glucose polymers are almost universally used to strengthen cell structure, these selections must have occurred early in the history of life.
127 Carbohydrates: Sugars & Polysaccharides
128 Lipids: Triglycerides & Phospholipids
129Proteins: Amino Acids & Polypeptides
130 DNA & RNA: Nucleotides & Nucleic Acids
To conclude this chapter and to emphasize the significance of chirality to life, here is what can happen when the wrong isomer ends up in the wrong place at the wrong time…
C. A Tale of Chirality Gone Awry
Consider the story of Thalidomide , a tragic example of what happens if we are unaware of enantiomeric possibilities. Introduced in 1957, Thalidomide sold as an over-the-counter anti-nausea drug for cancer treatments and as a very effective morning sickness remedy for pregnant women. However, by the early 1960s, the birth of about 10,000 infants with severely deformed limbs was connected to the drug. The half of the infants affected that survived did so with other defects as well. Of course, the response was to pull Thalidomide off the market.
Thalidomide is a teratogen . Teratogens are substances or conditions (drugs, chemicals, radiation, illness during pregnancy, etc.) that cause deformities during embryogenesis and fetal development. The chemical basis of Thalidomide’s effects are based on its enantiomeric ( chiral ) structure in which an amine-containing ring can exist in front of, or behind the rest of the molecule.
The structure of Thalidomide is shown below.
The two isomers are referred to as ‘S’ and ‘R’. Of these, the S isomer is the teratogen. While synthesis of pure R is possible, when used in treatment, R and S easily interconvert, creating a racemic mixture . In the mother, S is transferred to the embryo or fetus, with its terrible consequences. Remarkably, there were relatively few cases of Thalidomide-induced birth deformities in the United States because our FDA ( Food and Drug Administration ) had not yet approved the drug for clinical use. Of course, we already knew that cells synthesized polymers from specific optical isomers of their precursor monomers. So the sad Thalidomide story resulted from the untested effects of an unexpected optical isomer. Many countries quickly tightened their pre-approval drug testing regulations because of this tragedy.
In a more hopeful twist of the tale, Thalidomide has turned out to be effective in treating cancer, leprosy, rheumatoid arthritis and other autoimmune diseases. Such therapeutic benefits may be due to its anti-inflammatory effects . Its effects on tumor growth seems to be due to its inhibition of angiogenesis (development of blood vessels) in the tumors. Ironically, blockade of angiogenesis might also have contributed to the failure of proper limb growth during pregnancy.
To conclude, when all is normal, the shapes of molecules, particularly macromolecules, are essential for the specificity of reactions essential to life.


10.5: RL Circuits
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Learning Objectives
By the end of this section, you will be able to:
- Analyze circuits that have an inductor and resistor in series
- Describe how current and voltage exponentially grow or decay based on the initial conditions
A circuit with resistance and self-inductance is known as an RL circuit . Figure \(\PageIndex{1a}\) shows an RL circuit consisting of a resistor, an inductor, a constant source of emf, and switches \(S_1\) and \(S_2\). When \(S_1\) is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected across a source of emf (Figure \(\PageIndex{1b}\)). When \(S_1\) is opened and \(S_2\) is closed, the circuit becomes a single-loop circuit with only a resistor and an inductor (Figure \(\PageIndex{1c}\)).
We first consider the RL circuit of Figure \(\PageIndex{1b}\). Once \(S_1\) is closed and \(S_2\) is open, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady value of \(\epsilon/R\). However, from Faraday’s law, the increasing current produces an emf \(V_L = -L(dI/dt)\) across the inductor. In accordance with Lenz’s law , the induced emf counteracts the increase in the current and is directed as shown in the figure. As a result, \(I(t)\) starts at zero and increases asymptotically to its final value.
Applying Kirchhoff’s loop rule to this circuit, we obtain
\[\epsilon - L\dfrac{dI}{dt} - IR = 0, \label{eq1} \]
which is a first-order differential equation for \(I(t)\). Notice its similarity to the equation for a capacitor and resistor in series (see RC Circuits ). Similarly, the solution to Equation \ref{eq1} can be found by making substitutions in the equations relating the capacitor to the inductor. This gives
\[ \begin{align} I(t) &= \dfrac{\epsilon}{R}(1 - e^{-Rt/L}) \\[4pt] &= \dfrac{\epsilon}{R}(1 - e^{-t/\tau_L}),\label{eq3} \end{align} \]
where
\[\tau_L = L/R \label{eq5} \]
is the inductive time constant of the circuit.
The current \(I(t)\) is plotted in Figure \(\PageIndex{2a}\). It starts at zero, and as \(t \rightarrow \infty\), \(I(t)\) approaches \(\epsilon/R\) asymptotically. The induced emf \(V_L(t)\) is directly proportional to \(dI/dt\), or the slope of the curve. Hence, while at its greatest immediately after the switches are thrown, the induced emf decreases to zero with time as the current approaches its final value of \(\epsilon/R\). The circuit then becomes equivalent to a resistor connected across a source of emf.
The energy stored in the magnetic field of an inductor is
\[U_L = \dfrac{1}{2}LI^2. \nonumber \]
Thus, as the current approaches the maximum current \(\epsilon/R\), the stored energy in the inductor increases from zero and asymptotically approaches a maximum of \(L(\epsilon/R)^2 /2\).
The time constant \(\tau_L\) tells us how rapidly the current increases to its final value. At \(t = \tau_L\), the current in the circuit is, from Equation \ref{eq3},
\[I(\tau_L) = \dfrac{\epsilon}{R}(1 - e^{-1}) = 0.63 \dfrac{\epsilon}{R}, \nonumber \]
which is \(63\%\) of the final \(\epsilon/R\). The smaller the inductive time constant \(\tau_L = L/R\), the more rapidly the current approaches \(\epsilon/R\).
We can find the time dependence of the induced voltage across the inductor in this circuit by using \(V_L(t) = -L(dI/dt)\) and Equation \ref{eq3}:
\[V_L(t) = -L\dfrac{dI}{dt} = -\epsilon e^{-t/\tau_L}. \nonumber \]
The magnitude of this function is plotted in Figure \(\PageIndex{2b}\). The greatest value of \(L(dI/dt)\) is \(\epsilon\); it occurs when \(dI/dt\) is greatest, which is immediately after \(S_1\) is closed and \(S_2\) is opened. In the approach to steady state, \(dI/dt\) decreases to zero. As a result, the voltage across the inductor also vanishes as \(t \rightarrow \infty\).
The time constant \(\tau_L\) also tells us how quickly the induced voltage decays. At \(t = \tau_L\) the magnitude of the induced voltage is
\[|V_L(\tau_L)| = \epsilon e^{-1} = 0.37 \epsilon = 0.37 V(0). \nonumber \]
The voltage across the inductor therefore drops to about \(37\%\) of its initial value after one time constant. The shorter the time constant \(\tau_L\), the more rapidly the voltage decreases.
After enough time has elapsed so that the current has essentially reached its final value, the positions of the switches in Figure \(\PageIndex{1a}\) are reversed, giving us the circuit in part (c). At \(t = 0\), the current in the circuit is \(I(0) = \epsilon/R\). With Kirchhoff’s loop rule, we obtain
\[IR + L\dfrac{dI}{dt} = 0. \nonumber \]
The solution to this equation is similar to the solution of the equation for a discharging capacitor, with similar substitutions. The current at time t is then
\[I(t) = \dfrac{\epsilon}{R}e^{-t/\tau_L}. \nonumber \]
The current starts at \(I(0) = \epsilon/R\) and decreases with time as the energy stored in the inductor is depleted (Figure \(\PageIndex{3}\)).
The time dependence of the voltage across the inductor can be determined from \(V_L = -L(dI/dt)\):
\[V_L(0) = \epsilon e^{-t/\tau_L}. \label{14.32} \]
This voltage is initially \(V_L(0) = \epsilon\), and it decays to zero like the current. The energy stored in the magnetic field of the inductor, \(LI^2/2\), also decreases exponentially with time, as it is dissipated by Joule heating in the resistance of the circuit.
