Physics section test (6)

MCAT Section Tests
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PHYSICAL SCIENCES TEST 3 EXPLANATIONS
Passage I (Questions 1–5)
1.
The correct answer to question 1 is C. This question asks you to determine the percentage of protein in a
sample of meat, based on a calculation of the amount of nitrogen in the sample. Since the passage states that the
percentage of protein in a sample of meat is 6.25 times the percentage of nitrogen, you will have to include 6.25 in
your calculations. Therefore you can eliminate choices A and B right off the bat because they don't include this factor.
The stoichiometry involved in solving this question is simpler than it may appear at first. Each atom of nitrogen in the
sample will be converted into an ammonium ion by the treatment with hot concentrated sulfuric acid. Therefore, each
mole of ammonia produced by the reaction with NaOH will be equivalent to one mole of nitrogen contained in the
sample. In Reaction 2, the one with boric acid, a mole of borate ion is produced for every mole of ammonia. When a
borate ion, a fairly strong base, is titrated with the standardized HCl, the moles of HCl required to neutralize the base
are equivalent to the moles of nitrogen in the sample. Now to find that amount, you multiply the molarity of the HCl,
which is 0.01, by its volume, 0.0055 liters. This gives you the amount of HCl in moles, which is equivalent to the
amount of nitrogen in moles in the sample. You now have to convert the amount of nitrogen from moles to grams,
since the sample is 0.1 grams. To do this, you multiply by 14, the molecular weight of a mole of nitrogen atoms.
When you multiply this amount by 100 and divide by the weight of the sample, 0.1 grams, you have the percentage of
nitrogen in the original sample. By multiplying this amount by 6.25, you obtain the percentage of protein in the
sample and thus the answer is choice C.
2.
For question 2, the correct answer is D. To answer question 2, you need to be familiar with the BrønstedLowry acid-base theory, which states that an acid is a proton donor and a base is a proton acceptor. A Brønsted-Lowry
conjugate acid contains the same atoms as its conjugate base plus one additional proton. The conjugate acid is
converted to the conjugate base by giving up that proton.
With this information, finding the answer to this question should be pretty easy. The conjugate acid of NaOH
would be NaOH2+, but no such molecule exists. However, by remembering that NaOH in solution dissociates into its
component ions, then you can realize that the conjugate acid of NaOH is actually the conjugate acid of the hydroxide
ion, that is H2O; and that the sodium ion is separate. Likewise, the conjugate base of boric acid is found by removing
a proton. This gives you the borate ion and thus the correct answer is choice D.
3.
For question 3, the correct answer is A. In this question, you are asked to decide which acid-base indicator

would be best for determining the endpoint of the titration described in the passage. In an acid-base titration, we
normally assume that when all the base has been titrated the solution will be neutral. Therefore, you might jump to the
conclusion that choice D, phenol red, must be the correct answer. But in this case you would be wrong. This question
is a reminder of how necessary it is for you to pay attention to details in the passage. Because the last paragraph states
that the borate ion is contained in an acidic solution; thus the pH is already below 7. Adding HCl will only reduce the
pH further, so you wouldn't get any color change by using phenol red. Instead, you need to choose an acid-based
indicator with an acidic transition interval. Choice A, bromocresol green, is therefore correct. All other choices have
transition intervals in the neutral or basic range.
4.
The correct answer to question 4 is choice B. The passage tells you that heterocyclic compounds, which are
ring structures consisting of atoms of more than one kind, resist digestion by sulfuric acid. That means that the
compound that is least likely to need the addition of potassium sulfate is the compound that is not heterocyclic.
Pyridine, the example in the passage, is a six-membered aromatic ring made up of five carbon atoms and one nitrogen
atom. Choice A, a guanine base, is heterocyclic. Guanine is one of the bases found in DNA and RNA. It is based on
the purine ring, which is a double cyclic compound made up of five carbons and four nitrogens. So this one is wrong.
Choice B, a cyclic alkene, is a hydrocarbon and are certainly not heterocyclic; choice B is the correct response. Choice
C, a furan compound, is wrong because furans are closed ring structures composed of four carbon atoms and one
oxygen atom: a heterocyclic compound. Choice D, a pyrrole derivative, is a five-membered ring with four carbons and
one nitrogen atom: another heterocyclic compound.
5.
For question 5 the correct answer is A. Answering question 5 is simply a matter of being familiar with the
terminology. Choice A, a polyprotic acid, is an acid containing more than one hydrogen ion. That is certainly true of
boric acid. Remember the meaning of ''polyprotic'' by remembering that ''poly'' means many, and ''protic'' relates to
protons. Since borate is not a hydrocarbon, you can eliminate choice B. Choice C is incorrect because the conjugate

