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 99. The exam period was 90 minutes. The mean score was 81.2; the median was 84. Click here to see the formula sheet that came with the exam.

Two ice skaters of mass 70 kg and 50 kg, each having an initial velocity of 10 m/s in the directions shown, collide and fall and slide across the ice together. The ice surface is horizontal and frictionless.

What is the speed of the skaters after the collision?

(a) V = 0 m/s (b) V = 1.7 m/s (c) V = 2.7 m/s (d) V = 10 m/s (e) V = 20 m/s

(a) θ; = 41° (b) θ = 28° (c) θ = 25°

A cart of mass M = 9 kg rolls without friction on a horizontal surface. It is attached through a freely pivoting initially-horizontal massless rod of length L to a ball of mass m = 3 kg. The system is initially at rest when the ball is released. The pendulum swings down and to the left, and at the bottom of its swing the ball is observed to have a velocity of 3.5 m/sec to the left.

Which one of the following remain constant as the pendulum swings down?

(a) horizontal component of the momentum of the ball (b) horizontal component of the momentum of the cart (c) horizontal component of the momentum of the ball + cart

(a) V_{cart} = 1.17 m/s (b) V_{cart} = 1.75 m/s (c) V_{cart} = 2.44 m/s (d) V_{cart} = 2.91 m/s (e) V_{cart} = 3.37 m/s

(a) 0.59 m (b) 0.83 m (c) 1.18 m

(a) L / 2 (b) L / 3 (c) L / 4

(a) 12,900 m/s (b) 18,300 m/s (c) 23,700 m/s (d) 29,200 m/s (e) 33,800 m/s

(a) 5.8 m to the right (b) 3.2 m to the right (c) The boat does not move. (d) 3.2 m to left (e) 5.8 m to left

(a) x_{cm } = 0.50 m (b) x_{cm } = 0.58 m (c) x_{cm } = 0.76 m

An artillery shell of mass 20 kg is fired from a rail car which is initially at rest on a horizontal frictionless track. The combined mass of the car and cannon is 2000 kg. As viewed by someone on the ground the shell moves with an initial speed of 300 m/s at an angle of 27° above the horizontal and the rail car recoils to the right.

Relative to the ground, what is the speed of the rail car after the shell is fired?

(a) 1.36 m/s (b) 2.67 m/s (c) 3.00 m/s

(a) 200 N (b) 2,300 N (c) 15,000 N (d) 90,000 N (e) 200,000 N

A block of mass m = 1.8 kg starts at rest on a rough inclined plane a height H = 8 m above the ground. It slides down the plane, across a frictionless horizontal floor, and then around a frictionless loop-the-loop of radius R = 2.0 m. On the floor the speed of the block is observed to be 11 m/s.

What is the work done by friction on the block as it slides down the inclined plane?

(a) -49 J (b) -28 J (c) -78 J (d) -23 J (e) -32 J

(a) 0 N (b) 5.1 N (c) 9.8 N (d) 17.6 N (e) 20.6 N

A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5 meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.

What is the speed of the box at the bottom of the ramp?

(a) 5.4 m/s (b) 3.7 m/s (c) 2.8 m/s

(a) 0.50 m (b) 0.66 m (c) 0.83 m (d) 0.94 m (e) 1.21 m

(a) 1.1 m (b) 1.3 m (c) 1.5 m

Consider the following two cases:

In case 1 a ball of mass m is thrown horizontally with speed v_{0} at a stationary box of mass M. The ball bounces off the box and after the collision the box is moving to the right with V_{1} and the ball is moving to the left with speed v_{f} .

In case 2 a ball of mass m is thrown horizontally with speed v_{0} at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is moving to the right with speed V_{2}. In both cases the box slides without friction. Assume all motion is horizontal.

In which case is the change in momentum of the ball the biggest?

(a) Case 1 (b) Case 2 (c) The change in momentum of the ball is the same in both cases.

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

(a) M/m = 1/2 (b) M/m = 3/4 (c) M/m = 4/3 (d) M/m = 3/2 (e) M/m = 2

(a) V_{1}/v_{0} = 3M / 2m (b) V_{1}/v_{0} = 2M / 3m (c) V_{1}/v_{0} = 3m / 2M (d) V_{1}/v_{0} = 2m / 3M (e) V_{1}/v_{0} = m / 2M

Two blocks of mass m_{A} and m_{B} are placed side by side on a frictionless horizontal table. At time t_{0} both blocks are at rest and a constant force of the same magnitude is applied to each of the blocks. Block A has a smaller mass than block B (m_{A} < m_{B}).

How do the momenta of the two blocks compare 5 seconds after t_{0}?

(a) p_{A} < p_{B} (b) p_{A} > p_{B} (c) p_{A} = p_{B}

(a) K_{A} < K_{B} (b) K_{A} > K_{B} (c) K_{A} = K_{B}

(a) p_{A} = p_{B} (b) K_{A} = K_{B} (c) both of the above