AP Physics C Mechanics Practice Tests

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AP Physics C Practice Multiple Choice Ch10

10.4.1. Which one of the following equations is only valid when the angular measure is expressed in radians?
a) 2 02 2
b)
1 2
t
2
0t
c) vT
r
d)
t
e)
t
10.2.4. The hand on a certain stopwatch makes one complete revolution every three seconds. Express the magnitude of the angular velocity of this hand in radians per second.
d) Since the radian is a unitless quantity, the number of radians of angular displacement plays no role in the calculation.
e) The result of the calculation will always have the radian among the units.
a) 0 t
d) Since the radian is a unitless quantity, the number of radians of angular displacement plays no role in the calculation.
e) The result of the calculation will always have the radian among the units.

【AP物理C】【真题】解答题 C2000

AP® Physics C2000 Free response QuestionsThese materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and theirprograms, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students t o college and opportunity.Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major pr ograms and services incollege admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SA T®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commit ment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by t he College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.(2000 M1) You are conducting an experiment to measure the acceleration due to gravity g u at an unknown location. In the measurement apparatus, a simple pendulum swings past a photogate located at the pendulum's lowest point, which records the time t10 for the pendulum to undergo 10 full oscillations. The pendulum consists of a sphere of mass m at the end of a string and has a length l. There are four versions of this apparatus, each with a different length. All four are at the unknown location, and the data shown below are sent to you during the experiment.a.figures. Enter these results in the table above.b. On the axes below, plot the square of the period versus the length of the pendulum. Draw a best-fit straight lineAssuming that each pendulum undergoes small amplitude oscillations, from your fit determine the experimental value g exp of the acceleration due to gravity at this unknown location. Justify your answer.d. If the measurement apparatus allows a determination of g exp that is accurate to within 4%, is your experimentalvalue in agreement with the value 9.80 m/s2 ? Justify your answer.e. Someone informs you that the experimental apparatus is in fact near Earth's surface, but that the experiment hasbeen conducted inside an elevator with a constant acceleration a. Assuming that your experimental value g is exact, determine the magnitude and direction of the elevator's acceleration.2000M2. A rubber ball of mass m is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive force caused by the air). The drag force on the ball has magnitude bv2, where b is a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient b is directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.a. On the figure below, draw and label all the forces on the ball at some instant before it reaches terminal speed.b. State whether the magnitude of the acceleration of the ball of mass m increases, decreases, or remains the sameas the ball approaches terminal speed. Explain.c. Write, but do NOT solve, a differential equation for the instantaneous speed v of the ball in terms of time t, thegiven quantities, and fundamental constants.d. Determine the terminal speed v t in terms of the given quantities and fundamental constants.e. Determine the energy dissipated by the drag force during the fall if the ball is released at height h and reachesits terminal speed before hitting the ground, in terms of the given quantities and fundamental constants.2000M3. A pulley of radius R1and rotational inertia I1 is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass m attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts (a) and (b) in terms of m, R1, I1, and fundamental constants.a. Determine the tension T in the cord.b. One block is now removed from the right and hung on the left. When the system is released from rest, the threeblocks on the left accelerate downward with an acceleration g/3 . Determine the following.i. The tension T3 in the section of cord supporting the three blocks on the leftii. The tension T l in the section of cord supporting the single block on the rightiii. The rotational inertia I1of the pulleyc. The blocks are now removed and the cord is tied into a loop, which is passed around the original pulley and asecond pulley of radius 2R1 and rotational inertia 16I1. The axis of the original pulley is attached to a motor that rotates it at angular speed ω1, which in turn causes the larger pulley to rotate. The loop does not slip on the pulleys. Determine the following in terms of I1, R I, and ω1.i. The angular speed ω2of the larger pulleyii. The angular momentum L2 of the larger pulleyiii. The total kinetic energy of the system2000E1. Lightbulbs A, B, and C are connected in the circuit shown above.a. List the bulbs in order of their brightness, from brightest to least bright. If any bulbs have the same brightness,state which ones. Justify your answer.Now a switch S and a 5.0 mH inductor are added to the circuit; as shown above. The switch is closed at time t = 0.b. Determine the currents I A, I B, and I C for the following times.i. Immediately after the switch is closedii. A long time after the switch is closedc. On the axes below, sketch the magnitude of the potential difference V L across the inductor as a function of time,from immediately after the switch is closed until a long time after the switch is closed.d. Now consider a similar circuit with an uncharged 5.0 F capacitor instead of the inductor, as shown above. Theswitch is again closed at time t = 0. On the axes below, sketch the magnitude of the potential difference V cap across the capacitor as a function of time, from immediately after the switch is closed until a long time after the switch is closed.2000E2. Three particles, A, B, and C, have equal positive charges Q and are held in place at the vertices of an equilateral triangle with sides of length l, as shown in the figures below. The dotted lines represent the bisectors for each side. The base of the triangle lies on the x-axis, and the altitude of the triangle lies on the y-axis.a.i. Point P1, the intersection of the three bisectors, locates the geometric center of the triangle and is one pointwhere the electric field is zero. On Figure 1 above, draw the electric field vectors E A, E B, and E C at P, due to each of the three charges. Be sure your arrows are drawn to reflect the relative magnitude of the fields.ii. Another point where the electric field is zero is point P2 at (0, y2). On Figure 2 above, draw electric field vectors E A, E B, and E C at P2 due to each of the three point charges. Indicate below whether the magnitudeb. Explain why the x-component of the total electric field is zero at any point on the y-axis.c. Write a general expression for the electric potential V at any point on the y-axis inside the triangle in terms of Q,l, and y.d. Describe how the answer to part (c) could be used to determine the y-coordinates of points P1 and P2 at whichthe electric field is zero. (You do not need to actually determine these coordinates.)2000E3. A capacitor consists of two conducting, coaxial, cylindrical shells of radius a and b, respectively, and length L >> b. The space between the cylinders is filled with oil that has a dielectric constant κ. Initially bothcylinders are uncharged, but then a battery is used to charge the capacitor, leaving a charge +Q on the inner cylinder and -Q on the outer cylinder, as shown above. Let r be the radial distance from the axis of the capacitor.a. Using Gauss's law, determine the electric field midway along the length of the cylinder for the following valuesof r, in terms of the given quantities and fundamental constants. Assume end effects are negligible.i. a < r < bii. b < r << Lb. Determine the following in terms of the given quantities and fundamental constants.i. The potential difference across the capacitorii. The capacitance of this capacitorc. Now the capacitor is discharged and the oil is drained from it. As shown above, a battery of emf εis connectedto opposite ends of the inner cylinder and a battery of emf 3εis connected to opposite ends of the outer cylinder.Each cylinder has resistance R. Assume that end effects and the contributions to the magnetic field from the wires are negligible. Using Ampere's law, determine the magnitude B of the magnetic field midway along the length of the cylinders due to the current in the cylinders for the following values of r.i. a < r < bii. b <r << L。