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Kaplan MCAT Physical Sciences Test 3 Explanations
base of H2BO3- would contain one less proton, not one more as boric acid does. I.e. the conjugate base of H2BO3would be HBO32-. Boric acid is in fact, the conjugate acid of H2BO3-. Choice D is incorrect, even though reducing

agents sometimes do donate protons, because Reaction II is not a redox reaction. There is no change in the oxidation
state of the nitrogen; it simply gains a proton. Thus the correct answer is choice A.
Passage II (Questions 6–10)
This passage discusses the energy content of food and how it is measured. The basic concepts covered in this
passage fall under the heading of thermochemistry. We start with an introductory paragraph about how you can
measure the amount of energy a particular food gives to the body by measuring the energy released when the food is
burned. The next two paragraphs explain how the calorimeter works.
The important thing when reading the passage was to understand how the calorimeter works. The middle
paragraph was the essential part. But the description of the bomb calorimeter should sound familiar to you even
without analyzing that middle paragraph -- after all, just such an apparatus was described in chapter 6 of the General
Chemistry Review Notes. You could look it up. But enough introduction. Let's get to the questions.
6.
The correct answer is choice D. In the third paragraph of the passage, we are told that to calibrate a
calorimeter means determining its heat capacity. The question then translates as: “What information do we need to
calculate the heat capacity?” The heat capacity of an object is the amount of energy needed to raise its temperature by
1 °C or 1 K. This should be contrasted with the specific heat which is the amount of energy needed to raise 1 kg or 1 g
(depends on the unit in which it is reported, either way the idea is still the same) of the substance by 1 °C or 1 K: the
specific heat does not depend on the amount of stuff we have, whereas the heat capacity does. (The concept of the
specific heat is not particularly helpful for the calorimeter since it is presumably made up of different components
from different materials and also because we are not going to be changing the “amount of calorimeter”: we are
dealing with one calorimeter, not 1 kg versus 2 kg of calorimeters.)
The heat capacity of the calorimeter, in short, tells us how responsive its temperature is to heat input. The
two quantities that would allow one to calculate its value, then, would be the amount of heat supplied, Q, and the
corresponding temperature change of the calorimeter, ? T. The heat capacity is equal to Q/? T. None of the answer
choices corresponds to this particular pair of quantities, so we need to look for equivalents. In particular, we need to
find out what other quantities would give us the amount of heat supplied. In the question, it is stated that the heat is
supplied by placing a heater in the calorimeter. A heater, like most other electrical appliances, consumes electrical
power. Power is energy consumed or delivered per unit time, and so knowing the power of the heater and the time it
operated would enable us to calculate the energy delivered, which is the heat supplied to the system.
7.

The correct answer to this question is choice B. Question 7 tests your understanding of heat and energy. First
we must figure out what thermally isolated means. Since we use a bomb calorimeter to measure the energy content of
samples, all the energy released in the form of heat by the sample must stay in the bomb calorimeter system. So
thermally isolated must mean that none of the heat leaves the system. Now let's look at the answer choices. Choice A
states that all the heat released by the sample must be absorbed by the water. If none of the heat leaves the system, it
will have to be absorbed by the components that make up the system. They are the bomb calorimeter and the water. So
some heat is absorbed by the water, but some heat will also be absorbed by the bomb. So answer choice A is
incomplete and therefore incorrect. Answer choice B states that all the heat released by the sample will be absorbed by
the bomb and the water. This is just what we mentioned and is the correct choice. The container which holds the bomb
and the water must be thermally isolated so that all the heat released by the sample will be absorbed by the water and
the bomb. If any heat leaked out into the air, we would not get an accurate measure of the energy released by the
sample. So choice B is correct.
Now let's look at the other answer choices to make sure we are not missing anything. Choice C states that
the system must be thermally isolated so that it is always at thermal equilibrium. Well if a system is in thermal
equilibrium all the components of the system are at the same temperature at all times. When the sample in the bomb
has just been ignited, the temperature of the inside of the bomb will be different than that of the outside of the bomb
and of the water. So, clearly, the calorimeter system is not always in thermal equilibrium. So answer choice C must be
incorrect. Choice D states that the system is thermally isolated so that it doesn't conduct electricity. As we stated
before a thermally isolated system doesn't conduct heat. The term thermally isolated tells us nothing about the
electrical conductivity of the system. Therefore choice D is also incorrect.

