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. The exam period was 90 minutes; the average score was 87.0; the median score was 89. Click here to see the formula sheet that came with the exam.

A uniform disk of unknown mass M and radius R = 10 cm is free to rotate about its axis. A light cord is wrapped around the rim on the disk and then tied to a small can of mass m = 50 gm. The cord does not slip as it unwinds on the disk. When released the can moves down with acceleration 3.27 m/s^{2}. Take g = 9.81 m/s^{2}.

What is the angular acceleration of the disk?

(a) 0 rad/s^{2} (b) 8.2 rad/s^{2} (c) 65.4 rad/s^{2} (d) 16.4 rad/s^{2} (e) 32.7 rad/s^{2}

(a) 0 N (b) 0.164 N (c) 1.308 N (d) 0.327 N (e) 0.654 N

(a) 0.8 kg (b) 0.2 kg (c) 0.4 kg (d) 0.1 kg (e) 0.6 kg

(a) less than mgh. (b) equal to mgh. (c) larger than mgh.

(a) The disk. (b) The sphere. (c) They both have the same total kinetic energy.

A student on a piano stool rotates freely with an angular velocity of 20 rad/s. The student holds a 1.25-kg weight in each outstretched arm, 0.759 m from the axis of rotation. The combined moment of inertia about the rotation axis of the student and stool, without the two weights, is 5.43 kg-m^{2}, and this remains constant. Now the student pulls his arms inward to the rotation axis. What is the new angular velocity of the student?

(a) 15 rad/s (b) 20 rad/s (c) 25 rad/s (d) 30 rad/s (e) 35 rad/s

(a) greater than zero. (b) less than zero. (c) equal to zero.

A 3 kg block is attached to a massless spring and oscillates back and forth with simple harmonic motion according to the equation x(t) = 4cos(5t), where x is in meters and t is in seconds. What is the spring constant of the spring?

(a) 43 N/m (b) 12 N/m (c) 75 N/m (d) 20 N/m (e) 60 N/m

(a) 5 m/s (b) 20 m/s (c) 70 m/s (d) 100 m/s (e) 150 m/s

(a) The period will be doubled. (b) The period will be halved. (c) The period will be unchanged.

While waiting to get into the elevator that goes to the observation floor in the Sears Tower in Chicago, you suspend your keys from a thread and set the resulting pendulum oscillating. It completes exactly 90 cycles in 1 minute.

What is the length of the thread?

(a) 7 cm (b) 11 cm (c) 15 cm (d) 19 cm (e) 23 cm

(a) more than 90 cycles in 1 minute. (b) exactly 90 cycles in 1 minute. (c) less than 90 cycles in 1 minute.

A block of mass M = 11 kg and initial velocity v = 2.0 m/s slides on a frictionless horizontal surface and collides with a relaxed spring of spring constant k = 27 N/m. The other end of the spring is attached to a wall, as shown in the figure.

What is the maximum compression of the spring?

(a) 0.3 m (b) 0.7 m (c) 1.0 m (d) 1.3 m (e) 1.6 m

(a) 4 x (b) x / 2 (c) 2 x

A raft is 4.2 m wide and 6.5 m long and it floats on water (density of water = 1000 kg/m^{3}). When a horse is loaded onto the raft, it sinks an additional 0.027 m deeper into the water. What is the weight of the horse?

(a) 7200 N (b) 1400 N (c) 2400 N (d) 9500 N (e) 5700 N

(a) less than 0.027 m. (b) equal to 0.027 m. (c) greater than 0.027 m.

(a) 0.25 kg/m^{3} (b) 0.45 kg/m^{3} (c) 0.62 kg/m^{3} (d) 0.79 kg/m^{3} (e) 1.36 kg/m^{3}

(a) 0.85 × 10^{5} Pa (b) 0.91 × 10^{5} Pa (c) 0.99 × 10^{5} Pa (d) 1.02 × 10^{5} Pa (e) 1.05 × 10^{5} Pa

Water (density = 1000 kg/m^{2}) flows through a horizontal tube of diameter 2.8 cm that is joined to a second horizontal tube of diameter 1.6 cm. The pressure difference between the two tubes is 7.5 kPa. Which tube has the higher pressure?

(a) the one with the larger diameter. (b) the one with the smaller diameter

(a) 1.75 V (b) 3.06 V (c) 0.33 V

(a) 0.15 m/s (b) 1.9 m/s (c) 2.4 m/s (d) 1.0 m/s (e) 1.3 m/s

Early in the morning, when the temperature is 5.0°C, gasoline is pumped into the 51-liter steel tank of a car until it is filled to the top. Later in the day the temperature rises to 25°C. Given that the coefficient of volume expansion is 0.95 × 10^{-3} °C^{-1} for gasoline and 0.036 × 10^{-3} °C^{-1} for steel, how much gasoline spills out of the tank?

(a) 0.25 L (b) 0.67 L (c) 0.93 L (d) 1.7 L (e) 2.5 L

(a) greater. (b) less. (c) the same.

A 100 g ice cube having an initial temperature of 0°C is put into an insulated cup containing 200 g of water. After a long time, all the ice is melted and the remaining water is at 0°C. Assuming no heat flows into or out of the cup, what was the initial temperature of the water?

(a) 10°C (b) 20°C (c) 30°C (d) 40°C (e) 50°C

(a) a mixture of water and ice at 0°C (b) a mixture of water and ice at a temperature higher than 0°C (c) water at a temperature higher than 0°C

(a) The bucket with the aluminum block. (b) The bucket with the steel block. (c) Both buckets will be at the same temperature.