【AP物理C】【真题】解答题 C1994

AP® Physics C1994 Free response QuestionsThe materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. This permission does not apply to any third-party copyrights contained herein.These materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and theirprograms, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity.Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational TestingService.1994M1. A 2-kilogram block and an 8-kilogram block are both attached to an ideal spring ( for which k = 200 N/m) and both are initially at rest on a horizontal frictionless surface, as shown in the diagram above. In an initial experiment, a 100-gram (0.1 kg) ball of clay is thrown at the 2-kilogram block. The clay is moving horizontally with speed v when it hits and sticks to the block. The 8-kilogram block is held still by a removable stop. As a result, the spring compresses a maximum distance of 0.4 meters.a. Calculate the energy stored in the spring at maximum compression.b. Calculate the speed of the clay ball and 2-kilogram block immediately after the clay sticks to theblock but before the spring compresses significantly.c. Calculate the initial speed v of the clay.In a second experiment, an identical ball of clay is thrown at another identical 2-kilogram block, but this time the stop is removed so that the 8-kilogram block is free to move.d. State whether the maximum compression of the spring will be greater than, equal to, or less than 0.4meter. Explain briefly.e. State the principle or principles that can be used to calculate the velocity of the 8-kilogram block atthe instant that the spring regains its original length. Write the appropriate equation(s) and show the numerical substitutions, but do not solve for the velocity.1994M2. A large sphere rolls without slipping across a horizontal surface. The sphere has a constant translational speed of 10 meters per second, a mass m of 25 kilograms, and a radius r of 0.2 meter. The moment of inertia of the sphere about its center of mass is I = 2mr2/5. The sphere approaches a 25° incline of height 3 meters as shown above and rolls up the incline without slipping.a. Calculate the total kinetic energy of the sphere as it rolls along the horizontal surface.b. i. Calculate the magnitude of the sphere's velocity just as it leaves the top of the incline.ii. Specify the direction of the sphere's velocity just as it leaves the top of the incline.c. Neglecting air resistance, calculate the horizontal distance from the point where the sphere leaves theincline to the point where the sphere strikes the level surface.d. Suppose, instead, that the sphere were to roll toward the incline as stated above, but the incline werefrictionless. State whether the speed of the sphere just as it leaves the top of the incline would be less than, equal to, or greater than the speed calculated in (b). Explain briefly.1994M3. A satellite of mass m is in an elliptical orbit around the Earth, which has mass M e and radius R e. The orbit varies from closest approach of a at point A to maximum distance of b from the center of the Earth at point B. At point A, the speed of the satellite is v o Assume that the gravitational potential energy U g = 0 when masses are an infinite distance apart. Express your answers in terms of a, b, m, M e, R e, v o, and G.a. Write the appropriate definite integral, including limits, that can be evaluated to show that thepotential energy of the satellite when it is a distance r from the center of the Earth is given byU g = -GM e mrb. Determine the total energy of the satellite when it is at point A.c. What is the magnitude of the angular momentum of the satellite about the center of the Earth when itis at point A?d. Determine the velocity of the satellite as it passes point B in its orbit.As the satellite passes point A, a rocket engine on the satellite is fired so that its orbit is changed to a circular orbit of radius a about the center of the Earth.e. Determine the speed of the satellite for this circular orbit.f. Determine the work done by the rocket engine to effect this change.1994E1. A thin nonconducting rod that carries a uniform charge per unit length of λ is bent into a circle of radius R.as shown above. Express your answers in terms of λ, R. and fundamental constants.a. Determine the electric potential V at the center C of the circle.b. Determine the magnitude E of the electric field at the center C of the circle.Another thin nonconducting rod that carries the same uniform charge per unit length λ is bent into an arc of a circle of radius R.which subtends an angle of 2θ, as shown above. Express your answers in terms of λand the quantities given above.c. Determine the total charge on the rod.d. Determine the electric potential V at the center of curvature C of the arc.e. Determine the magnitude E of the electric field at the center of curvature C of the arc. Indicate thedirection of the electric field on the diagram above.1994E2. One of the space shuttle missions attempted to perform an experiment in orbit using a tethered satellite. The satellite was to be released and allowed to rise to a height of 20 kilometers above the shuttle. The tether was a 20-kilometer copper-core wire, thin and light, but extremely strong. The shuttle was in an orbit with speed 7,600 meters per second, which carried it through a region where the magnetic field of the Earth had a magnitude of 3.3 x 10-5 tesla. For your calculations, assume that the experiment was completed successfully, that the wire is perpendicular to the magnetic field, and that the field is uniform. a. An emf is generated in the tether.i. Which end of the tether is negative?ii. Calculate the magnitude of the emf generated.To complete the circuit, electrons are sprayed from the object at the negative end of the tether into the ionosphere and other electrons come from the ionosphere to the object at the positive end.b. If the resistance of the entire circuit is about 10,000 ohms, calculate the current that flows in thetether.c. A magnetic force acts on the wire as soon as the current begins to flow.i. Calculate the magnitude of the force.ii. State the direction of the force.d. By how much would the shuttle's orbital energy change if the current remains constant at the valuecalculated in (b) for a period of 7 days in orbit?e. Imagine that the astronauts forced a current to flow the other way. What effect would that have, ifany, on the orbit of the shuttle? Explain briefly.1994E3. A long coaxial cable, a section of which is shown above, consists of a solid cylindrical conductor of radius a, surrounded by a hollow coaxial conductor of inner radius b and outer radius c. The two conductors each carry a uniformly distributed current I, but in opposite directions. The current is to the right in the outer cylinder and to the left in the inner cylinder. Assume μ = μo for all materials in this problem. a. Use Ampere's law to determine the magnitude of the magnetic field at a distance r from the axis ofthe cable in each of the following cases.i. 0 < r < a ii. a < r < bb. What is the magnitude of the magnetic field at a distance r = 2c from the axis of the cable?c. On the axes below, sketch the graph of the magnitude of the magnetic field B as a function of r, forall values of r. You should estimate and draw a reasonable graph for the field between b and c rather than attempting to determine an exact expression for the field in this region.The coaxial cable continues to carry currents I as previously described. In the cross section above, current is directed out of the page toward the reader in the inner cylinder and into the page in the outer cylinder. Point P is located between the inner and outer cylinders, a distance r from the center. A small positive charge q is introduced into the space between the conductors so that when it is at point P its velocity v is directed out of the page, perpendicular to it, and parallel to the axis of the cable.d. i. Determine the magnitude of the force on the charge q at point P in terms of the given quantities.ii. Draw an arrow on the diagram at P to indicate the direction of the force.e. If the current in the outer cylinder were reversed so that it is directed out of the page, how wouldyour answers to (d) change, if at all?。

