Physics section test (2)

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MCAT Section Tests Dear Future Doctor, The following Section Test and explanations should be used to practice and to assess your mastery of critical thinking in each of the section areas Topics are confluent and are not necessarily in any specific order or fixed proportion This is the level of integration in your preparation that collects what you have learned in the Kaplan classroom and synthesizes your knowledge with your critical thinking Simply completing the tests is inadequate; a solid understanding of your performance through your Score Reports and the explanations is necessary to diagnose your specific weaknesses and address them before Test Day All rights are reserved pursuant to the copyright laws and the contract clause in your enrollment agreement and as printed below Misdemeanor and felony infractions can severely limit your ability to be accepted to a medical program and a conviction can result in the removal of a medical license We offer this material for your practice in your own home as a courtesy and privilege Practice today so that you can perform on test day; this material was designed to give you every advantage on the MCAT and we wish you the best of luck in your preparation Sincerely, Albert Chen Executive Director, Pre-Health Research and Development Kaplan Test Prep © 2003 Kaplan, Inc All rights reserved No part of this book may be reproduced in any form, by Photostat, microfilm, xerography or any other means, or incorporated into any information retrieval system, electronic or mechanical without the written permission of Kaplan, Inc This book may not be duplicated, distributed or resold, pursuant to the terms of your Kaplan Enrollment Agreement PHYSICAL SCIENCES TEST EXPLANATIONS Passage I (Questions 1–8) Passage I is about a set of experiments that were performed on the gemstone malachite The questions require you to understand stoichiometry, calculations of yield, and the nature of acids and bases Take note of how each experiment was performed and to the methods used to analyze the products The correct answer is C This question asks you to examine Experiments and and determine what gas was collected To answer it, you must look carefully at the starting material, malachite, and recognize the hints given to you in the descriptions of the experiments The first choice that can be eliminated is choice B, water vapor Since the gas was collected by water displacement, it seems unlikely that water vapor, which would probably condense as it bubbled through the water, could be collected in this way Next, you can eliminate oxygen and hydrogen since both will support combustion We were told that a burning splint inserted into the gas was extinguished almost immediately, so the gas has to be something that will stop the burning process Since carbon dioxide does this, it seems like the best answer, and it is indeed the correct answer So, the gas contained in the collection bottles was carbon dioxide, choice C Another way to arrive at the answer, or at least would make an intelligent guess, is to realize from the molecular formula of malachite that there are four elements that need to be accounted for: copper, oxygen, hydrogen, and carbon The copper and (part of) the oxygen appear in the black solid copper oxide The condensation is presumably water, which takes care of the hydrogen and (more) oxygen Where does the carbon go? A natural guess would be that it would be in the gas The correct answer for is choice B This question asks you to calculate the percent composition of oxygen in malachite This sort of calculation should be pretty routine The percent composition of an element in a compound is determined by dividing the total mass of that element in the compound by the molecular mass of the whole compound, and then converting that value into a percent The experiment outline tells us that the molecular formula for malachite is Cu 2(OH)2CO3 That lets us know that there are moles of copper, moles of oxygen, moles of hydrogen, and mole of carbon in every mole of malachite When we multiply these numbers by the molar masses of their respective elements and add the results together, we find that the molecular mass of malachite is 221 g/mol 80 of those 221 grams can be attributed to oxygen 80 is one-third of 240, and so is slightly more than one-third of 221 Inspection of the answer choices tells us that only choice B could be correct The correct answer to question is D This question asks you to classify the reaction that is occurring in Experiment 1, in which malachite is heated vigorously This heating produces a gas, condensation, and a black solid From the information given in the passage and interpreted above in the discussion for number 1, we know that the reaction is of the form: CuCO3•Cu(OH)2 ? CuO + H2O + CO2 Because this reaction involves only one reactant, which breaks down into several components, it can be classified as a decomposition reaction, answer choice D Neither acid nor base were added to the reaction vessel, choice A is incorrect Choice B, a double displacement reaction, is