Physics section test (4)

MCAT Section Tests
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PHYSICAL SCIENCES TEST 2 EXPLANATIONS
Passage I (Questions 1–6)
1.
The correct answer choice is B, slightly less than 90°. We are looking for the maximum angle the
accelerometer pendulum can make with the vertical. The passage tells us that the accelerometer pendulum is made up
of a small dense body of mass M suspended from a massless rod. This mass M is the pendulum bob. There are two
forces acting on the pendulum bob. The first is the force of gravity, or weight, acting vertically downward, and the
second is the tension in the rod acting along the rod. Since there is no vertical acceleration, the sum of the forces in
the vertical direction must equal zero. The downward force of gravity, Mg, must equal the upward vertical component
of the tension, Ty which should immediately eliminate choice A, for if the rod makes an angle of 90° with the vertical
there would be no vertical component to the tension to counteract the force of gravity. The fact that tension must be
pulling the mass upward means that the rod must be below the horizontal. In other words, the angle must be less than
90°, and its maximum value must be slightly less than 90°.
2.
The correct answer choice is A. The passage states in the first paragraph that an acceleration toward the right
will cause the pendulum to swing back toward the left. This is clockwise from the vertical. Therefore, we know that
when the pendulum makes a constant angle with the vertical of 2° in the clockwise direction, the system must be
accelerating toward the right with a constant acceleration. From the note at the end of the passage, we know that the
acceleration is positive since it is toward the right. Within these two seconds, then, the velocity is increasing. This
eliminates choices B and C. After the first two seconds, the pendulum is described as swinging abruptly to the right,
making the same angle as before, except that now it is counterclockwise. This indicates that the magnitude of the
acceleration remains the same, but the sign (and hence direction) has changed: the system is now decelerating; the
velocity decreases. Choice D is incorrect because it says that the velocity remains the same after 2 seconds, which
would be true if the acceleration changes to zero abruptly, rather than becoming negative. Note that the graph in
choice C is what the acceleration versus time graph would look like, and would have been an easy mistake to make if
we didn’t read the question carefully enough.
3.
The correct answer choice is C, a equals g tan θ. This question asks us to find an equation which relates the
acceleration of the system to the angle of displacement of the bob. As pointed out in question 1 above, there are two
forces acting on the pendulum bob. The first is the force of gravity, Mg, and the second is the tension in the rod, T. To

answer the question, we first resolve the forces into their vertical and horizontal components and then apply Newton's
second law in both the horizontal and vertical directions. First let's look at the horizontal or x direction. The force of
gravity, Mg, is vertical. The only horizontal force is the horizontal component of the tension, Tx, and this must equal
the mass times the acceleration in the horizontal direction, Ma. Now look at the vertical or y direction. There is no
vertical acceleration. The forces in the vertical direction must add up to zero. The downward force of gravity, Mg,
must equal the upward vertical component of the tension, Ty. Applying basic trigonometry gives Tx = T sinθ, and Ty =
T cosθ. Therefore, T sin θ = Ma, and T cos θ = Mg. We can eliminate T between these two equations by dividing the
first over the second to get
a
sin θ
= tan θ =
g
cos θ
Therefore, a = g tan θ, and choice C is the correct answer choice.
Tsin θ

Tcosθ

θ
θ

Τ

Mg

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Kaplan MCAT Physical Sciences Test 2 Explanations

4.
The correct answer choice is B. That the accelerometer gives a constant, positive value for 4 seconds means
that the car is accelerating at a constant value during this time. Its speed is increasing and therefore each subsequent
second would see it cover more distance. The readings given, and among which we have to choose, correspond to the
total distance traveled since start, not the distance traveled per second, and so it is not enough that the readings
themselves increase; the difference between one value and the previous one has to increase as well, because this
difference is the distance traveled within one second. Only choice B conforms to this: in the first second it travels 1
m; in the second 3 m, giving a total distance traveled of 4 m. In the third second, it travels a distance of (9 – 4) m = 5
m, etc. In fact, even though it is not asked in the question, one can see that the kinetics is what one would observe if
1
1
the acceleration is 2 m/s2: assuming that the car starts from rest, the kinetics equation would be ? x = v0t + at2 =
2
2
at2. If a = 2, this would give ? x = t2, which would fit the values given in choice B nicely.
Even though the readings in choice A increase, they actually describe a scenario in which the velocity is
constant (or acceleration is zero): in each second the car travels 4 m; i.e. it has a constant velocity of 4 m/s. Choice C
basically describes a car that is stationary at least for the last three seconds. Choice D describes deceleration.
1
g
, which means that the
2_ L
frequency of oscillation is inversely proportional to L. The period is just 1/frequency, and so the period is
proportional to L. If we double the length of the pendulum, then, the period increases by a factor of 2.