【AP物理C】【真题】解答题 C1976

AP® Physics C1976 Free Response QuestionsThe materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program®. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to-face teaching purposes but may not mass distribute the materials, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. This permission does not apply to any third-party copyrights contained herein.These materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, thePSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.1976M1. A small block of mass m slides on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. The coefficient of friction between the block and the wall is μ; therefore, the speed v of the block decreases. In terms of m, R. μ, and v, find expressions for each of the following.a. The frictional force on the blockb. The block's tangential acceleration dv/dtc. The time required to reduce the speed of the block from an initial value v0 to v o/31976M2. A cloth tape is wound around the outside of a uniform solid cylinder (mass M, radius R) and fastened to the ceiling as shown in the diagram above. The cylinder is held with the tape vertical and then released from rest. As the cylinder descends, it unwinds from the tape without slipping. The moment of inertia of a uniform solid cylinder about its center is ½MR2.a. On the circle below draw vectors showing all the forces acting on the cylinder after it is released. Labeleach force clearly.b. In terms of g, find the downward acceleration of the center of the cylinder as it unrolls from the tape.c. While descending, does the center of the cylinder move toward the left, toward the right, or straightdown? Explain.1976M3. A bullet of mass m and velocity v o is fired toward a block of thickness L o and mass M. The block is initially at rest on a frictionless surface. The bullet emerges from the block with velocity v o/3.a. Determine the final speed of block M.b. If, instead, the block is held fixed and not allowed to slide, the bullet emerges from the block with aspeed v o/2. Determine the loss of kinetic energy of the bulletc. Assume that the retarding force that the block material exerts on the bullet is constant. In terms ofL o, what minimum thickness L should a fixed block of similar material have in order to stop the bullet?d. When the block is held fixed, the bullet emerges from the block with a greater speed than when theblock is free to move. Explain.1976E1. A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q.a. On the diagram below, make a sketch of the electric field lines inside and outside the spheres.b. Use Gauss's law to find an expression for the magnitude of the electric field between the spheres at adistance r from the center of the inner sphere (R < r < 3R).c. Calculate the potential difference between the two spheres.d. What would be the final distribution of the charge if the spheres were joined by a conducting wire?1976E2. A conducting bar of mass M slides without friction down two vertical conducting rails which are separated by a distance L and are joined at the top through an unknown resistance R. The bar maintains electrical contact with the rails at all times. There is a uniform magnetic field B, directed into the page as shown above. The bar is observed to fall with a constant terminal speed v0.a. On the diagram below, draw and label all the forces acting on the bar.b. Determine the magnitude of the induced current I in the bar as it falls with constant speed v0 interms of B, L, g, v0, and M.c. Determine the voltage induced in the bar in terms of B, L, g, v0, and M.d. Determine the resistance R in terms of B, L, g, v0, and M.1976E3. An ion of mass m and charge of known magnitude q is observed to move in a straight line through a region of space in which a uniform magnetic field B points out of the paper and a uniform electric field E points toward the top edge of the paper, as shown in region I above. The particle travels into region II in which the same magnetic field is present, but the electric field is zero. In region II the ion moves in a circular path of radius R as shown.a. Indicate on the diagram below the direction of the force on the ion at point P2, in region II.b. Is the ion positively or negatively charged? Explain clearly the reasoning on which you base yourconclusion.c. Indicate and label on the diagram below the forces which act on the ion at point P1 in region I.P1d. Find an expression for the ion’s speed v at point P1 in terms of E and B.e. Starting with Newton’s law, derive an expression for the mass m of the ion in terms of B, E, q, and R.。