wrong as well, since it requires two reactants Finally, choice C says that the reaction outlined in Experiment is a redox reaction However, examination of the products reveals that none of the atoms has changed oxidation state, so choice C is incorrect Choice D is the correct answer to question This problem asks you to calculate how many 100 mL collecting bottles will be filled with gas at the completion of Experiment 22 grams of malachite were added to the reaction vessel, and we know from question 1, that the molecular weight of malachite is 221 g/mol That means that 0.1 mole of malachite were reacted We know that the gas produced was carbon dioxide So, how many moles of carbon dioxide are produced by the decomposition of one mole of malachite? From the balanced reaction written for number above, we know that the stoichiometric ratio is 1:1 So 0.1 mole of malachite produced 0.1 mole of CO2 Now, we know that at STP, the conditions presented in the question, a mole of any gas takes up a volume of 22.4 liters So, 0.1 moles of CO2 will occupy one tenth of that, or 2.24 liters Since each of the collection flasks holds 100 mL, or 0.1 liters, the total number of bottles we'll need is 2.24 liters divided by 0.1 liters, which is 22.4 bottles However, since the question asks us how many bottles we'll need to collect the gas and we can't have only four tenths of a bottle, it will take 23 bottles to hold all the gas That is choice D Kaplan MCAT Physical Sciences Test Explanations For question 5, choice B is the correct answer Answering this question correctly relies on your understanding of Experiment Experiment involved a reaction between aqueous sulfuric acid and malachite As a result of the reaction, gas was evolved and a neutral solution was left in the reaction vessel Which of the choices is consistent with all that? Choice A says that an excess of sulfuric acid was added to the reaction vessel If an excess of sulfuric acid had been added, the final solution in the reaction vessel would have been acidic, so it's pretty easy to eliminate this choice Choice B says that an aqueous solution of copper sulfate was formed The reaction between malachite and sulfuric acid is an acid-base reaction with H2SO4 as the acid and malachite as the base In an acid-base reaction, you know that water and salt are formed as products and, in this case, the extra atoms are released as a gas So carbon dioxide, a gas, water, and the salt copper sulfate are formed, so choice B is correct Now let's look at the last two choices Choice C say that an aqueous solution of copper hydroxide was formed Well, we already said that this is an acid-base reaction that ended up neutral when acid was added Any hydroxide ions produced would go into the formation of water, not copper hydroxide Furthermore, copper hydroxide would be basic Choice D says that the pH paper turned blue when placed in the reaction solution, which is not consistent with the description that the solution is neutral (pH paper turns blue in basic solutions.) Hence, the correct answer to this question is B The correct answer to question is A This question asks for the pH of the milky white mixture that is formed when stoichiometric amounts of calcium hydroxide solution are added to the gas filled collection bottle We know that the gas is carbon dioxide In order to answer this question, we must first determine what reaction is taking place in Experiment When water was added to the carbon dioxide in the bottle, and the bottle was shaken, the final solution was acidic This means that carbon dioxide reacted with water to produce an acidic solution, carbonic acid to be precise Therefore, when stoichiometric amounts of the aqueous base, calcium hydroxide, are added to the carbon dioxide, the carbonic acid formed and the base added should neutralize each other The products of this neutralization reaction are calcium carbonate and water; calcium carbonate is insoluble in water and thus precipitates, accounting for the milky white color, and the final solution would be neutral, as stated in choice A Choice B, which says that the pH would be acidic, would be correct only if calcium hydroxide were added at less than the stoichiometric amount, meaning that there was excess carbon dioxide Choice C, which says that the final solution would be basic, would be correct only if excess calcium hydroxide solution were added to the carbon dioxide, or if the carbonate ion were left in solution and could therefore hydrolyze (This latter would occur if a different base were used and a soluble carbonate were formed in the neutralization; for instance, if sodium hydroxide were added, soluble sodium carbonate would form and the solution would then be basic-but clear and colorless.) The correct choice is B This question asks you to predict the products of a reaction similar to the one performed in Experiment 2, but using hydrochloric acid rather than sulfuric acid From answering other questions in this problem set, we already know that the reaction between malachite and sulfuric acid is an acid-base reaction The products formed in this reaction were carbon dioxide, water, and