5.

The correct answer choice is C. The frequency of oscillation of a pendulum is

6.

The correct answer choice is D, (7/8)Mg. Here, the pendulum is submerged in mineral oil, which we are told
in the second paragraph of the passage has a density of one eighth the density of the pendulum bob. There are now
three forces on the pendulum bob. The first is the force of gravity, Mg, in the downward or negative y direction; the
second is the tension, T, along the rod; and the third is now the buoyant force, B, which is in the upward positive y
direction and which is equal to the weight of the displaced oil. Since the system is at rest, the angle θ is zero, and the
tension, T, will be along the positive y direction. Balancing the forces gives T = Mg – B. In order to find T, we must
find B.
According to Archimedes' principle, the buoyant force B equals the weight of the displaced oil. The mass of
the displaced oil equals the density of the oil, ρo, times the volume of the bob, Vb. But we already know that ρo equals
1
one eighth the density of the bob, ρb., so the mass of the displaced oil = ρb ∗ Vb. But ρb ∗ Vb. is just M, the mass of
8
the bob. So the mass of the displaced oil equals one eighth the mass of the bob. The weight of the displaced oil equals
1
1
its mass times the acceleration of gravity, g. Therefore, the buoyant force B = Mg, and the tension T = Mg – Mg =
8
8
7
Mg. So choice D is correct.
8
Passage II (Questions 7–12)
The second passage deals primarily with the energy of activation, kinetics, and the gas laws. In addition, you
need to be able to read a potential energy diagram for a reaction.
7.
The correct answer to question 7 is B. In Figure 1, the energy differences labeled 1 and 2 are the activation
energies of the reaction (2 can be thought of as the activation energy of the reverse reaction); 3 and 4 are the potential
energies of the reactants and products; and 5 is the potential energy difference of the reaction. A catalyst is a substance
that accelerates a reaction by lowering one or more of the activation energies of the reaction; it does not, however,
change the ? H of the reaction, which is a state function. Since a catalyst can only lower the activation energies of a

reaction, only energies 1 and 2 could be affected. Their values could be decreased by lowering the energy of the
transition states (the “hilltops”). Choice B is the correct response.
8.
The correct answer to question 8 is choice C. Le Châtelier's principle states that if a system at equilibrium is
subjected to a stress, it will react in such a way so as to alleviate that stress. The stress is alleviated by changes in the
concentrations of the reactants and products until equilibrium is once again reestablished. Examining choice C,

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Kaplan MCAT Physical Sciences Test 2 Explanations

removal of product D would be responded to by an increase in the rate of the forward reaction in an attempt to replace
the product—to put it another way, the rate of the forward reaction increases to keep the equilibrium constant
unchanged. This would also increase the concentration of C, so choice C is correct. All the other choices are
incorrect. Figure 1 shows that the potential energy of the products is lower than that of the reactants; this means that
the reaction is exothermic, so an increase in temperature, choice A, would shift the equilibrium to the left. While a
lower pH, choice B, if associated with acid smog, might catalyze this reaction, it would not shift the equilibrium to
the right since a catalyst does not affect the equilibrium constant. An increase in pressure, choice D, will also not
affect the reaction, since the three moles of reactant are converted into three moles of product. All gases exert an
equal pressure per mole so neither side of this reaction is favored by a change in pressure.
9.
The answer to question 9 is D. D is wrong is because the passage states that the slower step of the reaction
mechanism follows second order kinetics. The slowest step of a reaction mechanism is usually the rate-determining
step, and a step that involves second-order kinetics must only involve two reactant molecules. Choice D involves
three reactant molecules and therefore third order kinetics.
Although it is often said that the kinetics of a reaction cannot be derived from its stoichiometry, this is true
only of the overall reaction. When a complex reaction has been broken down into a series of elementary reactions, we
can then derive the rate law from the slowest of the elementary reactions. In this case, we know that the ratedetermining step must consist of an interaction between two molecules. This could be two molecules of A, two of B,
or one each of A and B.