Example \(\PageIndex{1}\): An RL Circuit with a Source of emf
In the circuit of Figure \(\PageIndex{1a}\), let \(\epsilon = 2.0 \, V, \, R = 4.0 \, \Omega\), and \(L = 4.0 \, H\). With \(S_1\) closed and \(S_2\) open (Figure \(\PageIndex{1b}\)), (a) what is the time constant of the circuit? (b) What are the current in the circuit and the magnitude of the induced emf across the inductor at \(t = 0,\) at \(t = 2.0 \tau_L\), and as \(t \rightarrow \infty\)?
Strategy
The time constant for an inductor and resistor in a series circuit is calculated using Equation \ref{eq5}. The current through and voltage across the inductor are calculated by the scenarios detailed from Equation \ref{eq3} and Equation \ref{14.32}.
Solution
- The inductive time constant is \[\tau_L = \dfrac{L}{R} = \dfrac{4.0 \, H}{4.0 \, \Omega} = 1.0 \, s. \nonumber \]
- The current in the circuit of Figure \(\PageIndex{1b}\) increases according to Equation \ref{eq3}: \[I(t) = \dfrac{\epsilon}{R}(1 - e^{-t/\tau_L}). \nonumber \] At \(t = 0\), \[(1 - e^{-t/\tau_L}) = (1 - 1) = 0; \, so \, I(0) = 0. \nonumber \] At \(t = 2.0 \tau_L\) and \(t \rightarrow \infty\), we have, respectively, \[I(2.0\tau_L) = \dfrac{\epsilon}{R}(1 - e^{-2.0}) = (0.50 \, A)(0.86) = 0.43 \, A \nonumber \] and \[I(\infty) = \dfrac{\epsilon}{R} = 0.50 \, A. \nonumber \] From Equation \ref{14.32}, the magnitude of the induced emf decays as \[|V_L(t)| = \epsilon e^{-t/\tau_L}. \nonumber \] At \(t = 0\), \(t = 2.0 \tau_L\), and as \(t \rightarrow \infty\), we obtain \[|V_L(0)| = \epsilon = \, V, \nonumber \] \[|V_L(2.0 \tau_L)| = (2.0 \, V) e^{-2.0} = 0.27 \, V \nonumber \] and \[|V_L(\infty)| = 0.\nonumber \]
Significance
If the time of the measurement were much larger than the time constant, we would not see the decay or growth of the voltage across the inductor or resistor. The circuit would quickly reach the asymptotic values for both of these (Figure \(\PageIndex{4}\)).
Example \(\PageIndex{1}\): An RL Circuit without a Source of emf
After the current in the RL circuit of Example \(\PageIndex{1}\) has reached its final value, the positions of the switches are reversed so that the circuit becomes the one shown in Figure \(\PageIndex{1c}\).
- How long does it take the current to drop to half its initial value?
- How long does it take before the energy stored in the inductor is reduced to \(1.0 \%\) of its maximum value?
Strategy
The current in the inductor will now decrease as the resistor dissipates this energy. Therefore, the current falls as an exponential decay. We can also use that same relationship as a substitution for the energy in an inductor formula to find how the energy decreases at different time intervals.
Solution
- With the switches reversed, the current decreases according to \[I(t) = \dfrac{\epsilon}{R}e^{-t/\tau_L} = I(0)e^{-t/\tau_L}.\nonumber \] At a time t when the current is one-half its initial value, we have \[I(t) = 0.50 I(0)\space so \, e^{-t/\tau_L} = 0.50,\nonumber \] and \[t = -[\ln(0.50)]\tau_L = 0.69 (1.0 \, s) = 0.69 \, s\nonumber \] where we have used the inductive time constant found in Example \(\PageIndex{1}\).
- The energy stored in the inductor is given by \[U_L(t) = \dfrac{1}{2}L[I(t)]^2 = \dfrac{1}{2}L\left(\dfrac{\epsilon}{R} e^{-t/\tau_L}\right)^2 = \dfrac{L\epsilon^2}{2R^2}e^{-2t/\tau_L}.\nonumber \] If the energy drops to \(1.0\%\) of its initial value at a time t , we have \[U_L(t) = (0.010)U_L(0) \, or \, \dfrac{L\epsilon^2}{2R^2} e^{-2t/\tau_L} = (0.010)\dfrac{L\epsilon^2}{2R^2}.\nonumber \] Upon canceling terms and taking the natural logarithm of both sides, we obtain \[-\dfrac{2t}{\tau_L} = \ln(0.010), \nonumber \] so \[t = -\dfrac{1}{2} \tau_L \ln(0.010).\nonumber \] Since \(\tau_L = 1.0 \, s\), the time it takes for the energy stored in the inductor to decrease to \(1.0\%\) of its initial value is \[t = -\dfrac{1}{2}(1.0 \, s)\ln(0.010) = 2.3 \, s.\nonumber \]
Significance
This calculation only works if the circuit is at maximum current in situation (b) prior to this new situation. Otherwise, we start with a lower initial current, which will decay by the same relationship.
Exercise \(\PageIndex{1}\)
Verify that RC and L/R have the dimensions of time
Exercise \(\PageIndex{2}\)
- If the current in the circuit of in Figure \(\PageIndex{1b}\) increases to \(90\%\) of its final value after 5.0 s, what is the inductive time constant?
- If \(R = 20 \, \Omega\), what is the value of the self-inductance?
- If the \(R = 20 \, \Omega\) resistor is replaced with a \(R = 100 \, \Omega\) resistor, what is the time taken for the current to reach \(90\%\) of its final value?
- Answer
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a. 2.2 s; b. 43 H; c. 1.0 s
Exercise \(\PageIndex{3}\)
For the circuit of in Figure \(\PageIndex{1b}\), show that when steady state is reached, the difference in the total energies produced by the battery and dissipated in the resistor is equal to the energy stored in the magnetic field of the coil


3.12: Review of Processing Steps
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Save as PDF
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To review, here are the steps we carried out in this chapter:
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Processed the single-participant to get an ERPset for each of our 10 participants
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I provided 3 different ways of doing this
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Examined the number of accepted and rejected trials, ERP waveforms, and data quality measures for each participant to check for problems
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EEGLAB > ERPLAB > Summarize artifact detection > Summarize ERP artifacts in a table (or type ERP.ntrials in the Matlab command window)
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EEGLAB > ERPLAB > Plot ERP > Plot ERP waveforms
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EEGLAB > ERPLAB > Data Quality options > Show Data Quality measures in a table
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Made a grand average from our 10 participants
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EEGLAB > ERPLAB > Average across ERPsets (Grand Average)
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Applied a low-pass filter to the grand average to attenuate the high-frequency noise
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EEGLAB > ERPLAB > Filter & Frequency Tools > Filters for ERP data
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Obtained N400 amplitude “scores” (mean voltage from 300-500 ms) for the related and unrelated targets in each participant’s averaged ERP waveforms
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EEGLAB > ERPLAB > ERP Measurement Tool
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Used the Viewer to see the measurements for each waveform
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Performed a simple statistical analysis with the data from a single channel and a more complex analysis with the data from multiple channels
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The N400 amplitude scores were exported into a text file and then imported into a statistical package
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ERPLAB does not perform statistical analyses—we did not want to “reinvent the wheel,” and it is difficult to anticipate every possible statistical analysis someone would want to perform
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We also compared the table of means from the statistical analyses with our grand average ERP waveforms to make sure that the analysis was performed correctly
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Created a new “cluster” channel that was an average of 9 of the original channels
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EEGLAB > ERPLAB > ERP Operations > ERP Channel operations
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Created a difference wave by subtracting one bin from another
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EEGLAB > ERPLAB > ERP Operations > ERP Bin operations


4.1: Stratification
Stratification is an intentionally vague term used to describe layering in a sedimentary rock without implying any specific scale or thickness. Layering can be obvious or subtle ... you need to look for some sort of difference in grain size, mineralogy, cements, color, texture, texture, etc.