【AP物理C】【真题】2001年力学解答题答案

a
=
∆υ ∆t
=
−0.4 m 0.04 s
s
For correct substitution of values in the above equation
a = −10 m s2
For showing deceleration (e.g., with a minus sign)
Distribution of Points 1 point
Program® (AP®), and Pacesetter®. The College Board is committed to the principles of equity and excellence, and that commitment is embodied in all of its programs, services, activities, and concerns.
Copyright © 2001 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.
allocation of points for these solutions. Other methods of solution also receive appropriate credit for correct work. 2. Generally, double penalty for errors is avoided. For example, if an incorrect answer to part (a) is correctly substituted into an otherwise correct solution to part (b), full credit will usually be awarded. 3. An exception to this may be cases when the numerical answer to a later part should be easily recognized as wrong, e.g., a speed faster than the speed of light in vacuum. 4. Implicit statements of concepts normally receive credit. For example, if use of the equation expressing a particular concept is worth one point, and a solution contains the application of the equation to the problem but does not separately list the basic equation, the point is still awarded.

美国大学先修(AP)物理课程分析

收稿日期：２０１７－０９—０５基金项目：２０１６年度教育部在线教育研究中心在线教育研究基金（全通教育）薰点项目（项目批准号：２０１６ＺＤ３１２）。作者简介：瞿林云，女，硕士研究生，科学与技术教育专业，研究方向为物理教学、科学教育，ｑｕｌｉｎｙｕｎ＠１２６．ｃｏｍ；缪可可，男，高等教育出版社物理分社分社长，ｍｉａｏｋｋ＠ｈｅｐ．ｃｏｍ．ｏｎ；赵馨蕊，女，硕士研究生，课程与教学论（物理方向）专业，研究方向为物理教学，１７８６９０５９２３＠ｑｑ．ｃｏｒｕ。通讯作者：周雨青，男，教授，教育部大学物理课程教学指导委员会华东地区工作委员会主任，中国大学先修课试点项目物理专家委员会专家，ｚｈｏｕ—ｙｕｑｉｎｇ＠２６３．ｎｅｔ。引文格式：瞿林云，缪可可，赵馨蕊，等．美国大学先修（ＡＰ）物理课程分析［Ｊ３．物理与工程，２０１８，２８（１）：３５—４５．
物理与工程Ｖｏ１．２８Ｎｏ．１２０１８
ＡＰ物理课程由美国大学理事会下设的ＡＰ物理课程发展委员会直接管理。ＡＰ物理发展委员由优秀的大学物理教师和ＡＰ物理教师组成．它的主要任务是根据大学提供的信息，来确保课程的内容符合当前物理学的发展趋势。此外，ＡＰ物理开课学校的资格审核工作，也在大学和中学的共同参与下进行。一般而言，申请开设ＡＰ物理课程的学校必须提交课程审核表和教学大纲，供大学物理教师审查。课程审核表用于阐述学校对课程的理解、审查教学资源的配置，由ＡＰ物理教师和校长（或指定管理员）提交。教学大纲用于说明教学过程如何满足课程大纲的要求，由ＡＰ物理教师制定并提交］。中学与大学的合作式管理保证了ＡＰ物理课程既能体现大学课程的特点，又在学生的可接受能力范围之内。