10.
The correct answer to question 10 is A. To answer this question correctly, you must understand the concepts
of equilibrium and Gibbs free energy, and you must be able to interpret the potential energy diagram in Figure 1. The
passage states that the reaction proceeds spontaneously to the right; therefore the equilibrium constant must be greater
than one. Choice B is incorrect because if ? G were greater than zero, the reaction would not be spontaneous. C is
incorrect because, according to the graph, the reaction is exothermic. If the reaction was endothermic, the potential
energy of the products--indicated by 4 in Figure 1--would be greater than the potential energy of the reactants-indicated by 3. Choice D is incorrect because we cannot say anything about the potential energy of A alone or of D
alone; we know only that the potential energy of 2A + B is greater than that of 2C + D.
11.
The correct answer is C. A reaction's activation energy is a measure of the potential energy difference
between the reactants and the transition state. The spontaneity of a reaction is determined by the difference in the
Gibbs free energy of the products and reactants. As has been stated numerous times in the past, whether or not a
reaction is possible is determined by thermodynamics; how fast the reaction occurs is determined by kinetics.
Certainly, if the activation energy of a reaction is very high, even though the energy of the products are lower than that
of the reactants, it will proceed very slowly. So whether or not a reaction occurs spontaneously has nothing to do with
the activation energy of the reaction--choice C is the correct response.
The other statements are all correct. The activation energy is the energy required to allow particles to react,
and a catalyst reduces the amount of activation energy required. A far as choice D is concerned, the activation energy
is not necessarily related to the change in enthalpy in any way.
12.
Choice C is the correct response for question 12. This question doesn't really relate to the information in the
passage, but this sort of thing is not unusual on the MCAT. In cases like this, you just need to pull out your own
chemistry knowledge. Here, you need to figure out which of the roman numeral choices will change when a substance
undergoes a change of phase. Roman numeral I is temperature--during a change of phase, the temperature remains
constant. After all of the material has changed phase, and heat is still being added to the system, the temperature will
increase. So I is wrong, which lets us eliminate choices B and D. Number II, density, does change when the phase
changes. One of the biggest differences between the phases of a substance is the density of the substances in the phase.
So number II seems correct which points to choice C, the only one with II in it that we haven't eliminated. Number III,
entropy, also changes with a change in phase. Freedom of movement of the individual substance particles is another
thing that defines a phase. Molecules have the most entropy in the gas phase and the least in solid phase. That makes

III correct and confirms that fact that choice C is the right answer.
Passage III (Questions 13–17)
13.
The correct answer choice is C, 2000 to 4000 hertz. This question tests how well you interpret information
presented in graph form. Let us examine the graph presented in the passage. It is a plot of sound level in decibels as a
function of frequency in hertz. The frequency is plotted on a log scale so that it can cover three orders of magnitude.
There are two curves marked on the graph. The lower one is labeled "threshold of hearing,” and represents the faintest
sound that human hearing can detect as a function of frequency. The other curve is labeled "threshold of pain,” and

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Kaplan MCAT Physical Sciences Test 2 Explanations

represents the loudest sound that a human ear can experience without pain as a function of frequency. The question
gives four frequency ranges and asks which one represents the region of highest sensitivity. Therefore, we are
concerned with the lower curve, and we would like to find the frequency range over which it is at its lowest. If you
have forgotten how to read a log scale, the vertical lines have the values 20, 40, 60, 80, 100, 200, 400, 600, 800,
1000, 2000, 4000, 6000, 8000, 10,000, and 20,000 Hz from left to right. The lowest region of the bottom curve is
between 2000 and 4000 Hz.
14.
The correct answer choice is A, 30 decibels. To answer this question correctly one needs to be able to
distinguish between intensity and intensity level. Intensity is the power per unit area carried by the sound: since power
is itself energy per unit time, intensity is the amount of energy one would absorb per unit area per unit time, e.g. the
amount of energy that a 1-m2 area would absorb from the sound in one second. The intensity level is a measure of the
intensity on a logarithmic level. In the passage we are given a formula which equates the intensity level, β, to ten times
the log of I over I0. I is the intensity of the sound, and I0 is the reference intensity. The question asks for βA minus βB.
I
I
This equals 10 ∗ log A – 10 ∗ log B. To proceed further, we have to remember that the difference of two logs is the