Beds and laminae
If you want to start talking about the scale of layering, we can break it down into two broad groups: layers that are less than 1 cm thick are called laminae and layers that are more than 1 cm thick are called beds . If you need more precise terminology, a table of more specific terms is provided below.
Internal changes in grain size
Normal grading
Within some strata, it is possible that there might be a systematic change in grain size. Normal grading is when a bed shows an upward decrease in grain size. This is usually caused by a decrease in flow velocity or particles falling out of suspension.
Reverse (inverse) grading
Reverse (inverse) grading is exactly the opposite … the largest grains are at the top of the bed and the smallest are at the bottom. Reverse grading typically occurs in response to shaking or winnowing in cohesionless sediment (grainflows) which causes the smallest grains to work their way downward through gaps between the larger grains.
Massive beds
And although relatively rare, internally massive beds that lack any sort of internal stratification can form when sediment is rapidly dumped or when previously stratified sediments are reworked via bioturbation .
Bed geometry and contacts
Once you’ve identified bedding, you might find it useful to describe the overall form of the bed by thinking about whether the beds are continuous or not, whether the contacts are planar or wavy, and whether the contacts are are parallel or truncate each other. Another aspect of bedding that you can describe is the nature of contacts between beds. Specifically, we find that phrases like sharp , gradational , interbedded are very useful especially when paired with a semi-quantitative estimate of scale (ex: gradational over 5 cm).
Resources and Readings
- North American Commission on Stratigraphic Nomenclature, 2005, North American Stratigraphic Code, AAPG Bulletin, v. 89, no. 11, p. 1547-1591
- Campbell, C.V., 1967, Lamina, laminaset, bed and bedset, Sedimentology, v. 8, p. 7-26.


6.7: Finding a Representation of an Interval Order
In this section, we develop an algorithm for finding an interval representation of an interval order. In fact, this algorithm can be applied to any poset. Either it will find an interval representation or it will find a subposet isomorphic to 2+2. As a consequence, we establish the other half of Fishburn's Theorem .
When \(P=(X,P)\) is an interval order and \(n\) is a positive integer, there may be many different ways to represent \(\textbf{P}\) using intervals with integer end points in \([n]\). But there is certainly a least \(n\) for which a representation can be found, and here we see that the representation is unique. The discussion will again make use of the notation for down sets and up sets that we introduced prior to the proof of Dilworth's Theorem . As a reminder, we repeat it here. For a poset \(P=(X,P)\) and a subset \(S \subset X\), let \(D(S)=\{y \in X\): there exists some \(x \in S\) with \(y<x\) in \(P\)}. Also, let \(D[S]=D(S) \cup S\). When \(|S|=1\), say \(S=\{x\}\), we write \(D(x)\) and \(D[x]\) rather than \(D(\{x\})\) and \(D[\{x\}]\). Dually, for a subset \(S \subseteq X\), we define \(U(S)=\{y \in X\): there exists some \(x \in X\) with \(y>x\) in \(P\)}. As before, set \(U[S]=U(S) \cup S\). And when \(S=\{x\}\), we just write \(U(x)\) for \(\{y \in X:x<y\) in \(P\)}.
Let \(P=(X,P)\) be a poset. We start our procedure by finding the following subsets of the ground set: \(D=\{D(x):x \in X\}\). We then distinguish two cases. In the first case, there are distinct elements \(x\) and \(y\) for which \(D(x) \nsubseteq D(y)\) and \(D(y) \nsubseteq D(x)\). In this case, we choose an element \(z \in D(x)−D(y)\) and an element \(w \in D(y)−D(x)\). It follows that the four elements in {\(x,y,z,w\)} form a subposet of \(P\) which is isomorphic to 2+2.
Our second case is that either \(D(x) \subseteq D(y)\) or \(D(y) \subseteq D(x)\) for all \(x,y \in X\). In this case, we will show that \(\textbf{P}\) is an interval order. Now find the family: \(\mathcal{U}=\{U(x):x \in X\}\). In this case, it is easy to see that we will always have either \(U(x) \subseteq U(y)\) or \(U(y) \subseteq U(x)\) for all \(x,y \in X\).
Let \(d=|\mathcal{D}|\). In the exercises, we will provide (actually in doing your homework, you will provide) the details for backing up the following statement: \(|\mathcal{U}|=|\mathcal{D}|\), so for now we assume that this statement is valid. Label the sets in \(\mathcal{D}\) and \(\mathcal{U}\) respectively as \(D_1, D_2,…,D_d\) and \(U_1, U_2,…,U_d\) so that
\(\emptyset = D_1 \subset D_2 \subset D_3 \subset \cdot \cdot \cdot \subset D_d\) and
\(U_1 \supset U_2 \cdot \cdot \cdot \supset U_{d-2} \supset U_{d-1} \supset \cdot \cdot \cdot \supset U_d = \emptyset\).
We form an interval representation \(I\) of \(\textbf{P}\) by the following rule: For each \(x \in X\), set \(I(x)=[i,j]\), where \(D(x)=D_i\) and \(U(x)=U_j\). It is not immediately clear that this rule is legal, i.e., it might happen that applying the rule results in values of \(i\) and \(j\) for which \(j<i\). But again, as a result of the exercises, we will see that this never happens. This collection of exercises is summarized in the following theorem.
If \(\textbf{P}\) is a poset excluding 2+2, then the following statements hold.
- The number of down sets equals the number of up sets. That is, \(|\mathcal{D}|=|\mathcal{U}|\).
- For each \(x \in X\) , if \(I(x)=[i,j]\) , then \(i \leq j\) in \(\mathbb{R}\) .
- For each \(x,y \in X\) , if \(I(x)=[i,j]\) and \(I(y)=[k,l]\) , then \(x<y\) in \(P\) if and only if \(j<k\) in \(\mathbb{R}\) .
- The integer \(d\) is the least positive integer for which \(\textbf{P}\) has an interval representation using integer end points from \([d]\) . This representation is unique.
Consider the poset shown in Figure 6.31 .
Then \(d=5\) with \(D_1= \emptyset\), \(D_2=\{c\}\), \(D_3=\{c,f,g\}\), \(D_4=\{c,f,g,h\}\), and \(D_5=\{a,c,f,g,h,j\}\). Also \(U_1=\{a,b,d,e,h,i,j\}\), \(U_2=\{a,b,e,h,i,j\}\), \(U_3=\{b,e,i\}\), \(U_4=\{e\}\), and \(U_5= \emptyset\). So
\(I(a)=[3,4]\) \(I(b)=[4,5]\) \(I(c)=[1,1]\) \(I(d)=[2,5]\) \(I(e)=[5,5]\)
\(I(f)=[1,2]\) \(I(g)=[1,2]\) \(I(h)=[3,3]\) \(I(i)=[4,5]\) \(I(j)=[3,4]\)
To illustrate the situation where this process can be used to determine when a poset is not an interval order, consider again the poset shown in Figure 6.31 . Erase the line joining points \(c\) and \(j\). For the resulting poset, you will then find that \(D(j)=\{f,g\}\) and \(D(d)=\{c\}\). Therefore, the four points \(c, d, f\) and \(j\) form a copy of 2+2 in this modified poset.


3.4: Nesting
Nesting lets you combine multiple searches into a single search. It allows you to group similar concepts or keywords together within parentheses so you don’t have to perform multiple searches. Combined with Boolean operators like AND and OR, nesting is an efficient and effective way to improve your keyword search results.
