This exam consists of 26 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 119. When the exam was given, the minimum "A" score was 106; the minimum "B" was 92; the minimum "C" was 77; the minimum "D" was 59. The mean was 97.8; the median was 101. Click here to see the formula sheet that came with the exam.

A solid spherical ball with mass M = 7 kg, radius R = 0.3 m, and initial velocity v_{i} = 5 m/s rolls without slipping up a ramp. (Recall I = 2/5 M R^{2} for a solid sphere.)

Calculate L_{i}, the initial angular momentum of the ball around its rotation axis before it goes up the ramp.

(a) L_{i} = 3.57 kg m^{2}/s (b) L_{i} = 4.20 kg m^{2}/s (c) L_{i} = 8.62 kg m^{2}/s (d) L_{i} = 13.3 kg m^{2}/s (e) L_{i} = 35 kg m^{2}/s

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

(a) E = 67.5 J (b) E = 84.3 J (c) E = 98.1 J (d) E = 123 J (e) E = 152 J

(a) v_{f} = 1.49 m/s (b) v_{f} = 3.15 m/s (c) v_{f} = 3.81 m/s (d) v_{f} = 4.10 m/s (e) v_{f} = 5.00 m/s

(a) v_{hoop} < v_{ball} (b) v_{hoop} = v_{ball} (c) v_{hoop} > v_{ball}

Mats is standing on a turntable in class holding a weight in each hand a distance 0.75 meters from the center of his body. He is originally rotating with an angular frequency w = 0.3 rad/s. He pulls the weights in so they are only 0.25 meters from the axis of rotation. The original moment of inertia of Mats, the turntable and the weights is I_{o} = 8 kg m^{2}. The final moment of inertia of Mats, the turntable and the weights is I_{f} = 5 kg m^{2}. (For these four questions, assume that friction doesn't dissipate any energy.)

Calculate the original moment of inertia I for the two weights held a distance of d = 0.75 meters from Mats. (Treat the weights as point particles).

(a) I = 2.90 kg m^{2} (b) I = 3.38 kg m^{2} (c) I = 4.82 kg m^{2} (d) I = 5.26 kg m^{2} (e) I = 6.00 kg m^{2}

(a) w_{f} = 0.30 rad/s (b) w_{f} = 0.39 rad/s (c) w_{f} = 0.48 rad/s (d) w_{f} = 0.63 rad/s (e) w_{f} = 0.91 rad/s

(a) increases. (b) remains the same. (c) decreases.

A block of mass 3.0 kg resting on a horizontal frictionless surface is attached to a spring with force constant k = 200 N/m. A force of 300 N is applied to the block in the x-direction, thereby compressing the spring (see picture). The block is initially at rest. At time t = 0, the force is removed and the block starts to oscillate.

What is the maximum compression of the spring?

(a) 0.4 m (b) 0.9 m (c) 1.2 m (d) 1.5 m (e) 1.9 m

(a) 13 (b) 52 (c) 67 (d) 95 (e) 110

(a) x(t) = A sin(wt) (b) x(t) = A cos(wt)

Which one of these plots best represents the kinetic energy of the block as a function of time?

(a) (b) (c)

These three questions are concerned with similar physical situations. In each situation you have an oscillator with a period of 1 second on Earth. You plan to bring the oscillator to planet X, where the force of gravity is two times that on earth (g_{X} = 19.6 m/s^{2}). You want to modify the oscillator so that it will have period of 1 second on planet X. In each of the following problems below, select the modification that will best achieve this.

Your oscillator is a simple pendulum consisting of a small sphere of mass M hanging vertically from a massless string of length L.

(a) Reduce the mass to M/2. (b) Reduce the length to L/2. (c) Increase the length to 2 L. (d) Increase the length to 4 L. (e) Do nothing.

(a) Reduce the mass to M/2. (b) Reduce the spring constant to k/2. (c) Increase the spring constant to 2k. (d) Increase the spring constant to 4k. (e) Do nothing.

(a) Reduce the spring constant. (b) Increase the spring constant. (c) Do nothing.

Hose A has an inner radius of 2.4 cm, and water flows through it with a speed of 5 m/s. Using this hose, how much time t does it take to fill a pool that has a volume of 75 m^{3}?

(a) t = 8.3 x 10^{3} s (b) t = 6.2 x 10^{3} s (c) t = 3.9 x 10^{3} s (d) t = 4.4 x 10^{4} s (e) t = 5.8 x 10^{4} s

(a) r_{B} = 0.4 cm (b) r_{B} = 0.8 cm (c) r_{B} = 0.6 cm (d) r_{B} = 1.2 cm (e) r_{B} = 1.6 cm

(a) P_{A} - P_{B} = -1.5 x 10^{6} Pa (b) P_{A} - P_{B} = -1.0 x 10^{6} Pa (c) P_{A} - P_{B} = 0 Pa (d) P_{A} - P_{B} = +1.0 x 10^{6} Pa (e) P_{A} - P_{B} = +1.5 x 10^{6} Pa

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

(a) Slightly above the line. (b) Slightly below the line. (c) At the line (unchanged).

(a) Ordinary water. (b) Salt water. (c) The same.

(a) 9.81 x 10^{4} Pa (b) 6.13 x 10^{4} Pa (c) 2.20 x 10^{5} Pa (d) 1.72 x 10^{5} Pa (e) 1.35 x 10^{5} Pa

Suppose you tie an aluminum block that has a volume of 0.004 m^{3} on the end of a string, and lower the block until it is completely submerged, hanging at rest just below the surface of the water. What is the tension T_{0} in the string? (The density of aluminum is 2700 kg/m^{3}).

(a) T_{0} = 39.2 N (b) T_{0} = 78.3 N (c) T_{0} = 66.7 N (d) T_{0} = 106 N (e) T_{0} = 137 N

(a) Greater than T_{0}. (b) Less than T_{0}. (c) Equal to T_{0}.