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Kaplan MCAT Physical Sciences Test 3 Explanations

8.
The correct answer is choice B. In order to arrive at the correct answer for this question it is important to not
be distracted by impressive-sounding answers that actually either do not make sense (choice A) or are not really
relevant (choice C). One must instead focus on the procedure with which the energy content is calculated. The heat

released upon combustion is transferred to the bomb and the water. This causes a temperature rise in the system. The
higher the temperature rise, the more heat that is released. If heat is lost to the surroundings because of inadequate
insulation, the temperature rise would not be as high and thus one would underestimate the caloric content of the
food.
Choice A is incorrect because enthalpy is a state function and thus the enthalpy released upon combustion
does not depend on the conditions of reaction. The enthalpy change is still the same for the combustion reaction
regardless of whether it is carried out under adiabatic conditions or not. Choice C is incorrect because the combustion
reaction is carried out to completion. We are not maintaining a dynamic equilibrium between reactants and products,
and so Le Châtelier’s principle does not apply.
9.
The correct answer is choice C. This question asks us to find the heat released when 2-methylnaphthalene is
ignited. Let q denote heat, m denote mass, c denote specific heat, and ∆T denote the change in temperature.
Furthermore, let's denote the sample or reactant with a subscript r, the bomb with a subscript b, and the water with a
subscript w.
Since the calorimeter is a closed system, no heat leaves the system, and we use the equations: qr = qw + qb,
and q = m c ∆T. Let's find qw, the heat absorbed by the water. We need the mass, the specific heat, and the change in
temperature, but we are told all that: the mass is 2 kilograms, the change in temperature is 2 °C and the specific heat
of water is 4190 J/kg•K which is the same as 4190 J/kg•°C from the passage. Therefore, qw = (2 ∞ 4190 ∞ 2) J.
Now we must do the same thing for the bomb. The heat of the bomb is qb = mb cb ∆T. We are given in the
question stem that the heat capacity (i.e. mbcb) equals 1620 J/°C. Since the bomb and the water are in thermal
equilibrium, if the temperature of the water changes by 2 degrees, the temperature of the bomb must also change by 2
degrees. Therefore, ∆T = 2 °C. Now we can solve for qb. It equals 1620 ∞ 2 J.
Now to find the heat produced by the combustion, qr, we add the heat absorbed by the bomb and water. So qb
= (2 ∞ 4190 ∞ 2 + 1620 ∞ 2) J = (1620 + 2 ∞ 4190) ∞ 2 J, where we have factored out the 2 that corresponds to the
temperature change. The quantity in parentheses is the heat capacity of the (bomb+water) system.
Choice B is what one might obtain if one forgot to take into account that temperature intervals are the same
in the Celsius and Kelvin system: a rise of 2 °C is the same as a 2K rise. Choice D is incorrect because if one is given
the heat capacity, one does not need to know the mass of the calorimeter separately.
10.
The correct answer is A, increases. This question asks how the entropy changes in the calorimeter system

after a sample has been burned. From the second law of thermodynamics, you should know that the entropy of an
isolated system can never decrease. Entropy remains the same for reversible processes and increases for irreversible
process. What type of process do we have here? Reversible process are ones that proceed very slowly, and that can be
stopped or reversed by making very small changes in the surroundings. Combustion is an irreversible process since the
sample is not going to reabsorb the energy it released by combustion and regain its original state before the
combustion by making very small changes in the surroundings. Furthermore, the calorimeter is an isolated system
because it exchanges neither matter nor energy with the surroundings (it is sealed and insulated from heat exchange).
The entropy must therefore increase.
Passage III (Questions 11–16)
Passage III is rather long and there's a lot to keep track of. First you have to absorb the details of the titration
of potassium iodide and sodium thiosulfate; then the end of the passage gives you a practical application of this
technique—determining the percentage of copper in a sample of brass. Maybe the best way to approach this passage is
to read it once just to get the general idea, and then read it again more carefully to absorb the details. I know with a
passage like this it's tempting to just skim over it, figuring that you can go back to the different reaction when you
need them to answer a question. But that's a mistake, because there ARE details you need to know are there in the first
place! For instance, the paragraph after Reactions 3 and 4 tells you that the molarity of the thiosulfate is determined
from the amount of iodate consumed in Reaction 1. That's an easy thing to skip over, yet you need to know that to
answer the first question, Question 11.
11.
For question 11 the correct answer is C. You can find this answer by considering, one step at a time, the
stoichiometric coefficients that you need. Since the passage states that the molarity of the thiosulfate is determined

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Kaplan MCAT Physical Sciences Test 3 Explanations

based on the amount of iodate consumed in Reaction 1, first you need to figure out how many moles of iodate were
consumed. To do this, you multiply the molarity of the iodate solution by the volume. This gives you 0.01 mol/L
times 0.05 L. You can cancel out liters, and you get the product of 0.01 ∞ 0.05 as the number of moles of iodate.