Boolean order of operations
Before we jump into how nesting works, you need to know how Boolean operators function without parentheses to group them in nests. Boolean operators follow an order of operations that determines how a finding tool will interpret your search. In a Boolean search NOT takes priority, followed by AND, and then OR. To use a combination of Booleans most effectively, you’ll want to use parentheses to make the order clear. It can be helpful to think of this like order of operations in math, where using parentheses impacts the order in which an operation is performed. By using parentheses, you control which action the finding tool you are using applies first. Here are some examples:
heavy AND metal
With this search, you may be interested in learning about heavy metals as a material, perhaps for industry production, chemistry, or the health aspects of exposure to heavy metals. However, if you just search “heavy metal,” your search will retrieve a mix of information, including resources talking about the heavy metal music genre.
heavy AND metal NOT music
By adding NOT, the index will follow the Boolean order of operations by first removing any results that contain the word “music.” This should help eliminate any references to bands or songs in the heavy metal genre. Finally, the database will search for records containing all of the remaining search terms connected by AND. But what if you have a longer list of keywords to search for?
Using nests
Let’s say you want to search for information about the causes of anxiety. After brainstorming synonyms for your keyword “causes,” you come up with “reasons” and “factors.” Databases may use different terminology to talk about the same subject. Instead of performing three separate searches for anxiety with each term, you can instead use the Boolean OR to search them all at once. Without parentheses, the search “anxiety AND reasons OR causes OR factors” would find sources containing “anxiety AND reasons,” or sources containing “causes” or “factors” without necessarily containing anything about anxiety. This will bring you way too many results, many of which will be irrelevant. To fix this search to find what you actually want, use nesting.
anxiety AND (reasons OR causes OR factors)
By combining the keywords “reasons,” “causes,” and “factors,” with OR inside the parentheses, the finding tool will first search for results containing any or all of those terms. By leaving “anxiety AND” outside of the parentheses, we are telling the finding tool that, no matter which of the three other terms it finds, “anxiety” must also be present in all of our results.
Using nested keywords lets us be more efficient by searching for all of these at the same time, rather than having to perform each search separately:
anxiety AND reasons
anxiety AND causes
anxiety AND factors
Using multiple nests
In this final example, you want to find resources discussing criticism of French cinema . Similar to the example above, using nested terms with OR lets you group related concepts to control the order in which they are searched. Because there are many ways to talk about cinema, you can connect synonyms within parentheses with OR. Similarly, you know authors may use either “French” or “France” when talking about this topic, so you create another nest with these terms.
(cinema OR movies OR film) AND (french OR france) AND criticism
The reason you don’t want to put all of the terms together with Boolean ORs in the same set of parentheses is because they are not interchangeable topics — both “France” and “cinema” are integral to our search. For this reason, we have included AND between the sets of parentheses. Boolean operators and nesting let you make your keyword search as simple or as complex as you wish. Most finding tools have features built into their advanced search to help you integrate Booleans, nesting, and more into your search process.


11.12B: Natural Passive Immunity
- Outline the various ways to obtain passive immunity
Immunity is the state of protection against infectious disease conferred either through an immune response generated by immunization or previous infection, or by other non-immunological factors. There are two ways to acquire passive resistance against disease: passive natural and passive artificial. Naturally acquired passive immunity occurs during pregnancy, in which certain antibodies are passed from the maternal blood into the fetal bloodstream in the form of IgG. Antibodies are transferred from one person to another through natural means such as in prenatal and postnatal relationships between mother and child. Some antibodies can cross the placenta and enter the fetal blood. This provides some protection for the child for a short time after birth, but eventually these deteriorate and the infant must rely on its own immune system. Antibodies may also be transferred through breast milk. The transfered IgG from mother to fetus during pregnancy generally lasts 4 to 6 months after birth. The immune responses reach full strength at about age 5.
Passive immunity can also be in the form of IgA and IgG found in human colostrum and milk of babies who are nursed. In addition to the IgA and IgG, human milk also contains: oligosaccharides and mucins that adhere to bacteria and viruses to interfere with their attachment to host cells; lactoferrin to bind iron and make it unavailable to most bacteria; B 12 binding protein to deprive bacteria of needed vitamin B 12; bifidus factor that promotes the growth of Lactobacillus bifidus, normal flora in the gastrointestinal tract of infants that crowds out harmful bacteria; fibronectin that increases the antimicrobial activity of macrophages and helps repair tissue damage from infection in the gastrointestinal tract; gamma-interferon, a cytokine that enhances the activity of certain immune cells; hormones and growth factors that stimulate the baby’s gastrointestinal tract to mature faster and be less susceptible to infection; and lysozyme to break down peptidoglycan in bacterial cell walls.
Key Points
- Immunity is transferred through the placenta in the form of antibodies, mainly IgG and IgA.
- Natural passive immunity can also be transferred through breast milk.
- Natural passive immunity is short-lived after the birth of the child.
Key Terms
- IgG : immunoglobulin G is an antibody isotype.
- IgA : immunoglobulin A is an antibody isotype.
- passive immunity : the translocation of active humoral immunity from one individual to another in the form of custom-made antibodies.


7.2: Parenteral Medications and Preparing Medications from Ampules and Vials
Parenteral refers to the path by which medication comes in contact with the body. Parenteral medications enter the body by injection through the tissue and circulatory system. Injection medications are absorbed more quickly and are used with patients who are nauseated, vomiting, restricted from taking oral fluids, or unable to swallow. Parenteral medications can be effective and safe when prepared and administered correctly. However, because they are invasive and absorbed readily and quickly into the body, there are numerous risks associated with administering them (Perry et al., 2014).
There are four routes for parenteral medications (also see Figure 7.1). Each type of injection requires a specific skill set to ensure the medication is prepared properly and administered into the correct location (Perry et al., 2014). The four types of injections are:
- Subcutaneous (SC): This injection places medication/solution the loose connective tissue just under the dermis.
- Intradermal (ID): This injection places the medication into the dermis just under the epidermis.
- Intramuscular (IM): This injection places the medication into the body of a muscle.
- Intravenous (IV): This injection places the medication/solution into a vein through an existing IV line or a short venous access device (saline lock). Medications given by the intravenous route can be given as an IV bolus, as an intermittent (piggyback) medication, or in a large volume continuous infusion.
To administer parenteral medications safely, it is imperative to understand how to prevent an infection, prevent medication errors, prevent a needle-stick injury, and prevent discomfort to the patient. Tables 7.1 to 7.4 address specific practices to eliminate safety hazards to patients and health care workers.
Preventing Infection During an Injection
According to Seigel et al, (2007), research has shown that unsafe injection practices have resulted in patient exposure to infections leading to outbreaks of infectious diseases. These unnecessary exposures were the result of deficient health care practices. Injectable medications must be given in a safe manner to maintain sterility of equipment and prevent the transmission of infectious diseases between patients and health care workers. Table 7.1 summarizes how to prevent an infection during an injection.
| Table 7.1 Preventing Infection During an Injection | |||
Safety consideration:
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Principle |
Additional Information |
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| Perform hand hygiene. | Always perform hand hygiene before administration and after removing gloves. For hand hygiene with ABHR, use 1 to 2 pumps of product; this volume requires a minimum of 15 seconds for hands to dry. | ||
| Prevent needle/syringe contamination. | Keep sterile parts of the needle and syringe sterile. Avoid letting the needle touch unsterile surfaces such as the outer edges of the ampule or vial, surface of the needle cap, or counter. Always keep the needle covered with a cap when not in use, and use the scoop-cap method to avoid needle-stick injuries. Avoid touching the length of the plunger. Keep the tip of the syringe sterile by covering with a cap or needle. | ||
| Prepare patient’s skin. | Wash the patient’s skin with soap and water when it is soiled with dirt, drainage, or fecal matter/urine. Follow agency policy for skin preparation. When using an alcohol swab, use a circular motion to rub the area for 15 seconds, and then let the area dry for 30 seconds. If cleaning a site, move from the centre of the site outward in a 5 cm (2 in.) radius. | ||
| Prevent contamination of solution. | Use single-dose vials/ampules whenever possible. Do not keep multi-dose vials in patient treatment area. Discard if sterility is compromised or questionable. Do not combine and administer medications from single-dose vials or ampules for later use. Ampules should not sit open and should be used immediately, then discarded appropriately. | ||
| Use new, sterile sterile equipment with each injection. | Single use syringe and needle must be used with each patient. Always inspect packaging for intactness; inspect for dryness, rips, torn corners and expiry date. If single use equipment is not available, use syringes and needles designed for steam sterilization. | ||
| Data source: CDC, 2015; Hutin et al., 2003; Perry et al., 2014; Provincial Infectious Disease Advisory Committee, 2014; Siegel et al., 2007. |
Safe Medication Administration
Medication errors have a substantial impact on health care in Canada (Butt, 2010). When preparing and administering medication, and assessing patients after receiving medication, always follow agency policy to ensure safe practice. Review Table 7.2 for guidelines for safe medication administration.