a copper sulfate salt So, since hydrochloric acid is a strong acid, just like sulfuric acid, the same sort of reaction should take place between HCl and malachite However, since there is no longer a sulfate anion in the reaction, but a chloride anion, the identity of the copper salt will change to copper chloride So the products of this reaction are carbon dioxide gas, water, and aqueous copper chloride salt This is choice B The correct answer is B This question tells us that four grams of copper oxide are formed from the reaction in Experiment 1, and asks us to calculate the percent yield of the experiment Percent yield is defined as the amount of product collected divided by the theoretical yield of the reaction Therefore, the first step is to calculate the theoretical yield of copper oxide from the decomposition of malachite The easiest way to this is to convert everything to moles We discussed earlier that the 22 grams of malachite used in Experiment represents 0.1 mole of malachite mole of malachite contains moles of copper, so mole of malachite will theoretically decompose to yield moles of copper oxide Using this ratio, we know that the theoretical yield of copper oxide from this experiment is 0.2 mole of copper oxide How many moles were actually produced? From the Periodic Table and the molecular formula of copper oxide, CuO, we know that the molecular weight of copper oxide is about 80 grams The question tells us we have grams of copper oxide produced The number of moles is therefore divided by 80, or about 05 mole of copper oxide We were expecting 0.2 mole and we got 0.05 mole Converting that into a percentage, we get 0.05/0.2 times 100%, or 25% That's choice B The other answers come from calculation mistakes like forgetting that there were moles of copper in mole of malachite or trying to find the percent yield by directly dividing the grams of copper oxide produced by the 22 grams of malachite used Passage II (Questions 9–13) Kaplan MCAT Physical Sciences Test Explanations The correct answer is choice C, strontium 94 Question gives a typical uranium fission reaction and asks you to identify one of the products To solve this problem all you need to is balance the mass numbers and atomic numbers on each side of the arrow The atomic number is the subscript which represents the number of protons in the nucleus On the left side of the arrow you have 92 protons from uranium, and on the right side you have 54 protons in xenon, which leaves 92 minus 54, or 38 protons for our unknown product Looking at the answer choices, we can eliminate A and D To distinguish between answers B and C, we need to look at the mass numbers The mass number is the superscript which represents the total number of protons and neutrons in the nucleus The total mass number on the left is given by 235 from the uranium and from the neutron, which adds up to a total of 236 Xenon has a mass number of 139, so adding this to the mass numbers of the neutrons gives a mass number of 142 Therefore, our product must have a mass number equal to 236 minus 142, which is 94 Now we know our product must have an atomic number of 38 and a mass number of 94 So the correct answer is C, strontium 94 10 The correct answer choice is C, the binding energy is equal to the mass defect of the nucleus times the speed of light squared This is an outside knowledge question that requires you to understand the concepts of mass defect and binding energy and how the two are related through Einstein’s equation E = mc2 As nucleons (neutrons and protons) come together to form a nucleus, some of the mass is converted into energy and released, analogous to the way that energy is released when a common chemical bond is formed Because of this conversion, the mass of the nucleus formed is less than the sum of the masses of the constituent nucleons The difference between the two mass values is known as the mass defect, and is related to the energy released by the equation E = mc2 Because c is such a large number, a small mass defect corresponds to a significant amount of energy The energy released is called the binding energy Its name implies that this binding energy is the energy holding the nucleus together, which is a valid description because this same amount of energy needs to be supplied to break apart the nucleus into individual nucleons, again analogous to the fact that breaking a bond is an endothermic process that requires energy input The missing mass will be restored through this input of binding energy 11 The correct answer is choice D, not deflected at all Because the neutron is electrically neutral, it does not interact either with the magnetic field or the electric field You can see this if you look at the equations for the forces due to an electric field and a magnetic field Both forces depend on the charge on the particle So if the charge of the particle is zero, the force must also be zero, and if no forces act on the particle it will be undeflected 12 The correct answer choice is B, 9.5 hours This question can be answered with a basic understanding of what a half-life is If we can figure out how many half-lives have passed