Now remember you don't need to multiply that out because you're looking to set up the equation, not solve it. Next,
you need to figure out how many moles of thiosulfate are titrated for each original mole of iodate. Equation one tells
you that each mole of iodate produces three moles of iodine: since potassium iodide is added in excess, the iodate is
the limiting reagent. Equations 3 and 4 tell you that each mole of iodine reacts with two moles of thiosulfate. (You
can tell this because the two half-reactions each involve two electrons.) Multiplying 3 times 2, you get 6 moles of
thiosulfate titrated for each original mole of iodate. So the number of moles of thiosulfate titrated is 0.01 ∞ 0.05 ∞
6. Finally, you need to determine the molarity of the thiosulfate solution. To do this you divide the number of moles
of thiosulfate by the volume of thiosulfate that was titrated. This gives you equation C.
12.
For number 12 the correct answer is D. To answer this question, you have to remember that oxidation is the
loss of electrons and reduction is the gain, if you have trouble with that use the mnemonic OIL RIG. In Equations 3
and 4, iodine is being reduced and thiosulfate is being oxidized. The thiosulfate is a reducing agent since it is oxidized
while its reaction partner is reduced. You may verify that the half-reactions as written would take place since adding
the two half-cell potentials yields a positive emf, which indicates a spontaneous reaction.
13.
The answer is C. You find the standard potential of a reaction by adding the half-cell potentials of the two
half reactions in the redox reaction. In this case, those potentials are given in Reactions 3 and 4. Thiosulfate is losing
electrons and becoming oxidized while iodine is gaining electrons and becoming reduced. Since the potentials given
are the half-cell potentials, all you have to do is add the two of them together. 0.54 plus – 0.09 gives you +0.45 volts,
choice C.
In general, one needs to be careful how to add half-cell potentials to construct the emf: if both half-cell
reactions are written as reduction reactions, and the half-cell potentials given as reduction potentials, then one needs
to reverse the sign of one of them before adding. In this case, since the half-cell reactions are already written one as
reduction and one as oxidation, we can add directly.
14.
For question 14 the correct answer is B. Statement I is incorrect because this reaction is not spontaneous. A
spontaneous reaction is one in which ? G is negative. When you combine the standard potentials for copper and
iodide, you find that the reaction potential is negative. Plugging this negative potential into the equation ? G = –nFE,
gives a positive ? G; corresponding to a nonspontaneous reaction. The reaction, therefore, cannot be
thermodynamically favored under standard conditions. Now statement II on the other hand correctly explains why the

reaction proceeds. The reaction conditions here are not standard for two reasons: the excess of iodide on the left side
of the equation drives the reaction to the right, and the precipitation of copper (I) iodide on the right has the same
effect. (Recall that standard conditions imply a concentration of 1M for all solutions.) Statement III refers to the
reaction of iodide with iodate in Equation 1. That has nothing to do with this reaction, which does not include iodate.
Since only statement II is relevant, the correct answer is B.
15.
The answer is C. This question asks you what the percentage of copper is in a brass sample. You just have to
convert the moles of copper to grams or the grams of brass to moles. We're going to have to change the moles of
copper to grams since we don't know the molar mass of brass. We can look the molar mass of copper up on the
Periodic Table. It is 63.5 g/mol. If we multiply that by 0.01 moles of copper, we get 0.635 grams of copper. Now
divide 0.635 grams of copper by 1.90 grams of brass. That gives us 0.333, or about 33% copper in brass.
16.
The correct answer is D. The equilibrium constant of a reaction is exactly what it says it is, a constant. The
only thing that changes it is the temperature. Adding sodium hydroxide to Reaction 1 will affect the concentrations of
iodine, iodide, and triiodate present in Reaction 2, but it will not affect the equilibrium constant, which is a ratio and
therefore a description of the relative concentrations. The Keq describes the reactant and product concentrations
present at equilibrium, not the other way around. Choices A and B neglect to take into account that any change in the
concentration of an iodine species will cause a change in the concentrations of the other species. When Reaction 2
reaches equilibrium, the Keq will be the same. Choice C is wrong because Reactions 1 and 2 are certainly related,
that's one of the main premises of the passage.
Discrete Questions

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Kaplan MCAT Physical Sciences Test 3 Explanations

17.
The correct answer is choice C. This is a straightforward optics problem. You are given the object distance
and focal length of a lens system. The image distance is to be calculated.