| Table 7.2 Guidelines for Safe Medication Administration | |||
Safety consideration:
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Principle |
Additional Information |
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| Be vigilant when preparing medications. | Avoid distractions. Some agencies have a no-interruption zone (NIZ), where health care providers can prepare medications without interruptions. | ||
| Check for allergies. | Always ask patient about allergies, types of reactions, and severity of reactions. | ||
| Use two patient identifiers at all times. Always follow agency policy for patient identification. | Use at least two patient identifiers before administration AND compare against the medication administration record (MAR). | ||
| Assessment comes before medication administration. | All medications require an assessment (review of lab values, pain, respiratory or cardiac assessment, etc.) prior to medication administration to ensure the patient is receiving the correct medication for the correct reason. | ||
| Be diligent in all medication calculations. | Errors in medication calculations have contributed to dosage errors, especially when adjusting or titrating dosages. | ||
| Avoid reliance on memory; use checklists and memory aids. | Slips in memory are caused by lack of attention, fatigue, and distractions. Mistakes are often referred to as attentional behaviours, and they account for most errors in health care. If possible, follow a standard list of steps for every patient. | ||
| Communicate with your patient before and after administration. | Provide information to patient about the medication before administering it. Answer questions regarding usage, dose, and special considerations. Give the patient the opportunity to ask questions. Include family members if appropriate. | ||
| Avoid workarounds. | A workaround is a process that bypasses a procedure, policy, or problem in a system. For example, nurses may “borrow” a medication from another patient while waiting for an order to be filled by the pharmacy. These workarounds fail to follow agency policies that ensure safe medication practices. | ||
| Ensure medication has not expired. | Medication may be inactive if expired. | ||
| Always clarify an order or procedure that is unclear. | Always ask for help whenever you are uncertain or unclear about an order. Consult with the pharmacist, charge nurse, or other health care providers and be sure to resolve all questions before proceeding with medication administration. | ||
| Use available technology to administer medications. | Bar-code scanning (eMAR) has decreased errors in administration by 51%, and computerized physician orders have decreased errors by 81%. Technology has the potential to help decrease errors. Use technology when administering medications, but be aware of technology-induced errors. | ||
| Report all near misses, errors, and adverse reactions. | Reporting allows for analysis and identification of potential errors, which can lead to improvements and sharing of information for safer patient care. | ||
| Be alert to error-prone situations and high-alert medications. | High-alert medications are those that are most likely to cause significant harm, even when used as intended. The most common high-alert medications are anticoagulants, narcotics and opiates, insulins, and sedatives. The types of harm most commonly associated with these medications include hypotension, respiratory depression, delirium, bleeding, hypoglycemia, bradycardia, and lethargy. | ||
| If a patient questions or expresses concern regarding a medication, stop and do not administer it. | If a patient questions a medication, stop and explore the patient’s concerns, review the physician’s order, and, if necessary, notify the practitioner in charge of the patient. | ||
| Data source: Agency for Healthcare Research and Quality, 2014; Canadian Patient Safety Institute, 2012; Debono et al., 2013; Institute for Healthcare Improvement, 2015; National Patient Safety Agency, 2009; National Priority Partnership, 2010; Prakash, et al., 2014 |
Promoting Safety and Comfort of a Patient During an Injection
Injections can be given safely and effectively, and harm can be prevented if proper injection technique is used. Most complications related to injections are associated with intramuscular injections, but may occur with any route. Complications can occur when an incorrect site is used, or with an inappropriate depth or rate of injection (Malkin, 2008). To promote patient safety and comfort during an injection, review the guidelines in Table 7.3.
| Table 7.3 Promoting Patient Safety and Comfort During an Injection | |||
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Principle |
Additional Information |
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| Correct needle |
For injections, use a sharp, beveled needle and place bevel side up. Change the needle if liquid coats the shaft of the needle. Correct needle length allows for correct delivery of medication into the correct site and can reduce complications such as abscesses, pain, and bruising. Needle selection should be based on size of patient, gender, injection site, and amount of medication injected. Women tend to have more adipose tissue around the buttocks and deltoid fat pad, which means more than half the injections given do not reach the proper IM depths in women. Large bore needles have been found to reduce pain, swelling, and redness after an injection, as less pressure is required to depress the plunger. |
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| Proper angle of insertion and removal (see Figure 7.1) |
Inserting the needle at the proper angle (depending on the type of injection) and entering the skin smoothly and quickly can reduce pain during injection. Hold the syringe steady once the needle is in the tissue to prevent tissue damage. Withdraw the needle at the same angle used for insertion. The angle for an IM injection is 90 degrees. With all injections, the needle should be inserted all the way up to the hub. Holding the syringe like a dart prevents the medication from being injected during insertion of needle. Removing residue (medication on the tip of the needle) has been shown to reduce pain and discomfort. To remove residue from the needle, change needles after preparation and before administration. |
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| Patient position | The patient’s position may affect their perception of pain. Proper position will also facilitate proper landmarking of the site. For IM injections, for example, the ventrogluteal site has the greatest muscle thickness and is free of nerves and blood vessels, with a small layer of fat. | ||
| Relaxation technique and distraction methods | Position the patient’s limbs in a relaxed, comfortable position to reduce muscle tension. For example, lying prone may help a patient relax prior to an IM injection. If giving a deltoid IM injection, have the patient relax the arm by placing the hand in the lap. If a patient is receiving an IM injection in the vastus lateralis or ventrogluteal site, encourage the patient to gently point toes outwards to relax the muscle. Relaxation skills of the health care provider will help decrease the patient’s anxiety-heightened pain. If possible, divert the patient’s attention away from the injection procedure. | ||
| Pre-medication, if required | To decrease pain upon insertion, a vapocoolant spray, topical anesthetic, or wrapped ice may be placed on the insertion site for a minute prior to injection. For IM injections, two studies found that applying pressure to the injection site for 10 seconds before the injection reduced pain. This data supports the gate theory of pain control. | ||
| Z-track method for IM injections | Some research shows that the Z-track technique results in reduced pain and complications, and fewer injection lesions. However, other research shows that Z-track injections result in more pain and bleeding at the injection site. (See 7.4 Intramuscular Injections for more on the Z-track method.) | ||
| Administration rate | Research has found that administrating medications at 10 seconds per ml is an effective rate for IM injections. Increasing the rate to 20 seconds per ml did not show any reduction in pain. Always review drug administration rate as per pharmacy or manufacturer’s recommendations. | ||
| Gentle touch with insertion sites | Gently apply a dry sterile gauze to the site after the injection. Rotate injection sites to prevent the development of indurations and abscesses. | ||
| Aspiration with IM injections | Review the latest research regarding the utility of aspirating IM injections. There is lack of strong evidence to support the technique of aspiration with IM injections. | ||
| Data source: Ağac & Günes, 2011; Canadian Agency for Drugs and Technologies in Health, 2014; Cocoman & Murray, 2008; Greenway, 2014; Hunter, 2008; Malkin, 2008; Mitchell & Whitney, 2001; Nisbit, 2006; Ogston-Tuck, 2014a; Perry et al., 2014; Rodgers & King, 2000; Sisson, 2015; Workman, 1999 |
Preventing Needle-Stick Injuries
Health care providers can be at risk for needle-stick injuries in any health care setting. The most common places for needle-stick injuries to occur are in the operating room and patient rooms. Tasks that place the health care provider at risk include recapping needles and mishandling IV lines. Table 7.4 provides guidelines to prevent needle-stick injuries.