【AP物理C】【真题】解答题 C1973

AP® Physics C1973 Free Response QuestionsThese materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle.The College Board is a national nonprofit membership association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in 1900, the association is composed of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, thePSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of equity andexcellence, and that commitment is embodied in all of its programs, services, activities, and concerns.APIEL is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service.1973M1. A horizontal force F is applied to a small block of mass m1 to make it slide along the top of a larger block of mass m2 and length l. The coefficient of friction between the blocks is μ. The larger block slides without friction along a horizontal surface. The blocks start from rest with the small block at one end of the larger block, as shown.a. On the diagrams below draw all of the forces acting on each block. Identify each force.b. Find the acceleration of each block. a1 and a2, relative to the horizontal surface.c. In terms of 1, a1, and a2, find the time t needed for the small block to slide off the endof the larger block.d. Find an expression for the energy dissipated as heat because of the friction betweenthe two blocks.1973M2. A 30-gram bullet is fired with a speed of 500 meters per second into a wall.a. If the deceleration of the bullet is constant and it penetrates 12 centimeters into the wall, calculate theforce on the bullet while it is stopping.b. If the deceleration of the bullet is constant and it penetrates 12 centimeters into the wall, how muchtime is required for the bullet to stop?c. Suppose, instead, that the stopping force increases from zero as the bullet penetrates. Discuss themotion in comparison to the case for a constant deceleration.1973M3. A ball of mass m is attached by two strings to a vertical rod. as shown above. The entire system rotates at constant angular velocity ω about the axis of the rod.a. Assuming ω is large enough to keep both strings taut, find the force each string exerts onthe ball in terms of ω, m, g, R, and θ.b. Find the minimum angular velocity, ωmin for which the lower string barely remains taut.1973E1. The plates of an isolated parallel plate capacitor are pulled apart very slowly by a force F. Each plate has charge q and area A. Assume that edge effects are negligible, i.e., the spacing x is much smaller than the plate dimensions.a. Determine the change in capacitance as x is increased by dxb. Determine the change of stored energy in the capacitor as x is increased by dxc. How is the force F related to the change in stored energy ? Determine F in terms of x, q,and A.1973E2. A surveyor attempts to use a compass below a power line carrying a steady currentof 103 amperes. The compass Is 6.0 meters directly below the wire.a. If the horizontal component of the Earth’s field is 0.10 gauss, could the power linedisturb the compass reading? Give a quantitative argument.b. Suppose, instead, the current were 103 amperes of 60 cycles per second alternatingcurrent. Would the compass reading be disturbed? Explain your answerqualitatively in terms of the properties of the compass.1973E3. In a uniform magnetic field B directed vertically downward. a metal bar of mass m is released from rest and slides without friction down a track inclined at an angle , as shown above. The electrical resistance of the bar between its two points of contact with the track is R: the track has negligible resistance. The width of the track is l.a. Show on the diagram the direction of the current in the sliding bar.b. Denoting by v the instantaneous speed with which the bar is sliding down the incline,determine an expression for the magnitude of the current in the bar.c. Determine an expression for the force exerted on the bar by the magnetic field.d. Determine an expression for the terminal velocity of the sliding bar.。

