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 108. The exam period was 90 minutes. The mean score was 78.1; the median was 79. Click here to see the formula sheet that came with the exam.

(a) (V_{x}, V_{y}) = (6.3 m/s, 1.6 m/s) (b) (V_{x}, V_{y}) = (2.8 m/s, 4.9 m/s) (c) (V_{x}, V_{y}) = (8.6 m/s, 2.6 m/s) (d) (V_{x}, V_{y}) = (9.3 m/s, 5.3 m/s) (e) (V_{x}, V_{y}) = (4.6 m/s, 1.4 m/s)

(a) |s_{cm}| < 75 mph (b) |s_{cm}| = 75 mph (c) |s_{cm}| > 75 mph

A 4.0 kg circular disk slides in the x-direction on a frictionless horizontal surface with a speed of 5.0 m/s. It collides with an identical disk that is at rest before the collision. The collision is elastic. Disk 1 goes off at an angle of 60° with respect to the x-direction. Disk 2 goes off at an angle of 30° with respect to the x-direction. Treat the disks as point objects and ignore the possible rotations of the disks.

Which one of the following statements is correct?

(a) Disk 1 has the greater kinetic energy after the collision. (b) Disk 2 has the greater kinetic energy after the collision. (c) The kinetic energies of the two disks are equal after the collision.

(a) 2.5 m/s (b) 2.8 m/s (c) 3.3 m/s (d) 3.9 m/s (e) 4.3 m/s

(a) 0 J (b) 25 J (c) 50 J (d) 75 J (e) 100 J

In a Physics 211 laboratory experiment one end of a string is tied to a cart. The other end of the string is tied to a force probe that is fixed to the track. The cart is free to move on the track. Initially the string is slack. The cart is given a velocity v_{o} and the magnitude of the momentum of the cart is 0.42 kg m/s. The experimental setup is shown below.

The string becomes taut, and a force is exerted on the cart by the string. The string then becomes slack again. The force on the cart is measured as a function of time by the force probe. The data from the force probe are shown below. The integral of force on the cart with respect to time is 0.66 kg m/s.

Find how long the string exerted a force on the cart.

(a) 0.2 s (b) 1.1 s (c) 2.4 s

(a) 0.24 kg m/s (b) 0.42 kg m/s (c) 0.66 kg m/s (d) 0.90 kg m/s (e) 1.24 kg m/s

Ricardo (R) and Maria (M) are in a canoe that is stationary and floating on a calm lake. They are 4.0 m apart, symmetrically located about the center of the canoe as shown in the figure on the left. Ricardo has mass 80 kg Maria has a mass of 62 kg. The canoe is massless and is free to move in the water without friction.

If Ricardo and Maria both move to the center of the canoe what distance d will the canoe move relative to a rock that is stationary in the water?

(a) d = 0 (The canoe will not move.) (b) d = 0.15 m (c) d = 0.25 m (d) d = 0.35 m (e) d = 0.55 m

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

A ballistic pendulum like the one demonstrated in lecture has mass M = 2 kg. The ballistic pendulum begins at rest and is struck by a ball of mass m = 0.25 kg, which sticks to the pendulum. The pendulum is observed to rise a maximum height h above its equilibrium position.

During which of the following intervals is the total horizontal momentum of the ball plus pendulum system conserved?

(a) while the ball is travelling through the air (before the collision) (b) while the ball is hitting the pendulum (during the collision) (c) while the pendulum is swinging up to its maximum height (after the collision) (d) both a. and b. (e) both b. and c.

(a) 9 m/s (b) 24 m/s (c) 27 m/s

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

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

A young boy of mass m = 25 kg sits on a coiled spring that has been compressed to a length 0.4 m shorter than its uncompressed length and then held at this length. Suddenly the spring is released, and the boy flies vertically into the air. He reaches a maximum distance 0.5 m above his initial position. The spring is ideal and massless and we ignore the air friction.

What is the spring constant k of the spring?

(a) 766.4 N/m (b) 1532.8 N/m (c) 613.1 N/m

(a) 1.1 m/s (b) 1.4 m/s (c) 1.7 m/s (d) 1.9 m/s (e) 2.1 m/s

(The mass and radius of the earth are M_{E} = 5.98 × 10^{24} kg and R_{E} = 6,380 km respectively, and Newton's gravitational constant is G = 6.67300 × 10^{-11} m^{3} kg^{-1} s^{-2}. You should ignore any effects due to air resistance and the rotation of the Earth)

(a) 6 km/s (b) 11 km/s (c) 14 km/s (d) 21 km/s (e) 25 km/s

Here is a graph from Physics 211 Lab 4. The basketball of mass m = 0.62 kg was released from the height h and it started bouncing. The numbers on the graph correspond to the maxima of its kinetic energy.

From what height h was the ball released? Ignore air friction.

(a) 1.01 m (b) 1.82 m (c) 2.23 m

(a) The step-like dependence of the "Total" energy on time demonstrates the violation of the energy conservation law. (b) The graph demonstrates that the "Total" energy is conserved throughout the entire four-second interval. (c) The step-like dependence of the "Total" energy on time corresponds to the mechanical energy dissipation via its transformation into other forms.

What is the speed V_{2} of the ball when it reaches a point in its swing which is level with O_{2}?

(a) 2.21 m/s (b) 3.96 m/s (c) 4.29 m/s (d) 4.83 m/s (e) 5.11 m/s

How much work W is done on this spring when it is stretched by an amount x from its relaxed position?

(a) W = (1/2)Kx^{2} (b) W = (1/3)Kx^{3} (c) W = (1/4)Kx^{4}

During a time interval Δt the magnitude of the work W done by the frictional force is

(a) |W| = Mg tanθ (VΔt) (b) |W| = Mg sinθ (VΔt) (c) unknown, since the coefficient of kinetic friction is not given.

A box of mass M slides on a horizontal floor with initial speed V_{0}. The kinetic coefficient of friction between the box and the floor is μ_{k}.

After sliding a distance D the speed of the box is ¾V_{0}. What is the magnitude of the macroscopic work W done by the frictional force on the box during this motion?

(a) |W| = (1/4) MV_{0}^{2} (b) |W| = (7/32) MV_{0}^{2} (c) |W| = (3/4) MV_{0}^{2} (d) |W| = (3/4) Mgμ_{k}D (e) |W| = Mgμ_{k} / D

(a) V_{1} < ¾ V_{0} (b) V_{1} = ¾ V_{0} (c) V_{1} > ¾ V_{0}

Identical constant forces push two blocks A and B over identical horizontal surfaces for identical periods of time. The masses are initially at rest. The mass of A is twice the mass of B.

Which block ends up with the biggest momentum?

(a) block A (b) block B (c) Both blocks end up with the same momentum.

(a) block A (b) block B (c) Both blocks end up with the same kinetic energy.

(a) 0.6 kg (b) 0.8 kg (c) 1.2 kg (d) 1.8 kg (e) 2.4 kg