I0
I0
log of the quotient, i.e.:
I
I
βA – βB = 10 ∗ log A – 10 ∗ log B
I0
I0
IB
IA
= 10 ∗ (log – log )
I0
I0
IA/I0
= 10 ∗ log (
)
IB/I0
I
= 10 ∗ log A
IB
The I0’s cancel in the quotient, so all we need to know is that IA over IB equals 1000 which is given in the question
stem. The log of 1000 is 3 since 103 = 1000. Therefore, βA – βB = 10 ∗ 3 = 30 decibels. Note that the frequency of
the sound does not come into play in this question.
15.
The correct answer choice is D, 2 meters. In order to answer this question, we must realize that a point
source emitting sound waves uniformly in all directions will emit spherical wavefronts. The intensity, as stated above
in question 14, is the power per unit area. The intensity of a spherical wave at some point a distance r from the source,
therefore, is the power divided by the surface area of a sphere of radius r. We are given that the total radiated power is
4
16 π, and this power is spread out over a surface of area 4πr2. So the intensity of the spherical wave is equal to 2.

r
The sound level at the threshold of pain is 120 decibels. This can be found in the last sentence of the first paragraph in
the passage or in the graph. The reference intensity, I0, is equal to 10-12 W/m2 as given in the last sentence of the
1
4 ∞ 1012
4
passage. Using the equation for β given in the passage, we get that 120 = 10 ∗ log ( 2 ∗ -12) = 10 ∗ log (
).
r2
r 10
12
4 ∞ 10
So first we divide both sides of this equation by 10 to obtain 12 = log (
). Now taking the anti-log of both
r2
4 ∞ 1012
sides, which implies using each side as an exponent of 10, gives 1012 =
. (The right hand side is as such
r2
because 10(log x) = x.) From this we get that r2 = 4 and therefore r = 2 meters.
The correct answer choice is C, 1.7 meters. In order to answer this question, we must remember that the
v
wavelength is inversely proportional to the frequency. Specifically, λ = ; the wavelength times the frequency of a
f
wave equals its speed. The question presents a tuning fork of wavelength 1.25 meters and frequency 272 Hz.
Therefore, the speed of sound must equal 272 Hz ∗ 1.25 meters, which equals 340 m/s. (A hertz is one inverse
second.) We are then asked for the wavelength of another tuning fork with frequency equal to 200 Hz. This
wavelength is then equal to the speed of sound which we just figured to be 340 m/s divided by the new frequency,
200 Hz. So the wavelength is equal to 340 divided by 200 which is 170 divided by 100 or 1.7 meters.
16.

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Kaplan MCAT Physical Sciences Test 2 Explanations

17.
The correct answer choice is A, beats. In order to answer this question, we must remember that beats are
heard when two tones are played simultaneously at slightly different frequencies. It is this exact situation that is
described in the question. Choice B is incorrect since resonance occurs when a driving frequency such as a tone from
a tuning fork is the same as a natural frequency of some vibrating system such as a wine glass. When the frequency of
the tone becomes equal to one of the natural frequencies of the glass, the glass will begin to vibrate and possibly even
break. This is clearly not the case here. Choice C is incorrect since harmonics are vibrations at frequencies of integer
multiples of some fundamental frequency. Choice D is incorrect since a half tone is the smallest interval between two
notes in a major scale. Neither of these describes the situation in the question.
Discrete Questions
18.
The correct answer for question 18 is choice D, the magnesium ion. This is a straightforward question
involving outside knowledge of periodic trends in ionic radii. Looking at the answer choices, and with a little help
from the Periodic Table, you should be able to deduce that they all have the same number of electrons; in other words,
they are isoelectronic. So, we have to decide which of these ions is the smallest based on the effective nuclear charge
of each.
Choices C and D, being cations, have lost electrons. This will result in a smaller radius because the electrons
left occupy shells with smaller principal quantum numbers. Because there is a decrease in the total number of
electrons, you get a greater average attraction of the nucleus per remaining electron, which is known as an increase in
effective nuclear charge. The greater the nuclear charge the smaller the ionic radius is in a series of isoelectronic ions
and atoms. So, knowing that a positive ion is smaller than a negative ion when they are isoelectronic, we can rule out
choices A and B. Comparing the sodium ion and magnesium ions, the Mg2+ ion has the same number of electrons as
Na+ but the Mg2+ has one more proton. Thus the electron cloud in Mg2+ is pulled inward more and so it has the
smallest ionic radius. Thus the correct answer is choice D.