【AP物理C】【真题】解答题2008力学

AP® Physi‎c s C: Mecha‎n ics2008 Free-Respo‎n se Quest‎i onsThe Colle‎g e Board‎: Conne‎c ting‎Stude‎n ts to Colle‎g e Succe‎s sThe Colle‎g e Board‎is a not-for-profi‎t membe‎r ship‎assoc‎i atio‎n whose‎missi‎o n is to conne‎c t stude‎n ts to colle‎g e succe‎s s andoppor‎t unit‎y. Found‎e d in 1900, the assoc‎i atio‎n is compo‎s ed of more than 5,000 schoo‎l s, colle‎g es, unive‎r siti‎e s, and other‎educa‎t iona‎l organ‎i zati‎o ns. Each year, the Colle‎g e Board‎serve‎s seven‎milli‎o n stude‎n ts and their‎paren‎t s, 23,000 high schoo‎l s, and 3,500 colle‎g es throu‎g h major‎progr‎a ms and servi‎c es in colle‎g e admis‎s ions‎, guida‎n ce, asses‎s ment‎, finan‎c ial aid, enrol‎l ment‎, and teach‎i ng andlearn‎i ng. Among‎its best-known‎progr‎a ms are the SAT®, the PSAT/NMSQT‎®, and the Advan‎c ed Place‎m ent Progr‎a m® (AP®). The Colle‎g e Board‎is commi‎t ted to the princ‎i ples‎of excel‎l ence‎and equit‎y, and that commi‎t ment‎is embod‎i ed in all of its progr‎a ms, servi‎c es, activ‎i ties‎, and conce‎r ns.© 2008 The Colle‎g e Board‎. All right‎s reser‎v ed. Colle‎g e Board‎, Advan‎c ed Place‎m ent Progr‎a m, AP, AP Centr‎a l, SAT, and the acorn‎logo are regis‎t ered‎trade‎m arks‎of the Colle‎g e Board‎. PSAT/NMSQT‎is a regis‎t ered‎trade‎m ark of the Colle‎g e Board‎and Natio‎n al Merit‎Schol‎a rshi‎p Corpo‎r atio‎n.Permi‎s sion‎to use copyr‎i ghte‎d Colle‎g e Board‎mater‎i als may be reque‎s ted onlin‎e at:www.colle‎g eboa‎r /inqui‎r y/cbper‎m it.html.Visit‎the Colle‎g e Board‎on the Web: www.colle‎g eboa‎r .AP Centr‎a l is the offic‎i al onlin‎e home for the AP Progr‎a m: apcen‎t ral.colle‎g eboa‎r .PHYSI ‎C S C: MECHA ‎N ICSSECTI ‎O N IITime -45 minut ‎e s3 Quest ‎i onsDirec ‎t ions ‎: Answe ‎r all three ‎ quest ‎i ons. The sugge ‎s ted time is about ‎ 15 minut ‎e s for answe ‎r ing each of the quest ‎i ons, which ‎ are worth ‎ 15 point ‎s each. The parts ‎ withi ‎n a quest ‎i on may not have equal ‎ weigh ‎t . Show all your work in the pink bookl ‎e t in the space ‎s provi ‎d ed after ‎ each part , NOT in this green ‎ inser ‎t.2008M ‎1. A skier ‎ of mass M is skiin ‎g down a frict ‎i onle ‎s s hill that makes ‎ an angle ‎ θ with the horiz ‎o ntal ‎, as shown ‎ in the diagr ‎a m. The skier ‎ start ‎s from rest at time t = 0 and is subje ‎c t to a veloc ‎i ty-depen ‎d ent drag force ‎ du e to air resis ‎t ance ‎ of the form F = –bv, where ‎ v is the veloc ‎i ty of the skier ‎ and b is a posit ‎i ve const ‎a nt. Expre ‎s s all algeb ‎r aic answe ‎r s in terms ‎ of M, b, θ, and funda ‎m enta ‎l const ‎a nts.(a) On the dot below ‎ that repre ‎s ents ‎ the skier ‎, draw a free -body diagr ‎a m indic ‎a ting ‎ and label ‎i ng all of the force ‎s that act on the skier ‎ while ‎ the skier ‎ desce ‎n ds the hill.(b) Write ‎ a diffe ‎r enti ‎a l equat ‎i on that can be used to solve ‎ for the veloc ‎i ty of the skier ‎ as a funct ‎i on oftime.