Physics C Mechanics: Sample Multiple-Choice Questions

Most of the following sample questions, illustrative of the Physics CMechanics exarnination, have appeared in past examinations.

I/ote: Units associated with numerical quantities are abbreviated, usingthe abbreviations fisted in the table of information inc]uded with theexarns. Tq simpiify calculations, you may use g = 10 m/sz in all problems.

Di,reclions: Each of the questions or inbomplete statements below isfollowed by five suggested answers or completions. Select the one thatis best in each case.

Questi.ons 1-2

The speecl o of an automobile moving on a straight road is given inmeters per second as a function of time f in seconds by the foilowingequation:

u=4+2tg

What is the acceleration of the automobile at t = 2 s?(e) 72 m/sz(e) 16 m/s2(c) 20 m/sz(o) 24m/sz(n) 28 m/sz

How far has the automobile haveled in the interval betweenf=0andt:2s?(a) 16 m(n) 20 m(c) 24m(o) 32 m(r) 72m

t.

2.

AP Physics C: Mechanics

b.

The constant force F with compolents .F| = 3 N and tr's = 4 N,shown above, acts on a body while that body moves frorn the pointP (n = 2 m, A = 5 m) to the point Q (fr = !4 rfi, U = 1 m). Hovr muchwork does the force do on the body during this process?(a) 16 J(e) 30 J(c) 46J(o) 56 J(o) 65 J

The sum of all the external forces on a system of particles is zero.Which of the following must be true of the system?(a) The total mechanical energy is constant.(e) The total potential energy is constant.(c) The total kinetic energy is constant.(o) The total Iinear momentum is constant.(e) It is in static equilibrium.

A? Physics C: Mecha:rics

o

. Disk(behind ring)

The ring and the disk shown above have identical masses, radi_i, andvelocities, and are not atiached to each other. If the ring and the diskeach roll without slipping up an inclined plane, how will-the ciis-tances that they move up the plane before coming to rest compare?(a) The ring win move farther than will the disk(e) The disk will move farther than will the ring.(c) The ring and the disk wi_lImove equal distances.(o) The relative distemces depend on the angle of elevation of the

piane.(r) The relative distances depend on the length of the plane.

Let g be ihe acceleration due to gravity at the surface of a planet ofradius r?- which of the following is a dimensionally correct formulafor the milimuil kinetic energy -K that a projectile of mass m musthave at the planet's surface if the projectile is to escape from theplanet's gravitational fi eld?

(e) K = yfiE(n) K = lvgP

(c) K = Tng

Rto(jJ/ rt = *Lft,

(n) K: sR

10_

)-

I'

{

1989M2. Block A of mdss 2M hangs from a cord that passes over a pulley and is connected to block B ofmass 3M that is free to move on a frictionless horizontal surface, as s'hown above. The pulley is a disk withfrictionless bearings, having a radius R and moment of inertia 3MR2. Block C of mass 4M is on top ofblock B. The surface between blocks B and C is NOT frictionless. Shortly after the system is releasedfrom rest, block A moves with a downward acceleration a, and the two blocks on the table move relative toeach other.

In terms of M, g, and a, determine thea. tension Tu in the vertical section ofthe cordb. tension T1 in the horizontal section of the cord

If a : 2 meters per second squared, determine thec. coefficient ofkinetic friction between blocks B and Cd. acceleration ofblock C

1989M3. A 2-kilogram block is dropped from a height of 0.45 meter above an uncompressed spring, as

shown above. The spring has an elastic constant of 200 newtons per meter and negligible mass. The block

strikes the end of the spring and sticks to it'a. Determine the speed of the block at the instant it hits the end of the spring.

b. Determine the period of the simple harmonic motion that ensues.

c. Determine the distance that the spring is compressed at the instant the speed of the block is maximum.

d. Determine the maximum compression of the spriag.

e. Determine the amplitude of the simple harmonic motion.

0.45 m

(

HorizontalAxis

l-IF--_-s--_-__{A long, uniform rod ofmass M and length / is supported at the left end by a horizontal axis intothe page and perpendiculai to the rod, as shown above. The right end is connected to the ceilingby a thin vertical thread so that the rod is horizontal. The moment of inertia of the rod aboutthe rxis at the end of the rod isVt4/2. Express the answers to all parts of this question in termsof M, { and g.

a. Determine the magnitude and direction of the force exerted on the rod by the axis.

The thread is then bumed by a rnalch. For the time immediately after the thread breaks, determine each ofthe following:b. The angular acceleration ofthe rod about the axisc. The translational acceleration of the center of mass of the rodd. The force exerted on the end ofthe rod by the axis

The rod rotates about the axis and swings down from the horizontal position.e. Determine the angular velocity of the rod as a function of 0, the arbitrary angle through which the

rod has swung.