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. The exam period was 90 minutes. THe mean score was 86.2; the median was 89. Click here to see the formula sheet that came with the exam.

(T) True (F) False

A small block having a mass 0.1 kg starts at rest at the top of a frictionless track a height 1.7 m above the horizontal floor. It slides down the track and then around a loop-the-loop having a diameter of 0.6 m.

What is the normal force exerted by the track on the small block as it goes around the top of the loop?

(a) 6.2 N (b) 5.6 N (c) 4.9 N (d) 3.8 N (e) 2.4 N

(a) 6.6 × 10^{2} N/m (b) 8.6 × 10^{2} N/m (c) 1.3 × 10^{3} N/m (d) 1.8 × 10^{3} N/m (e) 2.7 × 10^{3} N/m

After the block and bullet start moving to the right, a second bullet of mass m is now fired horizontally from the right with an initial speed v_{0} toward the block. The second bullet hits the block and becomes lodged inside it.

Which one of the following describes the motion of the block after both bullets are lodged inside it?

(a) The final velocity is to the left. (b) The final velocity is zero. (c) The final velocity is to the right.

In Figure C, the bob rises up to a height

(a) equal to the original height of the bob in Figure A. (b) greater than the original height of the bob in Figure A. (c) less than the original height of the bob in Figure A.

A planet of mass M and radius R and a smaller planet of radius R/2 and mass M/8 are separated by a distance 6R between their centers. How far from the center of the larger planet is the center of mass of this two-body system?

(a) 2 R / 3 (b) 4 R / 9 (c) R / 2 (d) 3 R / 5 (e) 3 R / 8

(a) 2.71 m/s (b) 4.13 m/s (c) 6.33 m/s (d) 8.37 m/s (e) 10.43 m/s

(a) 0.1 m (b) 0.2 m (c) 0.3 m (d) 0.4 m (e) 0.5 m

A block of mass m_{1} = 12.5 kg hangs from the ceiling on an ideal, massless spring with spring constant k = 65 N/m. With the block hanging on the spring, the total length of the spring is L = 3.5 m. When a second block with an identical mass of m_{2} = 10 kg is tied to the first with a massless string, the spring stretches an additional h_{0} = 1.5 m.

The string is cut so that mass m_{2} falls away. What is the maximum velocity of mass m_{1}?

(a) 2.77 m/s (b) 3.42 m/s (c) 4.68 m/s (d) 5.21 m/s (e) 6.39 m/s

(a) D < L - h_{0} (b) D = L - h_{0} (c) D > L - h_{0}

Two discs are free to move without friction on a horizontal table. The 0.4 kg disc is initially at the position (x = 0, y = 1.0) m, moving with velocity (v_{x} = 3.0, v_{y} = 0) m/s. The 0.6-kg disc is initially at (x = 1.5, y = 0) m, moving with velocity (v_{x} = 0, v_{y} = 2.0) m/s.

The figure displays the initial conditions for the two discs in the x-, y-coordinates.

The initial velocity of the center of mass of the two-disc system is:

(a) (v_{x}, v_{y}) = (3.0, 2.0) m/s (b) (v_{x}, v_{y}) = (2.0, 3.0) m/s (c) (v_{x}, v_{y}) = (2.7, 2.0) m/s (d) (v_{x}, v_{y}) = (1.8, 1.8) m/s (e) (v_{x}, v_{y}) = (1.2, 1.2) m/s

(a) less than before the collision (b) the same as before the collision (c) It depends on whether the collision is elastic or inelastic.

(a) 0.33 m (b) 0.50 m (c) 0.67 m (d) 0.73 m (e) 1.00 m

A box with mass M = 10 kg is pulled across a floor by a rope. There is friction between the box and the floor. The tension in the rope is T = 25 N. Consider an interval during which the box moves a distance of Δx = 3 m and its velocity increases from 2 m/s to 3 m/s.

How much work (W_{T}) is done on the box by the rope?

(a) 0 J (b) 45 J (c) 65 J (d) 75 J (e) 125 J

(a) 0 J (b) 15 J (c) 25 J (d) 65 J (e) 125 J

(a) W_{T} / (Mg Δx) (b) W_{net} / (Mg Δx) (c) Mg Δx / W_{T} (d) (W_{T} - W_{net}) / (Mg Δx) (e) (W_{net} - W_{T}) / (Mg Δx)

A man is standing at one end of a plank of length L = 10 m. The man has mass M_{man} = 100 kg and the plank has mass M_{plank} = 40 kg and the plank is atop a frictionless sheet of ice. At the other end of the plank sits a large rock of mass M_{rock} = 200 kg. The center of mass of the man+plank+rock is 6.5 m from the end of the plank where the man is standing.

The man walks to the other end of the plank and sits down on the rock. How far did the plank move along the ice?

(a) 0 m (b) 1.3 m (c) 1.7 m (d) 2.9 m (e) 3.3 m

A glider of mass m_{1} = 0.4 kg slides on a frictionless track with initial velocity v_{1,i} = 1.8 m/s. It hits a stationary glider of mass m_{2} = 0.8 kg. A spring attached to the first glider makes the collision elastic. What are the final velocities of the gliders?

(a) v_{1,f} = -0.6 m/s, v_{2,f} = 1.2 m/s (b) v_{1,f} = -0.2 m/s, v_{2,f} = 0.8 m/s (c) v_{1,f} = -1.4 m/s, v_{2,f} = 2.2 m/s (d) v_{1,f} = -0.4 m/s, v_{2,f} = 0.4 m/s (e) v_{1,f} = -1.4 m/s, v_{2,f} = 1.0 m/s

(a) increase. (b) decrease. (c) stay the same.

(a) Kinetic energy and momentum are conserved in the collision. (b) Kinetic energy is conserved, but momentum is not conserved in the collision. (c) Momentum is conserved, but kinetic energy is not conserved in the collision.

Two identical disks of mass M are sitting atop a frictionless table. For disk number 1, a string is attached to the center of mass of the disk. For disk number 2, the string is wrapped around the disk. Each string is pulled on by a force F which has the same direction and magnitude for both disks. The center of mass of disk 1 has acceleration A_{1} and the center of mass of disk 2 has acceleration A_{2} as shown in the figure.

How do A_{1} and A_{2} compare?

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

(a) P_{3} > P_{4} (b) P_{3} = P_{4} (c) P_{3} < P_{4}