To do this problem you must remember how to relate the object distance, o, image distance, i, and focal
length, f. The equation you need is: 1/o + 1/i = 1/f. Solving for 1/i, we find that 1/i = 1/f – 1/o. We are given that the
focal length of the converging lens is 100 millimeters. The fact that the lens is a converging lens implies that the focal
length is positive. Thus, f = 100 millimeters. We are also told that the object is viewed 80 millimeters from the lens,
which means that the object distance, o, is 80 millimeters. Since we are talking about a single-lens system, the object
distance is positive. Thus, o = 80 millimeters. Since both the object distance and the focal length are in the same units,
we need not convert to SI units. Our answer will just come out in millimeters.
Now, plugging o = 80 and f = 100 into the equation: 1/i = 1/f – 1/o, you find that 1/i equals – 20/8000 or –
1/400. Inverting, you find that, i = –400 millimeters. The minus sign tells us that the image is on the same side of the
lens as the original object. The distance from the lens is 400 millimeters. The question asks how far from the lens the
image will be, and we have found it to be 400 millimeters, which is answer choice C.
18.
The correct answer for question 18 is choice A. The key to question 18 is remembering the definition of
density. If you remember that you can manipulate the equation into a more useful form and then think over what else
you would need to know to answer the question. You should remember that density is mass divided by volume. If you
want to know the density of oxygen in a container, you need to know the mass of the oxygen divided by the volume of
the oxygen. This is true in spite of the fact that there may also be other gases present in the container. Since we are
required to use the formula PV = nRT, we'll rearrange this formula so that we have mass over volume on the left and
what it is equal to, in all those other terms, on the right. First, remember that P equals pressure, V equals volume, n
equals number of moles, T is temperature and R is the gas constant. How do we get mass into this equation? The
number of moles of oxygen, n is equal to the actual mass of oxygen, m, divided by the molar mass of oxygen, M.
Substituting into the PV = nRT equation we get PV = m/M ∞ RT. Next you have to rearrange the formula to solve for
density, that is, mass, m, over volume, V. The final formula is m/V = MP/RT. Now to figure out what values to plug
into the equation we need to answer two questions. First, should we use the number of moles of oxygen in the
container, or the total number of moles of gas in the container? And second, should we use the partial pressure of
oxygen in the container, or the total pressure of all the gases in the container? First let's consider the number of
moles. We are using the number of moles times the molecular weight of oxygen to equal the total mass of oxygen in
the container. If we multiplied the molecular weight of oxygen by the total number of moles of all of the gases in the
container, that would give us a value much greater than the mass of the oxygen alone. Thus we must use only the
number of moles of oxygen. If we use the total pressure of all the gases then the value on the right of our density

equation could be changed by adding or subtracting other gases, even though the amount of oxygen remained
constant. In order for the value on the right to be equal to the value on the left, which we just calculated based on the
actual amount of oxygen present, the ratio of the pressure on the right to the number of moles of oxygen on the left
must be constant. Therefore we have to use the partial pressure of oxygen together with the number of moles of
oxygen, and the answer choice is A.
19.
The correct answer is choice B. This is a tricky question! You must read carefully. Of course, it is a Doppler
effect question. You have a train traveling at a given speed blowing its train whistle, which has a given frequency.
You are asked what frequency a passenger traveling on the train hears.
A passenger who is on the train moves at the same relative speed as the train whistle. He doesn't approach or
recede from the whistle. Therefore, there is no change in the frequency he hears. A person standing on a station
platform, however, would hear a different frequency.
20.
The correct answer is A. To find the correct answer here, you have to be familiar with Raoult's law.
According to Raoult's law, the vapor pressure of a solution where the solute is miscible within the solution like here
is directly proportional to the mole fraction of the solvent in the solution. In other words, if a solution consists of 1
mole of solute in 9 moles of solvent, then the vapor pressure of the solvent will be 90% of what it would be for the
pure solvent. If you add 5 moles of solute to 5 moles of solvent, the vapor pressure of the solvent will be cut in half.
To find the change in vapor pressure for this solution, you need to determine how many moles of water were in the
original solution and how many moles of ethanol were added. You should remember that the molecular weight of
water is 18, so there are 10 moles of water. By checking the Periodic Table, you will find that 230 grams of ethanol is
equal to 5 moles. So the water, which was originally 100% of the solution, now makes up 10 moles out of a total of
15. Since the mole fraction of the water has been reduced by one third, the vapor pressure will also be reduced by one
third. Therefore the correct answer is A.

