This exam consists of 25 questions; true-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 111. When the exam was given, the minimum "A" score was 99; the minimum "B" was 85; the minimum "C" was 72; the minimum "D" was 55. The mean was 92.3; the median was 96. Click here to see the formula sheet that came with the exam.

(a) block 1 (b) block 2 (c) They end up with the same momentum.

(a) v/3 in +x direction (b) v/3 in –x direction (c) 2v/3 in +x direction (d) 2v/3 in –x direction (e) impossible to answer with the information given

(a) hoop (b) disk (c) sphere

Block A of mass M initially moves in the +x direction with velocity v. Block B of mass 3M is initially at rest. The two blocks collide, but do not stick together. After the collision Block B moves in the +x direction with velocity v/2. The surface is frictionless.

What is the momentum of block B after the collistion?

(a) Mv/2 (b) Mv (c) 3Mv/2 (d) 2Mv (e) 3Mv

(a) v/2 in +x direction (b) v/2 in –x direction (c) 0

(a) 2800 N (b) 5100 N (c) 6667 N (d) 12000 N (e) 18667 N

What is the height h_{1}?

(a) h_{0} (b) 2h_{0} (c) 4h_{0} (d) h_{0}/2 (e) h_{0}/4

Block 1 of mass 2 kg initially moves in the +x direction with velocity 4 m/s. Block 2 of mass 1 kg initially moves in the –x direction with velocity 6 m/s. The two blocks collide and stick together.

In what direction do the two blocks move after the collision?

(a) +x (b) –x (c) They are at rest.

(a) 25° (b) 37° (c) 45° (d) 53° (e) 62°

A car is traveling with speed V down a straight road. The wheels have a radius of 0.20 m and roll without slipping on the ground. The initial angular velocity of the wheels is w_{0}=100 rad/s.

What is the initial speed V of the car?

(a) 5 m/s (b) 10 m/s (c) 15 m/s (d) 20 m/s (e) 25 m/s

(a) 14.2 rad/s^{2} (b) 19.4 rad/s^{2} (c) 26.5 rad/s^{2} (d) 28.3 rad/s^{2} (e) 34.8 rad/s^{2}

(a) N = 30 (b) N = 60 (c) N = 120

A uniform plank of length 6 m and weight 450 N rests horizontally on two supports, as shown in the drawing, with 2 m of the plank hanging over the right support.

To what distance x can a person who weights 900 N walk on the overhanging part of the plank before it just begins to tip?

(a) 0.3 m (b) 0.5 m (c) 0.7 m (d) 0.8 m (e) 0.9 m

(a) F_{N} = 34 N (b) F_{N} = 63 N (c) F_{N} = 45 N (d) F_{N} = 97 N (e) F_{N} = 112 N

How does the tension in the string compare in each case?

(a) T_{1}>T_{2} (b) T_{1}<T_{2} (c) T_{1}=T_{2}

(a) object A (b) object B (c) Both objects have the same moment of inertia about the x axis.

A uniform disk of mass M = 3 kg and radius R = 0.08 m spins with an initial angular velocity of w_{0} = 2000 rad/s.

An external torque t is applied to the disk that slows it with a constant angular acceleration of a = -65 rad/s^{2}. What is the magnitude of the applied torque?

(a) t = 1.94 N-m (b) t = 0.26 N-m (c) t = 2.18 N-m (d) t = 1.35 N-m (e) t = 0.62 N-m

(a) 43 s (b) 31 s (c) 28 s (d) 22 s (e) 16 s

(a) W_{tot} = ^{1}/_{4} MR^{2}w_{0}^{2} (b) W_{tot} = ^{1}/_{2} MR^{2}w_{0}^{2} (c) W_{tot} = 0

Starting from rest, a 4 kg ball (solid sphere) rolls without slipping down a ramp. At the bottom of the ramp the total kinetic energy of the ball is 100 J, and speed of the ball is V_{1}.

The total kinetic energy of the ball is due to both rotation and translation (i.e. KE_{TOT} = KE_{TRANS} + KE_{ROT}). How do the magnitudes of these compare?

(a) KE_{TRANS} > KE_{ROT} (b) KE_{TRANS} < KE_{ROT} (c) KE_{TRANS} = KE_{ROT}

(a) H = 1.48 m (b) H = 2.12 m (c) H = 2.55 m (d) H = 3.04 m (e) H = 3.22 m

(a) V > V_{1} (b) V < V_{1} (c) V = V_{1}

A system is composed of two identical disks. Initially, the bottom disk is rotating with angular velocity w_{0} around a fixed frictionless axle, and the top disk is at rest. The top disk is now dropped onto the bottom one, and eventually both disks rotate with the same final angular velocity w_{f} (around the same axis). There is no net external torque acting on the two-disk system.

Compare the final angular momentum of the system, L_{F}, to the initial angular momentum of the system, L_{I}.

(a) L_{F} = L_{I} (b) L_{F} = L_{I} / 2 (c) L_{F }= L_{I} / 4

(a) w_{f} = w_{0} (b) w_{f} = w_{0} / 2 (c) w_{f} = w_{0} / 4

(a) KE_{F} = KE_{I} (b) KE_{F} = KE_{I} / 2 (c) KE_{F }= KE_{I} / 4