| Table 7.4 Recommendations for Prevention of Needle-Stick Injuries | |||
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Principle |
Additional Information |
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| Avoid recapping needles. |
Recapping needles has led to the transmission of infection. If possible, always use devices with safety features — i.e., safety shield. |
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| Dispose of the needle immediately after injection. |
Immediately dispose of used needles in a sharps disposal container (puncture-proof and leak-proof) to avoid unsafe disposal of a sharp. |
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| Reduce or eliminate all hazards related to needles. | Avoid using needles if possible. Use a needle only when performing an SC, ID, or IM injection. Use a needleless system and engineered safety devices for prevention of needle-stick injuries. | ||
| Plan disposal of sharps before injection. | Plan the safe handling and disposal of needles before beginning a procedure that requires a sharp needle. Bring sharps container close to the bedside prior to injection. Sharps containers should be at eye level and within arm’s reach. | ||
| Follow all standard policies related to prevention / treatment of injury. | Follow all agency policies regarding infection control, hand hygiene, standard and additional precautions, and blood and body fluid exposure management. | ||
| Report all injuries. | Report all needle-stick injuries and sharp-related injuries immediately. Data collected regarding the nature of injuries help guide needle-stick prevention strategies for new practices and devices. Review how to manage needle-stick injuries and follow agency policy regarding exposure to blood-borne pathogens. Policies help decrease the risk of contracting a blood-borne illness. | ||
| Participate in required training and education. | Attend training on injury-prevention strategies related to needles and safety devices as per agency policy. Participate in and evaluate the selection of safety devices, and report known needle-stick hazards to managers. | ||
| Data source: American Nurses Association, 2002; Centers for Disease Control, 2012; National Institute for Occupational Safety and Health, 1999; Perry et al., 2014; Pratt et al., 2007; Wilburn, 2004; Wilburn & Eijkemans, 2004 |
Preparing Medications from Ampules and Vials
Specific equipment, such as syringes and needles, is required to prepare and administer parenteral medications. The selection of the syringe and needle is based on the type and location of injection; amount, quality, and type of medication; and the body size of the patient. Many syringes come with needleless systems or needles with safety shields to prevent injuries (Perry et al., 2014). Aseptic technique is paramount to the preparation and administration of these medications.
Parenteral medications are supplied in sterile vials, ampules, and prefilled syringes. Ampules are glass containers in 1 ml to 10 ml sizes that hold a single dose of medication in liquid form. They are made of glass and have a scored neck to indicate where to break the ampule (see Figure 7.2). Medication is withdrawn using a syringe and a filter needle. A blunt fill needle with filter (see Figure 7.3) must be used when withdrawing medication to prevent glass particles from being drawn up into the syringe (see Figure 7.4). Never use a filter needle to inject medication (Perry et al., 2014).
A vial is a single- or multi-dose plastic container with a rubber seal top, covered by a metal or plastic cap (see Figure 7.5). A single-use vial must be discarded after one use; a multi-dose vial must be labelled with the date it was opened. Check hospital policy to see how long an open vial may be used. The vial is a closed system, and air must be injected into the vial to permit the removal of the solution (Perry et al., 2014) (see Figure 7.6).
A syringe (see Figure 7.7)is a sterile, single-use device that has a Luer lock (see Figure 7.8) or non-Luer lock tip, which influences the name of the syringe. Syringes come in various sizes from 0.5 ml to 60 ml. Syringes may come with or without a sterile needle and will have a safety shield on the needle.
Insulin is only given using an insulin syringe (see Figure 7.9). Insulin is ordered in units. It is important to use the correct syringe and needle for the specific injection. Always examine the measurement scale on the syringe to determine that you have the correct syringe (Lynn, 2011).
Needles are made of stainless steel, are sterile and disposable, and come in various lengths and sizes. The needle is made up of the hub, shaft, and bevel. The bevel is the tip of the needle that is slanted to create a slit into the skin. The hub fits onto the tip of the syringe. All three parts must remain sterile at all times. The length of the needle will vary from 1/8 in. to 3 in., depending on the injection. The gauge of a needle is the diameter of the needle. Gauges can vary from very small diameter (25 to 29 gauge) to large diameter (18 to 22 gauge). A needle will have its gauge and length marked on the outer packaging; choose the correct gauge and length for the injection ordered (Lynn, 2011) (see Figures 7.10, 7.11, and 7.12).
Critical Thinking Exercises
- What are three strategies that can be implemented to reduce distractions while preparing medication?
- What are two ways to prevent needle-stick injuries?


8: Oceans and Climate
After reading this chapter you should:
- understand the concept of the heat budget of the earth (you do not need to remember all of the percentages, just general trends)
- know the difference and relative importance of radiation, conduction and phase change in exchanging heat with the atmosphere
- understand the mechanisms and causes of the greenhouse effect and global warming
- understand how evaporation and condensation transport heat in the atmosphere and oceans
- understand how the curvature of the Earth results in differential heating of the surface
- understand the role played by albedo in radiation reaching the Earth
- understand how and why atmospheric convection cells form
- understand the reasons for and the results of the Coriolis Effect
- be able to derive the major wind patterns on Earth
- understand the relationship between climatic zones and convection cells – e.g. why are rainforests along the equator?
- understand the effects of altitude on air masses and climate
- understand how seasonal and daily cycles effect things like land and sea breezes
- understand how hurricanes form
- understand the potential impacts of climate change
The ultimate source of energy driving the motion of the atmosphere and the ocean is radiant energy from the sun, which falls on different parts of the Earth in differing amounts. The oceans are the recipient of most of this solar energy, and they are therefore a major factor in regulating Earth’s climate. Remember that compared to land temperatures, ocean temperatures do not undergo large swings from day to night or seasonally. This is due to a number of factors;
- Water has a very high heat capacity, so it can absorb a large amount of heat without much of an increase in temperature. Water can also release large amounts of heat back to the atmosphere without its temperature declining as much as land temperatures would.
- On land, the solar energy only hits the surface, which can heat up dramatically, but the heat does not penetrate very far below the surface. In water, light penetrates for a few hundred meters, so the heat is distributed through a greater area, and water does not heat up as quickly as land.
- Mixing of water in the top few hundred meters also distributes heat. Mixing does not happen on land.
Because of water’s ability to regulate heat exchange and climate, areas near the oceans usually have a much milder climate than regions in the center of the continents. Furthermore, areas in the Southern Hemisphere have a much more moderate climate than regions of similar latitude in the Northern Hemisphere, because a larger proportion of the Southern Hemisphere is covered by oceans.
In this chapter we will examine the ways that the oceans and atmosphere interact with solar radiation to influence wind and atmospheric circulation, local weather phenomena, and global climatic zones.
Thumbnail: The movement of upper-air water vapor over the Eastern Pacific is shown using GOES satellite air temperature data. High, cold clouds are white. High, cold, clear air (around -28 F) is blue. Lower, warmer, dry air (around -10 F) is magenta (where clear, dry air penetrates lower in the atmosphere). (Public Domain; NASA/NOAA GOES Project Dennis Chesters )


9.13: Electromagnetic Induction (Answers)
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Check Your Understanding
13.1. 1.1 T/s
13.2. To the observer shown, the current flows clockwise as the magnet approaches, decreases to zero when the magnet is centered in the plane of the coil, and then flows counterclockwise as the magnet leaves the coil.
13.4. \(\displaystyle ε=Bl^2ω/2\), with O at a higher potential than S
13.5. 1.5 V
13.6. a. yes;
b. Yes; however there is a lack of symmetry between the electric field and coil, making \(\displaystyle ∮\vec{E}⋅d\vec{l}\) a more complicated relationship that can’t be simplified as shown in the example.
