This exam consists of 25 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 87. The exam period was 90 minutes; the average score was 68.4; the median score was 70. Click here to see page1 page2 of the formula sheet that came with the exam.

A block of mass m_{1} = 3 kg is attached by a rope passed over a pulley to another block of mass m_{3} = 8 kg, as shown in the figure below. The first block slides on a frictionless table surface. The pulley is a uniform cylinder of mass m_{2} and radius 12 cm ( I = ½ M R^{2} ). The suspended block accelerates downward with an acceleration a = 6.7 m/s^{2}.

Compute T_{2}

(a) T_{2} = 10.9 N (b) T_{2} = 24.8 N (c) T_{2} = 39.7 N (d) T_{2} = 43.5 N (e) T_{2} = 58.4 N

(a) 0.5 kg (b) 0.8 kg (c) 1.1 kg (d) 1.4 kg (e) 1.7 kg

(a) smaller than 6.7 m/s^{2}. (b) equal to 6.7 m/s^{2}. (c) larger than 6.7 m/s^{2}.

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

A uniform disc of mass M = 20 kg and radius R = 60 cm is rotating about an axis through the center as shown in the figure, with an angular velocity ω = 120 rad/s. A block of mass m = 3 kg falls vertically on the top surface of the disc at a distance r = 35 cm from the axis of rotation and sticks to the surface.

What is the angular velocity of the disc and the block after the block has fallen on the disc?

(a) 69 rad/s (b) 83 rad/s (c) 109 rad/s

(a) smaller than ω_{f}. (b) equal to ω_{f}. (c) larger than ω_{f}.

A sphere of radius R = 30 cm is initially rotating at an angular speed of 250 revolutions per minute (rpm). A tangential force is applied to the sphere. As a result, the sphere slows down with a constant angular acceleration of 3 rad/s^{2}.

How long does it take for the sphere to stop?

(a) 8.7 s (b) 12.1 s (c) 15.9 s

(a) 10.3 revolutions (b) 18.1 revolutions (c) 23.4 revolutions

(a) less than n revolutions. (b) n revolutions. (c) more than n revolutions.

To lift a small sunken ship from the bottom of the ocean two ballasts of equal volumes are attached to the ship. The ballast are filled with air. The mass of the ship is 50,000 kg and the mass of each ballast is 50 kg. The density of ocean water is 1027 kg/m^{3}. The density of air is 1.25 kg/m^{3}.

What is the minimum volume V each ballast should be in order to lift the ship to the surface of the ocean?

(a) V = 13.3 m^{3} (b) V = 24.4 m^{3} (c) V = 36.6 m^{3} (d) V = 47.7 m^{3} (e) V = 51.1 m^{3}

(a) F_{B} would increase. (b) F_{B} would stay the same. (c) F_{B} would decrease.

A block of unknown mass M is attached to the ceiling by a spring with force constant k = 130 N/m. A force of 200 N is applied to the block compressing the spring from its equilibrium position. At time t = 0, the force is removed and the block starts to oscillate up and down with angular frequency ω = 1.4 s^{-1}.

What is the maximum compression of the spring during these oscillations?

(a) 0.72 m (b) 1.23 m (c) 1.54 m

(a) M = 38 kg (b) M = 66 kg (c) M = 92 kg

(a) y(t) = -y_{max} sin(ωt) (b) y(t) = -y_{max} cos(ωt) (c) y(t) = +y_{max} cos(ωt)

(a) 154 J (b) 189 J (c) 237 J

(a) ω > 1.4 s^{-1} (b) ω = 1.4 s^{-1} (c) ω < 1.4 s^{-1}

A large container with height 0.5 m is filled with water ( ρ = 1000 kg/m^{3} ). A pipe is attached to the reservoir and is plugged at the far end as shown in the figure so the water is not flowing. In regions a, and b the pipe has a diameter 0.04 m. Region c has a slight constriction reducing the diameter to 0.03 m.

Calculate ΔP, the pressure difference between the top of the container, and the bottom of the container.

(a) ΔP = 2300 N/m^{2} (b) ΔP = 3900 N/m^{2} (c) ΔP = 4900 N/m^{2}

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

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

(a) v_{c} = 1.5 m/s (b) v_{c} = 2 m/s (c) v_{c} = 3.6 m/s

A grandfather clock keeps time with a simple pendulum. Unfortunately the clock is running fast, (e.g. the period of the motion is 0.9 sec).

Which of the following changes could improve the clock’s performance?

(a) increase the length of the pendulum (b) decrease the length of the pendulum (c) increase the amplitude of the pendulum’s swing

(a) slower. (b) at the same rate. (c) faster.

A hydraulic lift consists of a narrow piston (diameter 0.25 m) connected to a large piston (diameter 1.5 m). A 500 Kg mass is placed on the large platform as shown in the diagram.

Calculate F the minimum force which must be applied to the small piston necessary to lift the 500 Kg block.

(a) 85 N (b) 136 N (c) 269 N (d) 490 N (e) 770 N

(a) h = 2.8 cm (b) h = 47.3 cm (c) h = 100 cm