in 19 hours, then we can divide to get the value for the half-life itself After one half-life, 50% of the sample will remain by definition After two half-lives have passed, 50% ∗ 50% or 25% of the sample will remain We don't need to go further since if 25% of the sample remains then 75% of the sample has decayed Since two half-lives have passed in 19 hours, the half-life must be 19 divided by giving 9.5 hours 13 The correct answer choice is D In order for fission to occur, energy must be supplied to the nucleus to initiate the reaction This energy comes from the kinetic energy of the particle that is used to bombard the nucleus In order for this kinetic energy to be transferred to the nucleus, the particle must be able to get within close proximity to it Protons would not work well because being positively-charged themselves, they would experience repulsion from the positively-charged nucleus Passage III (Questions 14–18) 14 For question 14 the correct answer is C You are told in the first paragraph of the passage that enzymes catalyze reactions The passage also tells you that catalysts increase the rate of reactions by decreasing the amount of energy needed to bring the reactants to the transition state This energy is called the activation energy Like all catalysts, enzymes nothing to change the equilibrium of a reaction The only thing that it changes is the rate of reaction by making the transition states more accessible 15 For question 15 the correct answer is A If you know the equation for a line, which is required knowledge for the MCAT, you shouldn't have had any problem with this one Looking at Equation 1, since it's already in linear Kaplan MCAT Physical Sciences Test Explanations form, you should be able to see that the slope of the line is equal to KM over Vmax and that the y-intercept is equal to 1/Vmax Now, if you examine the plot for competitive inhibition in Figure the top one you can see that the yintercept, 1/Vmax, is the same for both the inhibited and the uninhibited reactions So, in this case, the slope is directly proportional to the KM for both the uninhibited and the inhibited reactions Since the slope is greater for the inhibited reaction, it has the greater KM and choice A is the correct response Choices C and D can be eliminated because you know that the Vmax,'s for both the inhibited and the uninhibited reactions are the same Choice B can be eliminated because, as you just determined, the KM increases, not decreases Again, choice A is the correct response 16 For question 16 the correct answer is D According to the passage, Table contains data from experiments run with and without a noncompetitive inhibitor The first thing you need to is look at the plot in Figure that deals with noncompetitive inhibition, the lower one From this plot you should be able to see that the intercept with the y-axis is equal to 1/Vmax, and that the reaction with inhibitor the dashed line has a smaller Vmax, than the one without inhibitor We now know that the Vmax, decreases in the presence of a noncompetitive inhibitor, but what happens to KM ? Solving Equation for 1/[S] by setting y = 1/V = 0, you can see that the intercept with the x-axis is equal to -1/KM , and since both lines in figure two have the same x-intercept, KM is the same with and without inhibitor So, with inhibitor, Vmax, decreases, but KM stays the same Choice D is the correct response 17 For question 17 the correct answer is C To answer this question, you didn't need to know much science since the important information is in the passage The passage describes the two types of inhibition, telling you that competitive inhibitors bind to the same site on the enzyme that the substrate does and can be overcome by increasing the substrate concentration In contrast, noncompetitive inhibitors bind to different sites on the enzyme and cannot be overcome by increasing the substrate concentration Noncompetitive inhibitors work by binding to the enzyme and changing its configuration, making it unable to recognize its substrate It may be interesting to note that the reverse has also been observed, there are some chemicals, called enzyme cofactors, that bind to a site on the enzyme and change its configuration so that the enzyme can recognize its substrate Anyway, the question tells you that the inhibition on enzyme a caused by substance B is overcome by increasing the concentration of substance A, the substrate of enzyme a Therefore B is a competitive inhibitor, and molecules of substance B must bind at the catalytic site That information lets you eliminate choices B and D However, the inhibition by substance D cannot be overcome by increasing the concentration of substance A Therefore, substance D must be a noncompetitive inhibitor that binds at a different regulatory site That makes choice C the correct answer 18 Choice B is the correct answer As stated in the passage, KM represents the substrate concentration that lets the reaction proceed at half its maximum rate Anything that will affect the reaction rate or the amount of substrate the enzymes can bind to at any one time will affect the KM of a given reaction We