13.7. \(\displaystyle 3.4×10^{−3}V/m\)
13.8. \(\displaystyle P_1,P)2,P_4\)
13.9. a. \(\displaystyle 3.1×10^{−6}V;\)
b. \(\displaystyle 2.0×10^{−7}V/m\)
Conceptual Questions
1. The emf depends on the rate of change of the magnetic field.
3. Both have the same induced electric fields; however, the copper ring has a much higher induced emf because it conducts electricity better than the wooden ring.
5. a. no; b. yes
7. As long as the magnetic flux is changing from positive to negative or negative to positive, there could be an induced emf.
9. Position the loop so that the field lines run perpendicular to the area vector or parallel to the surface.
11. a. CW as viewed from the circuit; b. CCW as viewed from the circuit
13. As the loop enters, the induced emf creates a CCW current while as the loop leaves the induced emf creates a CW current. While the loop is fully inside the magnetic field, there is no flux change and therefore no induced current.
15. a. CCW viewed from the magnet;
b. CW viewed from the magnet;
c. CW viewed from the magnet;
d. CCW viewed from the magnet;
e. CW viewed from the magnet;
f. no current
17. Positive charges on the wings would be to the west, or to the left of the pilot while negative charges would be pulled east or to the right of the pilot. Thus, the left hand tips of the wings would be positive and the right hand tips would be negative.
19. The work is greater than the kinetic energy because it takes energy to counteract the induced emf.
21. The conducting sheet is shielded from the changing magnetic fields by creating an induced emf. This induced emf creates an induced magnetic field that opposes any changes in magnetic fields from the field underneath. Therefore, there is no net magnetic field in the region above this sheet. If the field were due to a static magnetic field, no induced emf will be created since you need a changing magnetic flux to induce an emf. Therefore, this static magnetic field will not be shielded.
23. a. zero induced current, zero force; b. clockwise induced current, force is to the left; c. zero induced current, zero force; d. counterclockwise induced current, force is to the left; e. zero induced current, zero force.
Problems
25. a. 3.8 V;
b. 2.2 V;
c. 0 V
27. \(\displaystyle B=1.5t,0≤t<2.0ms,B=3.0mT,2.0ms≤t≤5.0ms,\)
\(\displaystyle B=−3.0t+18mT,5.0ms<t≤6.0ms,\)
\(\displaystyle ε=−\frac{dΦm}{dt}=−\frac{d(BA)}{dt}=−A\frac{dB}{dt},\)
\(\displaystyle ε=−π(0.100m)^2(1.5T/s)\)
\(\displaystyle =−47mV(0≤t<2.0ms),\)
\(\displaystyle ε=π(0.100m)^2(0)=0(2.0ms≤t≤5.0ms),\)
\(\displaystyle ε=−π(0.100m)^2(−3.0T/s)=94mV(5.0ms<t<6.0ms).\)
29. Each answer is 20 times the previously given answers.
31. \(\displaystyle \hat{n}=\hat{k},dΦ_m=Cysin(ωt)dxdy,\)
\(\displaystyle Φ_m=\frac{Cab^2sin(ωt)}{2}\),
\(\displaystyle ε=−\frac{Cab^2ωcos(ωt)}{2}\).
33. a. \(\displaystyle 7.8×10^{−3}V\);
b. CCW from the same view as the magnetic field
35. a. 150 A downward through the resistor;
b. 232 A upward through the resistor;
c. 0.093 A downward through the resistor
37. 0.0015 V
39. \(\displaystyle \varepsilon=-B_{0} l d \omega \cos (\Omega t) \mathrm{ld}+B_{0} \sin (\Omega t) \mathrm{lv}\)
41. \(\displaystyle ε=Blvcosθ\)
43. a. \(\displaystyle 2×10^{−19}T\);
b. 1.25 V/m;
c. 0.3125 V;
d. 16 m/s
45. 0.018 A, CW as seen in the diagram
47. 9.375 V/m
49. Inside, \(\displaystyle B=μ_0nI,∮\vec{E}⋅d\vec{l}=(πr^2)μ_0n\frac{dI}{dt},\) so, \(\displaystyle E=\frac{μ_0nr}{2}⋅\frac{dI}{dt}\) (inside). Outside, \(\displaystyle E(2πr)=πR^2μ_0n\frac{dI}{dt}\), so, \(\displaystyle E=\frac{μ_0nR^2}{2r⋅\frac{dI}{dt}}\) (outside)
51. a. \(\displaystyle E_{inside}=\frac{r}{2}\frac{dB}{dt}, E_{outside}=\frac{r^2}{2R}\frac{dB}{dt}\);
b. \(\displaystyle W=4.19×10^{−23}J\);
c. 0 J;
d. \(\displaystyle F_{mag}=4×10^{−13}N, F_{elec}=2.7×10^{−22}N\)
53. \(\displaystyle 7.1μA\)
55. Three turns with an area of \(\displaystyle 1 m^2\)
57. a. \(\displaystyle ω=120πrad/s,ε=850sin120πt V\);
b. \(\displaystyle P=720sin^2120πtW;\);
c. \(\displaystyle P=360sin^2120πtW\)
59. a. B is proportional to Q ;
b. If the coin turns easily, the magnetic field is perpendicular. If the coin is at an equilibrium position, it is parallel.
61. a. 1.33 A;
b. 0.50 A;
c. 60 W;
d. 22.5 W;
e. 2.5W
Additional Problems
63. \(\displaystyle 4.8×10^{6}\) A/s
65. \(\displaystyle 2.83×10^{−4}A\), the direction as follows for increasing magnetic field:
67. 0.375 V
69. a. 0.94 V;
b. 0.70 N;
c. 3.52 J/s;
d. 3.52 W
71. \(\displaystyle (\frac{dB}{dt})\frac{A}{2πr}\)
73. a. \(\displaystyle R_f+R_a=\frac{120V}{2.0A}=60Ω\), so \(\displaystyle R_f=50Ω\);
b. \(\displaystyle I=\frac{ε_s−ε_i}{R_f+R_a},⇒ε_i=90V\);
c. \(\displaystyle ε_i=60V\)
Challenge Problems
75. N is a maximum number of turns allowed.
77. 5.3 V
79. \(\displaystyle Φ=\frac{μ_0I_0a}{2π}ln(1+\frac{b}{x})\), so \(\displaystyle I=\frac{μ_0I_0abv}{2πRx(x+b)}ε=\frac{μ_0I_0abv}{2πx(x+b)}\)
81. a. \(\displaystyle 1.01×10^{−6}V\);
b. \(\displaystyle 1.37×10^{−7}V\);
c. 0 V
83. a. \(\displaystyle v=\frac{mgRsinθ}{B^2l^2cos^2θ}\);
b. \(\displaystyle mgvsinθ\);
c. \(\displaystyle mcΔT\);
d. current would reverse direction but bar would still slide at the same speed
85. a. \(\displaystyle B=μ_0nI,Φ_m=BA=μ_0nIA\),
\(\displaystyle ε=9.9×10^{−4}V\);
b. \(\displaystyle 9.9×10^{−4}V\);
c. \(\displaystyle ∮\vec{E}⋅d\vec{l}=ε,⇒E=1.6×10^{−3}V/m\)
d. \(\displaystyle 9.9×10^{−4}V\);
e. no, because there is no cylindrical symmetry
87. a. \(\displaystyle 1.92×10^6rad/s=1.83×10^7rpm\);
b. This angular velocity is unreasonably high, higher than can be obtained for any mechanical system.
c. The assumption that a voltage as great as 12.0 kV could be obtained is unreasonable.