19.
The correct answer choice is D: the spacing would increase. The locations of the dark fringes (minima) in a
diffraction pattern are given by the equation:
a sinθ = nλ
where a is the width of the slit, n is a positive integer (1, 2, 3, …) that indicates which dark fringe we are talking
about, λ is the wavelength of the light, and θ is defined as in the following diagram:
Second minimum: n = 2

first minimum: n = 1

x

θ2
a

θ1

central maximum

d

screen
The dashed lines are drawn such that they converge at the midpoint of the slit. In any given set-up, a and λ will be
constant, while the angle and n would change based on which dark fringe we are talking about. In this question we are
asked about the second minimum, corresponding to n = 2. The distance between the central maximum and the second
minimum, which we shall call x, can be expressed in terms of θ and the distance from the center of the slit to the
screen d: x = d sinθ = dnλ/a, or, since n = 2, x = 2dλ/a. From this, one can easily see that if the wavelength were
increased, the spacing would increase as well.
20.
The answer to question 20 is A, 11.2 liters. You can estimate this answer quickly by approximating the

effects of molecular weight, temperature, and pressure on the volume of the gas. You could use the equation, PV =
nRT and solve for volume, but there is a faster way. You know that at STP, one mole of any (ideal) gas occupies a

5


Kaplan MCAT Physical Sciences Test 2 Explanations

volume of 22.4 liters. You also know that the pressure and volume of a gas are inversely related and that temperature
and volume are directly related. So, since STP stipulates a temperature of 273K and a pressure of 1 atm, you can see
that the temperature and pressure are both double on the gas in the question in relation to STP. That means that the
volume would be doubled from the effects of higher temperature and halved by the effects of pressure. These effects
cancel out and the volume of one mole of gas at 546K and 2 atm is also 22.4 liters But don't jump to choice B yet.
Remember, you only have 14g of N2 gas. The molar weight of N2 is 28g, so that means you only have half a mole of
gas. Therefore, you only have half of your 22.4 L, or 11.2 liters, choice A.
Multiplying 2, 0.5, 0.5, and 22.4 together is a lot easier than multiplying 0.5, 546, and 0.082 together and
then dividing by 2, and you don't have to come up with the universal gas constant from memory. It is always easier to
take shortcuts like these if you can see them and a good basis of chemical knowledge will make them easy to see.
Here, you could have saved yourself a lot of calculation simply by remembering the molar volume of a gas at STP and
the effects that changing temperature and pressure have on the volume of a gas.
21.
The correct answer choice is C, the current is halved. The formula for the resistance of a resistor in terms of
its physical properties is R equals ρ times L over A, where ρ is the resistivity, L is the length of the resistor, and A is
the cross sectional area of the resistor. Therefore if the length of a resistor doubles, its resistance also doubles. Ohm's
law says that voltage equals current times resistance. Assuming that the voltage across the resistor remains the same,
the current will be halved if the resistance is doubled.
22.
The correct to question 22 answer is B, a silvery-white element that ignites explosively with water. The
Periodic Table shows that rubidium, element 37, is found in group 1, the alkali metals, so it should be highly reactive.
You may recall that sodium reacts vigorously, even violently, with water. Well, since the alkali metals become more