can go through the choices and see which could that The pH of the reaction will affect this because enzymes are proteins and the pH of a solution can interfere with the secondary and tertiary structure of a protein, a change in pH can change the conformation of the enzyme, making the enzyme less likely to recognize the substrate Since the catalyst is thus less effective, the rate of reaction will change, which also changes the KM Anyway, since roman numeral I appears in all the answer choices, we knew it had to be right Roman Numeral II also appears in all the answer choices, so it must also be right The temperature also affects the enzyme conformation and the rate of reaction Since the rate of reaction changes with temperature, KM changes, too So that leaves roman numerals III and IV The KM is also affected by the concentration of enzyme because the greater the number of enzyme molecules in the reaction mixture, the greater the degree of catalysis The greater the catalysis, the faster the reaction, so the KM will also change Since III is correct, we know that the answer is either B or D So, looking at statement IV, we know that the answer is choice B KM is a constant that describes a substrate concentration at a particular pH, temperature, and enzyme concentration No matter what the substrate concentration in the reaction mixture is, the KM will be the same if the other factors are held constant So the correct answers are I, II, and III, which corresponds to answer choice B Discrete Questions 19 The correct answer choice is C Since the change in temperature can be calculated from the equation E = mc? T, where m and c are constant, the rate at which the temperature increases will be dependent on the rate at which heat is supplied to the system The immersion heater is rated at 2000W, which means that it delivers 2000 J every second This rate is constant, and therefore the temperature will be increasing at a constant rate, i.e., it will increase linearly The choice is then between A and C, and we can see that C is correct because the initial temperature is given as 30 °C in the question Kaplan MCAT Physical Sciences Test Explanations It may be worth pointing out that since we are not given the specific heat of water, there is in principle the possibility that the heat supplied may have been sufficient to cause the water to undergo a phase change (to boil), which would show up as a flat portion of the temperature versus time graph Since this is not given as a choice, we not have to worry about this scenario And in fact, the specific heat of water is high enough (about 4000 J/kg.K) such that this is not the case; given the numbers in the problem, the temperature after 100 seconds can be verified to be 50 °C 20 For question 20 the correct answer is D Elements with partially filled d subshells are located in the block of transition elements of the Periodic Table Boron and silicon, choices A and B, are both p-block elements Their valence electrons are in the p subshell Since the valence shell is the only one that is partially filled in ground state elements, these two choices cannot be correct Magnesium, choice C, is an s-block element on the left of the periodic table Its valence electrons are in the s subshell, so this too is an incorrect answer That leaves chromium, choice D Chromium is element 24, the fourth element in the fourth period transition elements It has four unpaired electrons in its 3d subshell, so this is indeed the correct answer If you did not remember how to find this information from the structure of the Periodic Table, you could have written out the electron configurations of all the choices It would have been a bit more time consuming, but equally effective For the record, you can quickly determine that any element with an atomic number lower or equal to 18 will not even begin to fill the 3d subshell 21 The correct answer choice is D, 9F over This question requires you to have a good understanding of Coulomb's law, and the flow of charge Originally the two charges of Q and 2Q are separated by a distance d, and exert a force of F on one another In terms of Coulomb's law, F is equal to Coulomb's constant k times Q times 2Q 2kQ2 Now the charges are brought together and made to touch one another all over d squared which is equal to d2 What happens to the charge on the two spheres? The total charge on the two spheres was Q plus 2Q or 3Q When the spheres, which have the same size, touch, the charge becomes evenly distributed Each sphere now carries a total charge of 3Q over The spheres are then separated again by a distance d, but because they are now carrying the new charges the force between them has changed We'll call this new force F From Coulomb's law, F is equal to k, times 9kQ2 9kQ2 2kQ2 F 3Q over 2, times 3Q over 2, all over d squared, which equals Dividing F = by F = , we find that 2 4d 4d d F 9F = Therefore, F = , which is answer choice D 8 22 The correct answer to this question is choice D When you are asked to match up electronic configurations, the easiest thing to is count the number of electrons After all, since orbital filling is the same, a certain