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 110. The exam period was 90 minutes. The mean score was 85.1; the median was 89. Click here to see the formula sheet that came with the exam.

A puck of mass 1 kg collides with a wall. The puck will explode if hit with a force greater than 15 N. Before the collision the puck's velocity is 10 m/s. After the collision the puck's velocity is -10 m/s. Assume a constant force is applied to the puck during the collision.

What is the shortest time interval over which this puck could have been hit such that it did not explode?

(a) 2.33 s (b) 1.33 s (c) 0.33 s (d) 0.033 s (e) 0.0033 s

(a) The puck doesn't explode. (b) The puck explodes. (c) Not enough information is given to determine if the puck explodes.

A 0.001 kg bullet is fired from a gun and lodges inside a wooden block of mass 0.2 kg. The block and bullet then slide on a rough floor with a coefficient of kinetic friction μ_{k} = 0.4 before coming to rest after sliding a distance of 3 m.

Compare KE_{i}, the initial kinetic energy of the bullet, with W_{f}, the macroscopic work done by the frictional force between the block and the floor in stopping the block.

(a) KE_{i} < W_{f} (b) KE_{i} = W_{f} (c) KE_{i} > W_{f}

(a) 440 m/s (b) 680 m/s (c) 975 m/s (d) 1175 m/s (e) 1600 m/s

A 5 kg block slides on a horizontal, frictionless surface with a velocity of 2 m/s. It collides with an ideal, massless spring which is attached to a 15 kg block which is initially at rest. The spring has a spring constant of k = 50 N/m.

At the instant the spring is maximally compressed, both masses will be traveling with a common velocity of:

(a) 0.25 m/s (b) 0.5 m/s (c) 1 m/s (d) 1.5 m/s (e) 2 m/s

(a) The acceleration of the 5 kg block is 3 times the acceleration of the 15 kg block. (b) The acceleration of the 15 kg block is 3 times the acceleration of the 5 kg block. (c) The acceleration of the 5 kg block equals the acceleration of the 15 kg block.

(a) 0.24 m (b) 0.55 m (c) 0.74 m (d) 0.94 m (e) 1.32 m

A small block having a mass of 2 kg is in contact with an ideal spring of relaxed length 1 m and spring constant k = 100 N/m . The spring is compressed to a length of 0.5 m. The block is released from rest at x = 0.5 m. At x = 1 m the mass leaves the spring and comes to rest at x = 2 m. Throughout its entire motion the block slides on a rough surface with a coefficient of kinetic friction μ_{k} .

The maximum acceleration of the block occurs the instant the block begins to move.

(T) True (F) False

(a) x_{fast} = 1 m (b) x_{fast} < 1m (c) x_{fast} > 1m

(a) 0.12 (b) 0.42 (c) 0.36 (d) 0.53 (e) 0.62

A small box of mass M = 10 kg is released from rest at a height of 2 meters on a frictionless incline as shown. At the bottom of the ramp, it encounters a 1 meter long rough surface with μ_{k} = 0.25, and then a frictionless circular rise.

At what height h does the box stop on the circular rise?

(a) 2 meters (b) 1.75 meters (c) 1.50 meters (d) 1.25 meters (e) 1.0 meters

(a) |W_{gravity}| > |W_{friction}| (b) |W_{gravity}| < |W_{friction}| (c) |W_{gravity}| = |W_{friction}|

(a) KE_{1} / KE_{2} = M_{1} / M_{2} (b) KE_{1} / KE_{2} = M_{2} / M_{1} (c) KE_{1} / KE_{2} = 1

(a) 3.13 m/s (b) 77 m/s (c) 102 m/s (d) 151 m/s (e) 204 m/s

A small steel ball of mass M is attached to the end of a massless string of length L which is fixed at the opposite end. The string is pulled taut and held horizontally, as shown above. The ball is then released from rest. At the bottom of the path, the ball strikes a steel block of mass 3M initially at rest on a horizontal frictionless surface.

What is the speed of the steel ball just before the collision?

(a) sqrt(2gL) (b) sqrt(gL) (c) sqrt(L/g)

(a) 4 v / 9 (b) 2 v / 3 (c) 3 v / 4 (d) 3 v / 2 (e) v

A 6 kg box is pulled across a rough floor by a rope. There is friction between the box and the floor. The tension in the rope is T = 5 N. Consider a time interval during which the box moves a distance of 2 m, and its velocity decreases from 1.5 m/s to 0.8 m/s.

How much work is done on the box by the rope?

(a) 0 J (b) 10 J (c) -10 J

(a) -4.83 J (b) -6.91 J (c) -8.11 J (d) -9.25 J (e) -14.83 J

A glider of mass m_{1} slides on a frictionless track with initial velocity v_{1i} = 2 m/s. It hits a stationary glider of mass m_{2}. A spring attached to the first glider compresses and relaxes during the collision so that mechanical energy is conserved and the collision is elastic. The velocity of the center of mass of the system is V_{CM} = 0.3 m/s.

How does m_{1} compare to m_{2}?

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

(a) v_{1f} = -0.6 m/s (b) v_{1f} = -1.2 m/s (c) v_{1f} = -1.4 m/s (d) v_{1f} = -1.6 m/s (e) v_{1f} = -2.0 m/s

(a) m v^{2} / 2 (b) m v^{2} (c) 2 m v^{2} (d) 3 m v^{2} (e) 5 m v^{2}

A hunter with a mass of 80 kg stands on a frictionless horizontal ice surface and fires a 12 gram bullet in the horizontal direction from a 5 kg rifle. The hunter, still holding the rifle, recoils with a velocity of 0.15 m/s with respect to the ice. What must be the horizontal component of the speed of the bullet with respect to the ice?

(a) 304 m/s (b) 531 m/s (c) 1062 m/s (d) 1220 m/s (e) 1500 m/s

(a) 12.5 N (b) 1290 N (c) 12750 N

When he reaches the end of the boat (the end towards shore), how far is he from the shoreline? (Assume that there are no horizontal forces applied by the water on the boat.)

(a) He is exactly at the shoreline, where he wanted to be. (b) He is 5 meters away from the shoreline. (c) He is 10 meters away from the shoreline. (d) He is 15 meters away from the shoreline. (e) There is no unique answer because when he reaches the end of the boat, he is travelling away from the shoreline with a constant velocity.