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Kaplan MCAT Physical Sciences Test 3 Explanations

21.
The correct answer is choice A. Depth and pressure are related via the formula P = ρ g h, where P is the
gauge pressure (pressure above atmospheric pressure), ρ is the density, g is the acceleration due to gravity, and h is the
depth. Since gauge pressure is directly proportional to depth, as the depth increases the pressure increases. Just to
make sure, though, we should look at the other answer choices and make sure they are false. Answer choice B must be
false. We have already found that pressure increases with depth. Answer choice C suggests that pressure depends upon
the shape of the container. Well, that is not true. The shape of the container does not affect pressure, only the density
of the liquid and the depth make a difference.
By this same argument, answer choice D which suggests that pressure depends on the total volume of the
fluid must also be false. The pressure only depends on the initial pressure, density of the fluid, and depth. Thus,
answer choice A, pressure increases with depth, is correct.
Passage IV (Questions 22–29)
This passage describes the workings of a cyclotron. As I was reading through this passage, I didn't need to
underline heavily. I did underline the fact that within the dee the electric field was zero. Of course, I noted the
equation that was nicely separated from the rest of the passage. The only other thing I noted was the sentence that
described how the frequency does not depend on the speed and that as the object traveled faster its circle got wider.
Those were the main qualitative ideas to understand.
The other significant pieces of information were contained in the last paragraph of the passage -- the
numbers. Besides underlining them, I noted the symbols next to Figure 1. We are given that the radius of the dee, R, is
0.5 meters. Therefore, I drew a line from point S to the edge of the dee and labeled it R. Next, near the oscillator, I put
a ν to stand for frequency, and a Vmax to stand for the maximum voltage. Also, to remind myself of the magnetic field
over each dee, I wrote the letter B. Now I had all the given information annotated on the diagram.
Let's get on to the questions at hand.
22.
The correct answer is choice A. Here we are asked to identify the velocity and acceleration vectors for a
particle traveling in the dee. The acceleration is due to the forces acting on the particle. What are they when the
particle is within the dee? Basically, we have magnetic fields and electric fields acting on the particle when it is in the
cyclotron. However, the dee effectively shields the electric field, and so within the dee the electric field is zero. We
are told this in the second paragraph of the passage. In that paragraph we are also told that within the dee the particle
executes uniform circular motion.

The phrase "uniform circular motion" means that the particle is traveling in a circle at a constant speed.
When a particle travels in a circle, the velocity vector is tangent to the path. So that tells us what our velocity vector
should look like. How about the acceleration? Even though the speed is constant, the velocity, which has a direction
as well as magnitude, is not constant. The direction of the velocity is always changing. Therefore, it does have some
acceleration, called the centripetal acceleration. The magnitude of this acceleration is given by the formula a = v2/r.
The direction of this centripetal acceleration is always towards the center of the circle. So, we know that the velocity
vector is tangent to the circle and the acceleration vector points to the center of the circle. Therefore, answer choice A
is the correct answer.
23.
The correct answer is choice A, out of the page. Here we are trying to find the direction of the magnetic field
with reference to Figure 1.
The first thing that should pop into your mind when a question asks you about direction in a magnetism
question is the right hand rule. Remember, in the right hand rule the thumb of your right hand points in the direction
of the vector qv, where q is the charge and v is the velocity. If q is negative, your thumb should point in the opposite
direction of the velocity. Your remaining fingers point in the direction of the magnetic field. Finally, your palm points
in the direction of the magnetic force. Usually we use this rule to find the direction of the magnetic force -- but here
we want to find the direction of the magnetic field. So we need to find the direction of the vector qv and the direction
of the magnetic force.
Let's find the direction of the vector qv. We are told that the proton circles clockwise. Therefore, when it is
nearest to the top of the page, it is traveling from left to right. Therefore, the velocity vector points to the right. Since
a proton has a positive charge, the vector q v is in the direction of the velocity v -- toward the right.
Now because the proton is traveling in uniform circular motion -- we knew that from the passage -- we
know that the magnetic field is perpendicular to the motion. That means it's either into or out of the page -- but how
do we determine which way it points? Well, we also know that there is centripetal acceleration, directed towards the