89. \(\displaystyle \frac{2μ_0πa^2I_0nω}{R}\)
91. \(\displaystyle \frac{mRv_o}{B^2D^2}\)


18.4: Industrial IR
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No academic development has had a greater impact on IR’s recent history than the rise of think tanks. This is a big claim, to be sure, so let me illustrate it with a story from my own country. In the post-apartheid years, the emergence of a think tank called the Institute for Security Studies (ISS) shifted the hopes of the immediate post-apartheid years from the high idealism of the Nelson Mandela presidency towards a security-centred society. This, in a country where some ten million children – over 54 per cent – live in poverty. Elsewhere, as others have shown (see Ahmad 2014), think tanks have and continue to play a critical role in making the case for war against Islam in the United States, and in pushing the UK’s Blair government to enthusiastically support the invasion of Iraq in 2003 (on this, see Abelson 2014).
Rather than viewing think tankers as neutral and disinterested parties in the making of IR, we must take them seriously. As the German-born critical thinker, Hannah Arendt (1970, 6), put it in her book, On Violence :
There are … few things that are more frightening than the steadily increasing prestige of scientifically minded brain trusters in the councils of government during the last decades. The trouble is not that they are cold-blooded enough to ‘think the unthinkable,’ but that they do not think.
In the economic-speak of our times, think-tankers are ‘norm-entrepreneurs’; protagonists for one or another position on policy and its outcomes who, while claiming to provide objective analysis, are in fact complicit in pursuing particular agendas: political, economic and social.
Invariably, think-tankers are well schooled in the repertoire of IR; they have mastered its vocabulary and are familiar with its disciplinary traditions. Using this, think-tankers are encouraged to promote the current policy fashion by drawing uncritically on the prevailing meta-narrative. During the Cold War, for instance, think tanks in the West promoted the ‘threat’ posed by the Soviet Union (and its allies) in much of their work, which was also embedded within different shades of realist thinking.
Early in my own pilgrimage I worked for one such think tank: the South African Institute of International Affairs (SAIIA) which, nowadays, calls itself the country’s ‘premier research institute on international issues’. It was never branded as such when I worked there – perhaps that was because I was one of only two academic professionals on the staff. The other professional was John Barratt, my boss, who was a former South African diplomat. He had not studied IR, but read modern history at Oxford after taking a first degree – also in history – in South Africa. The watchwords for our work were ‘facts’ and ‘objectivity’ – to seek ‘truth’ in the way that practitioners in the natural sciences do. In this view of scholarship, knowledge was neutral and the role of SAIIA was to present as many opinions as possible in international affairs so that the public could make up their own minds. This was in the ‘nonpolitical’ spirit of London’s Chatham House on which the SAIIA was modelled.
Sustaining this position in the South Africa of the 1970s was bizarre. The apartheid government had cracked down on internal dissent with the result that censorship was pervasive, even in universities. There was, for example, no access to the vigorous debates on the liberation of South Africa that were taking place amongst exiled groups. More seriously, the country’s black community had absolutely no voice in the management and the affairs of the SAIIA: they did serve the tea, however. In the 1970s I often thought that the good and the great who gathered in the SAIIA classical-styled headquarters were of the view that those on the other side of apartheid’s cruel divide had no imaginary, or, indeed, experience, of the international.
John Barratt was often as frustrated by this state of affairs as was I, and we made several efforts – mostly unsuccessful – to cross the divide. What the corporate sponsors of the SAIIA would have made of these efforts is unknown. What I do know is that on many occasions I faced the raised eyebrows of the white liberals – and the not so liberal – who gathered, say, to deliberate on whether South Africa’s outreach to independent black states was compatible with the policy of apartheid, or the unquestioning fealty of the white state towards the West in the face of sanctions (Vale 1989).
We need to pause here and return to Hannah Arendt’s concerns: who stands to benefit from the work of think tanks? In the main, the funding is linked to the business sector. The assumption is that the work of think tanks – publications, public commentary, conferencing – reflects the interests of their sponsors and the status quo. Certainly, the conservative inclination of the SAIIA, when I worked there, was a reflection of the interests of South African business in the 1970s, as successive waves of critical scholars, including myself, have been keen to point out. This personal experience confirms four things. First, access to the discipline – certainly in South Africa, but elsewhere too – was a closed shop. IR was an elitist pursuit. Second, the conversations were limited by particular vocabularies. Certainly, they were not critical in the sense of asking deep questions and, in the press of the everyday, reflecting on what we were doing. Third, a particular meta-narrative – the Cold War – framed all the analysis. But mostly, and fourth, think tanks are what sociologists have called ‘total institutions’ – institutions with tight regimens, tight supervision and rules that ‘routine’ professional behaviour. These observations were confirmed when, a few years later, I spent some time as a research associate in a more cosmopolitan think tank community at the International Institute for Strategic Studies (IISS) in London.
As the Cold War ended, the meta-narrative of IR shifted. Today, the almost pre-packaged understanding of the ‘advantages’ of liberal reform – often simply a code for economic austerity – is stock-in-trade for contemporary think tanks. While neoliberal economics as an instrument of social engineering, both domestically and internationally, has increasingly hovered over the discipline, security and geopolitics remain the staple diet of the policy end of IR. In fact, threading these together is not new. The most famous example (yet notoriously overlooked in IR circles) is the Nixon administration’s intervention in Chile in September 1973. This coup against the democratically elected government occurred almost at the mid-point of the United States’ two-decades-long direct involvement in this country. Driven by Cold War anti-communism, the United States was determined to keep the Marxist-inclined government of Salvador Allende in check. The successful right-wing military coup was a precursor to a policy of social control, which gathered force from 1975 onwards, and was based on neoliberal economic policies. But in its more recent incarnation, under the utopian guise of globalisation, there is a sense that a ‘neo-liberal corporate takeover … has asserted America’s centrality in the world’ (Buell 2000, 310).
Three further points on think tanks need to be aired. First, as the discipline has become a popular academic subject, more and more IR graduates have entered the work place, and think tanks are significant places of employment. Indeed, it is possible to talk about IR as an academic ‘industry’ grounded in think tanks. This is linked to the second of my points, that there exists a triangular relationship between think tank, sponsors and the press or social media. Finally, the interaction of people trained in the same grammar and vocabulary often produces groupthink and a closed insider terminology. It becomes impossible to see beyond closed and often self-selecting groups – called ‘experts’ – who are pre-destined, almost, to repeat the same ideas to each other. Can any of these practices be conducive to sound policy outcomes? This is where the ‘critical turn’ in IR, which began in the early 1980s and spread in the course of the decade to several of its sub-fields, is especially important for understanding the future of IR and the world it makes. The arrival of critical theories opened up a space to question legitimately the theory and practice of an inner sanctum in the discipline. It certainly enabled me to be self-reflexive of my own thinking and to ask searching questions about the theory and practice of security in southern Africa (Vale 2003).
As in every discipline, and in every facet of life and knowing, sources of certainty have to be questioned continuously and critical perspectives have freed the space for doing so in IR. The constant challenge in our professional lives – especially in IR – is to negotiate the space between understanding what questions are intellectually interesting and which will truly make the world a better place.


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1: On Knowledge and Wanting to Know
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1.1: Can We Learn?
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Socrates has been challenging Meno to provide a definition of Virtue. Meno has been unable to provide a whole or complete definition of virtue without breaking the definition into parts or merely providing a good example of virtue. Socrates and Meno are now discussing whether or not it is possible for anybody to learn what virtue is. Their conversation applies well beyond the scope of whether or not it is possible to learn about virtue, but whether or not it is possible to learn something at all
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1.2: Why, How, and When Should We Learn?
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The following section includes comments from three of Aristotle’s books. The sections are ordered from the most abstract to the most concrete. 1) Why do men desire to know? 2) How do we know that we know? 3) What obligations do societies have to educate?
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2.3: What is the Appropriate Use of Curiosity
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In this section, you will find two passages. The first is from Augustine's Confessions. He frames his version of what it means to be curious. In the second passage, you will find a passage from Aquinas' Commentary on the Metaphysics of Aristotle. In that passage, he lays out his competing vision of what it means to be curious.