number of electrons will always have the same electronic configuration around a nucleus So how many electrons are there in the configuration described in the question? Adding the superscripted numbers which show the number of electrons in each subshell, we see that there are 18 electrons here So let's look at the choices Choice A, argon, has an atomic number of 18, so in its ground state, there are 18 electrons and it will have the indicated configuration Chlorine has an atomic number of 17, but we need to add one for its negative charge That brings the number up to 18 and choice B is also wrong Choice C, K+, is also wrong, since its atomic number minus one electron for its +1 charge also equals 18 So all three of these species have the described electronic configuration That leaves Ga3+ as the answer we're looking for It's atomic number of 31, minus for its +3 charge gives 28, so there are 28 electrons in Ga3+ In fact, its electronic configuration is the same as the one in the question, except that it also has a full 3d subshell, adding a 3d10 to the end of the question's configuration 23 The correct answer choice A, ∗ 106 To this question, we must first find the period of the wave, which is the time it takes for a wave to complete one cycle However, in order to find the period we must know the frequency of the wave since the period is one over the frequency In the question we are given the wavelength and the speed of light, and the equation that relates these two values to the frequency is f = Error! So putting in values gives ∗ 108 m/s divided by 600 ∗ 10–9 m, which gives a frequency of ∗ 1014 Hertz This is equivalent to a period of ∗ 10–15 seconds If one wavelength has a period of ∗ 10–15 seconds, there will be 0.01 ∗ 10–6 over ∗ 10–15 complete waves in 0.01 µs, or ∗ 106, which is answer choice A Passage IV (Questions 24–31) Kaplan MCAT Physical Sciences Test Explanations The correct answer is choice B, 1:3 To find the distance traveled in the first four seconds, we can use the equation x - x0 = v0t + at2, where the left-hand side is the distance traveled Since the car starts from rest, its initial velocity, v0, is zero The distance traveled in the first four seconds is therefore a (4)2, or 8a There are two ways to find the distance traveled in the next four seconds: one can determine the velocity at the end of the first four seconds via the equation v = v0 + at, and use this value as the new v0 in the equation x - x0 = v0t + at2 again with t = s; or, alternatively, one can just determine the total distance traveled at the end of seconds, and subtract 8a from that We shall try this latter approach Using the same equation, again with v0 = 0, but this time with t = s, we find that the distance traveled is a (8)2, or 32a The distance traveled in the last four seconds is therefore 32a - 8a = 24a, and the ratio of the distances is 8a:24a = 1:3 24 25 The correct answer choice is B This problem requires two formulas The first is F = ma Since the mass of the car remains constant, if the net force doubles then so will the acceleration The second formula states when acceleration is constant, the change in velocity equals acceleration times time: v = v0 + at The change in velocity of 28 m/s is the same in both cases Therefore, if the acceleration doubles, the time will only be 1/2 the old value 26 The correct answer choice is C, increase if the mass of the car increases The maximum force that an object can sustain without sliding is equal to µs times the normal force In the present case the normal force is just the weight of the car, mg Therefore, we can immediately rule out answer choices A and B since this force does not depend on velocity Since the force is directly proportional to the mass of the car, it will increase if the mass increases Once again, C is the correct choice mg This question requires you to know that pressure is force divided by the 4A area over which the force is applied In this case, the force is the weight of the car, W = mg, and the area over which it is applied is the contact patch of the tires It is important to note that this weight is equally distributed between the four tires; so the force on each of the contact patches is one quarter of the total weight of the car, mg/4 Since the area mg of the contact patch for each tire is A, the pressure is 4A 27 The correct answer choice is C, 28 The correct answer is choice A There are two forces acting on the car along the direction of the plane: the force acting down the slope due to the weight of the car, and the force of friction acting in the opposite direction to the motion of the car First, let us consider the force due to friction This equals the normal force on the car exerted by the surface of the slope multiplied by the coefficient of friction, where the normal force is equal to the weight of the car times cosθ: normal force friction θ mg θ This friction force remains constant since the angle of the slope is constant and the coefficient of friction remains constant Now let us consider the force down the slope This is equal to the weight of the car times sinθ, and this value also remains constant since the