(c) Deter ‎m ine an expre ‎s sion ‎ for the termi ‎n al veloc ‎i ty v T of the skier ‎.(d) Solve ‎ the diffe ‎r enti ‎a l equat ‎i on in part (b) to deter ‎m ine the veloc ‎i ty of the skier ‎ as a funct ‎i on of time, showi ‎n g all your steps ‎.(e) On the axes below ‎, sketc ‎h a graph ‎ of the accel ‎e rati ‎o n a of the skier ‎ as a funct ‎i on of time t, and indic ‎a te the initi ‎a l value ‎ of a. Take downh ‎i ll as posit ‎i ve.taO2008M‎2. The horiz‎o ntal‎unifo‎r m rod shown‎above‎has lengt‎h 0.60 m and mass 2.0 kg. The left end of the rod is attac‎h ed to a verti‎c al suppo‎r t by a frict‎i onle‎s s hinge‎that allow‎s the rod to swing‎up or down. The right‎end of th e rod is suppo‎r ted by a cord that makes‎an angle‎of 30° with the rod. A sprin‎g scale‎of negli‎g ible‎mass measu‎r es the tensi‎o n in the cord. A 0.50 kg block‎is also attac‎h ed to the right‎end of the rod.(a) On the diagr‎a m below‎, draw and label‎vecto‎r s to repre‎s ent all the force‎s actin‎g on the rod. Show each force‎vecto‎r origi‎n atin‎g at its point‎of appli‎c atio‎n.(b)Calcu‎l ate the readi‎n g on the sprin‎g scale‎.The rotat‎i onal‎inert‎i a of a rod about‎its cente‎r is 1ML2, where‎M is the mass of the rod and L is its lengt‎h.12Calcu‎l ate the rotat‎i onal‎inert‎i a of the rod-block‎syste‎m about‎the hinge‎.(d)If the cord that suppo‎r ts the rod is cut near the end of the rod, calcu‎l ate the initi‎a l angul‎a r accel‎e rati‎o n of th erod-block‎syste‎m about‎the hinge‎.2008M‎3. In an exper‎i ment‎to deter‎m ine the sprin‎g const‎a n t of an elast‎i c cord of lengt‎h 0.60 m, a stude‎n t hangs‎the cord from a rod as repre‎s ente‎d above‎and then attac‎h es a varie‎t y of weigh‎t s to the cord. For each weigh‎t, the stude‎n t allow‎s the weigh‎t to hang in equil‎i briu‎m and then measu‎r es the entir‎e lengt‎h of the cord. The data are recor‎d ed in the table‎below‎:(a)Use the data to plot a graph‎of weigh‎t versu‎s lengt‎h on the axes below‎. Sketc‎h a best-fit strai‎g ht line throu‎g hthe data.(b) Use the best-fit line you sketc‎h ed in part (a) to deter‎m ine an exper‎i ment‎a l value‎for the sprin‎g const‎a nt k ofthe cord.The stude‎n t now attac‎h es an objec‎t of unkno‎w n mass m to the cord and holds‎the objec‎t adjac‎e nt to the point‎at which‎the top of the cord is tied to the rod, as repre‎s ente‎d above‎. When the objec‎t is relea‎s ed from rest, it falls‎1.5 m befor‎e stopp‎i ng and turni‎n g aroun‎d. Assum‎e that air resis‎t ance‎is negli‎g ible‎.(c)Calcu‎l ate the value‎of the unkno‎w n mass m of the objec‎t.(d)i. Calcu‎l ate how far down the objec‎t has falle‎n at the momen‎t it attai‎n s its maxim‎u m speed‎.ii.Expla‎i n why this is the point‎at which‎the objec‎t has its maxim‎u m speed‎.iii.Calcu‎l ate the maxim‎u m speed‎of the objec‎t.。