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Kaplan MCAT Physical Sciences Test 3 Explanations

center of the circle. Since this centripetal acceleration is caused by the magnetic force, the magnetic force must also
point to the center of the circle.
So put the thumb of your right hand towards the right, and your palm towards the center of the circle. With
your hand in that position, your fingers should point straight up. Thus, the magnetic field is out of the page and
answer choice A is correct.
24.
The correct answer is choice B. Here we are asked to find the energy of a proton inside one of the dees. The
energy the proton has is entirely kinetic. Kinetic energy, K, is given by the formula: K = 1/2 m v2, where m is the
mass, and v is the speed. Well, that formula accurately describes the energy, but it's not one of the answer choices. We
want the energy in terms of other quantities: q, B, and r. We have to substitute some other expression for v into the
equation 1/2 m v2.
Well, the passage won't be much help here -- the formula here doesn't involve v at all. But, what else do we
know? We have a magnetic force that acts as a centripetal force. Therefore, we can say that the magnetic force equals
the mass times the centripetal acceleration. The magnetic force is given by the equation F = q v B sin θ, where F is the
force, q is the absolute magnitude of the charge, v is the speed, B is the magnetic field strength, and θ is the angle
between the vector qv and B. In this case, since the proton travels perpendicular to the magnetic field, θ equals 90°.
Since the sin (90°) = 1, the formula for the force due to the magnetic field becomes: F = q v B. In uniform circular
motion the centripetal acceleration equals v2/r. So the centripetal force, which here is the magnetic force q v B = m a
or, mv2/r. Solving for v, we find that: v = qBr/m.
Now we can substitute this expression for v into the formula K = 1/2 m v2 to find the kinetic energy in terms
of q, m, B, and r. K = (m/2)(qBr/m)2. This means that K = mq2B2r2 /(2m2) and canceling the m's we get q2 B2 r2 /2m,
which is answer choice B.
25.
The correct answer is choice C. This question asks us to determine when the particles are accelerating and
then to articulate precisely how and why they are accelerating. Acceleration is defined as a change in velocity.
Velocity is a vector quantity that has both magnitude and direction. Acceleration can therefore occur either by a
change in the velocity’s magnitude (speed) or its direction (or both). As described in the passage, the cyclotron works
by circulating the particles through the dees. Within the dees, the particles interact with a magnetic field which causes
them to move with uniform circular motion, which is another way of saying constant speed. They are, however,
constantly changing direction and therefore are undergoing acceleration. This means that choice B can be eliminated.

Between the dees the particles are being accelerated by an electric field. They pick up speed as they go across
the potential difference. Electric fields can do work on charged particles and therefore, from the work-energy
theorem, can change their kinetic energy. Magnetic fields, on the other hand, can only exert forces perpendicular to the
direction of motion and can do no work. Kinetic energy, and hence speed, cannot change from a magnetic field itself.
This is consistent with choice C.
26.
The correct answer is choice D. This question asks us to write an equation that describes the voltage at any
given time. The equation is of the form V = Vmax sin ω t, where V is the voltage at a time t, Vmax is the maximum
voltage, and ω is the angular frequency.
Since the question stem doesn't give us any numerical information, let's go back to the last paragraph of the
passage. There it says that the maximum voltage is 100 kilovolts. So the maximum voltage is 100 ∞ 103, or 105 volts.
So our equation now is V = 105 sin ω t. Now we need to find ω. We can relate angular frequency to frequency by the
equation: ω = 2πν, where ν is the frequency. We are told in the passage that the frequency is 10 megahertz, or 10 ∞
106 = 107 Hz. That means that ω = 2π ∞ 107 radians per second. Therefore, our equation is V = 105 ∞ sin (2π ∞ 107
t), which is answer choice D.
If you chose A, you may have calculated the root mean square voltage, instead of using the actual voltage
straight-off. If you chose B, you may have thought that the standard equation used the product of the period and the
time, instead of the angular frequency and the time. And if you chose C, you probably used frequency instead of
angular frequency. Again, the correct answer is choice D.
27.
The correct answer is choice A, 1 to 1. This question required you to have read the passage carefully. In the
third paragraph of the passage, we are told that the frequency of the oscillator and the frequency of the particle remain
constant. Frequency is related to period by the following equation: ν = 1/T, where ν is the frequency, and T is the
period of the particle. From this equation it should be clear that if ν doesn't change, then T won't either. And since the
period at a radius of 0.5 meters exactly equals the period at a radius of 0.25 meters, the ratio is 1 to 1.