electropositive as you go down the group, rubidium is much more reactive in water than sodium--anyway, the point
is, that due to periodicity, rubidium will react violently with water much in the same way as does sodium. So
rubidium is probably too reactive to be used in constructing airplanes as choice D says. As one of the heavier alkali
metals, you can pretty safely assume that rubidium is not gaseous under normal atmospheric conditions, so choice C
is wrong. As for choice A, metals in general are good conductors. Since rubidium can readily lose an electron, it is a
better conductor than semiconductor, so choice A isn't a very likely choice.
Passage IV (Questions 23–27)
This passage deals primarily with enthalpy, entropy, and Gibbs' free energy. Essentially, it explores the
thermochemistry of photosynthesis. Pay special attention to the table and its list of heat or formation values. Chances
are, you'll be using them in a calculation.
23.
The correct answer is C. The MCAT will sometimes have a problem involving numbers but which simply
asks you to identify the correct set-up rather than perform the actual arithmetic. It is therefore important to give a
brief glance to the answer choices beforehand to make sure you don’t waste any time doing unnecessary calculations.
Dimensional analysis is always a powerful tool in approaching questions of this type, and especially for ones that are
complicated: answer choices can be eliminated if the units do not cancel in the right way. For this particular question,
we first need to convert the amount of water into moles, and then determine the number of moles of sugar that would
be produced, then convert it back to a mass quantity. The number of moles of a compound is the mass divided by the
molar mass (or molecular weight); there is thus 11 g/(18 g/mol) = 11/18 mol of water. From reaction 1, we know
that 6 moles of water are consumed for every mole of sugar produced. 11/18 mol of water will thus yield 11/18 ∗
1/6 mol sugar. To convert this into mass, one multiples by the molar mass of sugar, 180 g/mol.
24.
B is the correct answer. This answer is actually given in the text of the passage. A substance which is
oxidized loses electrons, while a substance which gains electrons is said to be reduced. The passage states that
electrons are taken from the hydrogen of the water, so water is oxidized and the correct answer is B.
25.
The correct answer is B. This question requires you to be able to interpret the information given in the
passage about Gibbs free energy and different aspects of the chemical equation. The sign of ? G tells us whether or not
the reaction is spontaneous. Here the sign is positive, so the reaction is not spontaneous. Thus I is true. You can make
a good estimate of the change in entropy during the reaction by considering two factors: the number of moles of

reactants and products and any phase changes. Entropy increases when there is an increase in randomness in a system.
In this case there are twelve moles of reactants and only seven of products; this would indicate a decrease in entropy.

6


Kaplan MCAT Physical Sciences Test 2 Explanations

There is also a change in phase from gaseous reactants to a solid in one of the products. This also indicates a decrease
in entropy, since in a solid there is less movement and therefore less disorder than there is in a gas. Taking both these
factors together, you can be fairly certain that there is a decrease in entropy; so II is also true. Since the reaction clearly
is taking in energy in the form of light, it is an endothermic reaction and III is not true. The only two correct
statements are I and II, so choice B is correct.
26.
The correct answer choice is A. To solve this problem, you must remember several facts concerning ? H. The
first and most important thing to know is that the ? H for a reaction is equal to the sum of the ? H of formation of the
products, minus the sum of the ? H of formation of the reactants. For both sums, you must remember that each ? H of
formation must be multiplied by the stoichiometric coefficient of the compound in the reaction. The second thing to
remember is that the ? H of formation of an element in its standard state is always zero. Therefore, by substituting the
values you are given in the table, and noting that the ? H of formation of O2 is zero, you get the overall ? H equal to
+2801.3, or choice A. It is interesting to note that this positive ? H coupled with a negative ? S (from the decrease in
entropy) indicates that this reaction has a positive free energy change.
27.
Choice C is the correct answer. This question requires you to understand how the light energy in the form of
photons affects atoms and compounds. Let's go through the four answer choices individually. Choice A states that
energy absorbed is used to ionize the reactants. This can be correct, but isn't necessarily, since there is not always
sufficient energy absorbed to actually remove an electron from an atom. Choice B states that energy is released from
the bonds of the reactants, which you should know is incorrect because energy must be absorbed in order for bonds to
be broken. Choice C is always correct, because when an atom absorbs energy, its electrons move from their ground
state to a higher excited state. Choice D states that electrons return to their ground state. We know this cannot be true,

because electrons are in their most stable, lowest energy state when they are in their ground state. Therefore,
absorbing energy could not put an electron into its ground state.

7