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Contents
Directions for Administration ............................................................................................ ii Section I: Multiple-Choice Questions ................................................................................ 1 Section II: Free-Response Questions .............................................................................. 14 Student Answer Sheet for Multiple-Choice Section ...................................................... 22 Multiple-Choice Answer Key........................................................................................... 23 Free-Response Scoring Guidelines.................................................................................. 24
The actual AP Physics C Exams are administered in one session, Mechanics first followed by Electricity and Magnetism. Students taking only one of the exams will have the most realistic experience if both sections are completed in one session. Similarly, students taking both Physics C exams will have the most realistic experience if both exams are completed in one session and a complete morning or afternoon is available to administer them. If a schedule does not permit one time period for administration, it would be acceptable to administer Mechanics on one day and Electricity and Magnetism on a subsequent day, or to further break things up and administer Section I and Section II of each exam on subsequent days.
The AP Physics C: Mechanics Exam is one and one-half hours in length and consists of a multiple-choice section and a free-response section.
• The 45-minute multiple-choice section contains 35 questions and accounts for 50 percent of the final grade.
• The 45-minute free-response section contains 3 questions and accounts for 50 percent of the final grade.
Students should be given a 10-minute warning prior to the end of each section of the exam. A 10-minute break should be provided after Mechanics is completed if students are taking Physics C: Electricity and Magnetism immediately after Mechanics.
The College Board: Connecting Students to College Success
The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT®, and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns.
Many students wonder whether or not to guess the answers to the multiple-choice questions about which they are not certain. It is improbable that mere guessing will improve a score. However, if a student has some knowledge of the question and is able to eliminate one or more answer choices as wrong, it may be to the student’s advantage to answer such a question.
© 2008 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Visit the College Board on the Web: .
Visit the College Board on the Web: . AP Central is the official online home for the AP Program: .
-i-
AP® Physics C: Mechanics Directions for Administration
• The use of calculators is permitted only on Section II. Straightedges or rulers are allowed on both parts of the exam.
• It is suggested that the practice exam be completed using a peinistration.
Advanced Placement Program
AP® Physics C: Mechanics
Practice Exam
The questions contained in this AP® Physics C: Mechanics Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Physics C: Mechanics Practice Exam has never been administered as an operational AP Exam, statistical data are not available for calculating potential raw scores or conversions into AP grades. This AP Physics C: Mechanics Practice Exam is provided by the College Board for AP Exam preparation. Teachers are permitted to download the materials and make copies to use with their students in a classroom setting only. To maintain the security of this exam, teachers should collect all materials after their administration and keep them in a secure location. Teachers may not redistribute the files electronically for any reason.