Physics section test (6)

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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 1–5) The correct answer to question 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 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 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 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 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 The correct answer to question 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 For question the correct answer is A Answering question 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 Kaplan MCAT Physical Sciences Test 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 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 of the General Chemistry Review Notes You could look it up But enough introduction Let's get to the questions 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 we need to calculate the heat capacity?” The heat capacity of an object is the amount of energy needed to raise its temperature by °C or K This should be contrasted with the specific heat which is the amount of energy needed to raise kg or g (depends on the unit in which it is reported, either way the idea is still the same) of the substance by °C or 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 kg versus 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 The correct answer to this question is choice B Question 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 Kaplan MCAT Physical Sciences Test Explanations 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 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 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 kilograms, the change in temperature is °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 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 degrees, the temperature of the bomb must also change by degrees Therefore, ∆T = °C Now we can solve for qb It equals 1620 ∞ 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 ∞ + 1620 ∞ 2) J = (1620 + ∞ 4190) ∞ J, where we have factored out the 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 °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 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 and tells you that the molarity of the thiosulfate is determined from the amount of iodate consumed in Reaction 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 Kaplan MCAT Physical Sciences Test 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 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 and 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 times 2, you get moles of thiosulfate titrated for each original mole of iodate So the number of moles of thiosulfate titrated is 0.01 ∞ 0.05 ∞ Finally, you need to determine the molarity of the thiosulfate solution To 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 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 and 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 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 That has nothing to 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 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 reaches equilibrium, the Keq will be the same Choice C is wrong because Reactions and are certainly related, that's one of the main premises of the passage Discrete Questions Kaplan MCAT Physical Sciences Test 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 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 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 mole of solute in 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 moles of solute to 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 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 Kaplan MCAT Physical Sciences Test 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 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 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 we determine which way it points? Well, we also know that there is centripetal acceleration, directed towards the Kaplan MCAT Physical Sciences Test 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 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 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 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, to 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 to Kaplan MCAT Physical Sciences Test 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 = 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 ...PHYSICAL SCIENCES TEST EXPLANATIONS Passage I (Questions 1–5) The correct answer to question is C This question asks... can eliminate choice B Choice C is incorrect because the conjugate Kaplan MCAT Physical Sciences Test Explanations base of H2BO3- would contain one less proton, not one more as boric acid does... which is the heat supplied to the system The correct answer to this question is choice B Question tests your understanding of heat and energy First we must figure out what thermally isolated means
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