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Kaplan MCAT Physical Sciences Test 3 Explanations

Why doesn't the period change? Well, as the velocity of the particle increases, the radius increases, so that the
time it takes to make one round trip stays constant. That is the reason that the frequency of oscillation can be kept
constant.
28.
The correct answer is choice C. Well, this question is about a one-dimensional collision between a stationary
hydrogen ion and a proton accelerated by the cyclotron. We are asked which answer choice is true. So before we make
any needless calculations, let's examine the answer choices one by one.
Answer choice A states that the collision is completely inelastic. A completely inelastic collision is one in
which the particles stick together after the collision. This implies that the particles would have to have the same
velocity after the collision. Since a hydrogen ion is just a proton, the particles in the collision have the same mass. The
energy is kinetic energy, or mv2 /2. So the energy depends only on the mass and velocity. We already know they have
the same mass, and in an inelastic collision they would have the same velocity, so their energies would be equal. But
we know that's not the case from the information given in the passage -- so the collision can't be completely inelastic,
and answer choice A is wrong.
Answer choice B says that the collision is completely elastic. A completely elastic collision is one in which
kinetic energy is conserved. Is that the case here? We are given an initial kinetic energy of 10 MeV, and final kinetic
energies of 6.4 MeV and 0.42 MeV. Note that the target particle is initially stationary and therefore, does not have any
kinetic energy. 6.4 + 0.42 is only around 6.8 MeV, which is significantly less that 10 MeV. So kinetic energy is not
conserved, and choice B is not correct.
Now choice C looks like a lot of work, so let's look at choice D first. And choice D is easy to eliminate.
You should know that in any collision you always have conservation of momentum, so choice D is wrong. Now, if
you had eliminated choices A and B, and if you knew that choice D had to be wrong, then by elimination choice C
must be the correct answer, without doing any calculations.
However, let's confirm that choice C is correct. To check on choice C, we have to find the final speed of the
incident proton. Conservation of momentum can be used to find the final speed of the incident proton. The
momentum before the collision equals the momentum after the collision. Momentum is the product of mass and
velocity. Remembering that a hydrogen ion is simply a proton, what we have is two particles of the same mass
colliding. So the mass before is the same as the mass after, and we can just compare the velocities before and after.
Originally we have the accelerated proton traveling at 4.4 ∞ 107 meters per second; the target proton is stationary, so

its velocity is zero. After the collision the target proton is traveling at 3.5 ∞ 107 meters per second. So the accelerated
proton must be traveling at 4.4 ∞ 107 - 3.5 ∞ 107 or 0.9 ∞ 107 meters per second, which is choice C.
29.
The correct answer is choice B. This is a reasoning question. We are told that the magnetic field increases,
but the final velocity of an accelerated beam remains the same. We are asked what factor must change.
What is the effect of increasing the magnetic field B? We have previously seen that q v B = mv2/r, so that the
speed v = qBr/m. Increasing the magnetic field B also increases the speed v, so we need something that will have the
opposite effect, that is, something that will decrease v. Right off we see that if we decrease q or r or increase m, we
can balance the effect of raising B. Well we can't change the charge, q, or the mass, m, of a proton. A proton has a
specific charge and mass. However, we can decrease the radius of the dees. So right off we see that choice B is most
likely the correct answer. Now let's look over the other answer choices to make sure we aren't overlooking anything.
Choice A suggests we must decrease the oscillator frequency. Well, from the equation in the passage, we
know that q B = 2 π m ν, so the frequency ν is proportional to the magnetic field B. Therefore, if we increase the
magnetic field, we also automatically increase the frequency because we can't change either the charge or mass of the
protons. So choice A must be incorrect. Choice C says increase the maximum voltage. Well, changing the voltage
changes the acceleration given to the protons each time they go between the dees, but it won't change the final velocity
-- just how long it takes to get to that speed. The velocity at any given time is given by: v = qBr/m. The speed is
dependent only on the radius and the magnetic field, not on the voltage. So choice C is incorrect. Choice D suggests
we increase the radius of the dees. As we've seen earlier, this would not balance the effect of the magnetic field. It
would only serve to further increase the final speed of the protons. So choice D is also incorrect. Therefore, the
correct answer is choice B.

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