angle of the slope is constant We have already said that the total force acting on the car on the slope is equal to the force due to the weight of the car minus the force due to friction, and since both of these values remain constant the force acting on the car must be constant This implies that the acceleration of the car must be constant, and the only graph where this is the case is graph A So the correct answer choice is A Kaplan MCAT Physical Sciences Test Explanations 29 The correct answer is 4.1 seconds, choice B As long as the tires not start to slide or skid, the force of friction is static friction The question asks for the least time, which means that the static force of friction is at its maximum value, which is µs times N, where µs is the coefficient of static friction and N is the normal force The normal force N is equal to the weight of the car, which is m ∗ g or 1,000 kg ∗ 10 m/s2 which is 10,000 N Note that we approximated g to be 10 m/s2, to make the calculations more straightforward The coefficient of static friction, µs, is given as 0.6, so the maximum static friction force is 0.6 ∗ 10,000 N which equals 6,000 N From Newton's second law, the acceleration is the force, 6,000 N, divided by the mass, 1,000 kilograms, or m/s2 Because the car is stopping, the acceleration is opposite to the direction of the motion If we take the direction of motion to be in the positive direction, then the velocity vectors are in the positive direction and the acceleration vector is in the negative direction The equation that we need to use to find the stopping time is v = v0 + at Rearranging this we get that the time equals the final velocity minus the initial velocity divided by the acceleration Substituting our values into this (0 – 24) = seconds Since we made an approximation earlier, we must pick the equation, we get that the time equals –6 closest answer and this is answer choice B, 4.1 seconds 30 The correct answer here is choice A This question requires an understanding of the principle behind the hydraulic lever—namely, Pascal’s principle This principle states that the pressure exerted on a fluid is transmitted throughout the entire fluid Since pressure is force/area, if the pressure were to remain constant over the entire fluid, this would have to imply that a small force exerted over a small area would create a large force over a larger area This is how one could exert a large force somewhere else by exerting a small one locally The force required to stop the wheel from turning is expected to be quite large; this is how the mechanism described in the passage is helpful: the driver exerts a force f on the brake pedal piston which has an area a The pressure is thus f/a This pressure is transmitted to the brake shoe piston which has an area A The force at the brake shoe piston F thus satisfies: F f = , or A a A F=f∗ a If we want to magnify the force (have F > f), we would want A to be greater than a, i.e to have the brake shoe piston larger than the brake pedal piston Choice B is incorrect because there is no evidence that the coefficient of friction is dependent on the area of the brake shoe piston Choice C is incorrect because a larger brake pedal piston would actually decrease the pressure given the same force Choice D is incorrect because the brake pedal piston is not actually in direct contact with the brake shoe piston 31 The correct answer choice is B, 4900 N This question is based on Archimedes' principle which states that if a body is partially or totally immersed in water, it will be buoyed up by a force equal to the weight of water that it displaces In this problem we are asked to find the apparent weight of the car given that it displaces 0.5 m3 of water when it rolls into a lake The apparent weight of the car is the weight of the car in air minus the buoyant force due to the weight of water displaced To calculate the buoyant force, we need to find the mass of the water displaced, which we can work out from the equation: ρ = m/V, where ρ is the density, m the mass, and V the volume We know that the density of water is 1000 kg/m3 and that the volume of water displaced is 0.5 m3 So putting these numbers into the equation and rearranging, we get that the mass of water displaced is 500 kg This is equivalent to a buoyant force of 4900 N since the buoyant force is the mass of water displaced times the acceleration due to gravity The weight of the car in air is 1,000 kg times 9.8 m/s2, which equals 9,800 N Therefore, the apparent weight of the car is 9800 – 4900, or 4900 N which is answer choice B ...PHYSICAL SCIENCES TEST EXPLANATIONS Passage I (Questions 1–8) Passage I is about a set of experiments that were performed... bottle, it will take 23 bottles to hold all the gas That is choice D Kaplan MCAT Physical Sciences Test Explanations For question 5, choice B is the correct answer Answering this question correctly... produced by the 22 grams of malachite used Passage II (Questions 9–13) Kaplan MCAT Physical Sciences Test Explanations The correct answer is choice C, strontium 94 Question gives a typical uranium
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