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 102. The exam period was 90 minutes; the average score was 79.0; the median score was 83. Click here to see page1 page2 of the formula sheet that came with the exam.

Unless told otherwise, you should assume that the acceleration of gravity near the surface of the earth is 9.8 m/s^{2} downward and ignore any effects due to air resistance.

A 3 kg pendulum is placed on an elevator next to a 3 kg mass hung vertically by a spring with spring constant 200 N/m. When the elevator is at rest, the pendulum and the mass on the spring oscillate with the same period.

What is the length of the pendulum?

(a) 9 cm (b) 15 cm (c) 23 cm (d) 27 cm (e) 32 cm

(a) 0.55 m (b) 0.69 m (c) 0.83 m

(a) 3.4 m/s (b) 4.2 m/s (c) 5.1 m/s

Compare the period of the pendulum T_{pendulum} to the period of the mass on the spring T_{masss on spring} when the elevator is accelerating up.

(a) T_{pendulum} < T_{mass on spring} (b) T_{pendulum} = T_{mass on spring} (c) T_{pendulum} > T_{mass on spring}

At an air show, a jet flies past you. The sound from the engine is 90 dB when it is 700 meters away.

How far away must the engine be, so that the intensity of the sound is reduced by a factor of 8?

(a) 8 × 700 m (b) 4 × 700 m (c) sqrt(8) × 700 m

(a) 89 dB (b) 81 dB (c) 11 dB

(a) 129 Hz (b) 240 Hz (c) 310 Hz (d) 380 Hz (e) 420 Hz

A piano string is fixed at both ends 0.78 meters apart and has a mass of 0.0028 kg.

What is the fundamental wavelength of this string?

(a) 0.39 m (b) 0.78 m (c) 1.56 m

(a) 550 N (b) 990 N (c) 1220 N (d) 1550 N (e) 1770 N

(a) 0.75 m (b) 1.56 m (c) 2.41 m

(a) 0.91 liters (b) 1.4 liters (c) 2.4 liters

(a) 5.03 × 10^{-4} liters (b) 9.54 × 10^{-3} liters (c) 14.1 × 10^{-3} liters

What is the density of Fluid B?

(a) 400 kg/m^{3} (b) 600 kg/m^{3} (c) 1000 kg/m^{3} (d) 1250 kg/m^{3} (e) 2500 kg/m^{3}

(a) 19.8 × 10^{3} N (b) 21.5 × 10^{3} N (c) 23.0 × 10^{3} N (d) 25.5 × 10^{3} N (e) 27.0 × 10^{3} N

A string holds an oak cube (ρ_{O} = 600 kg/m^{3}, volume V = 0.8 m^{3}) to the bottom of a pool. The pool is filled with water (ρ_{W} = 1000 kg/m^{3}). The tension in the string is T = 2500 N.

What is the volume of the part of the cube under water, V_{1}?

(a) V_{1} = 0.60 (b) V_{1} = 0.64 (c) V_{1 }= 0.70 (d) V_{1} = 0.74 (e) V_{1} = 0.80

(a) V_{2} / V_{ }= 0.4 (b) V_{2} / V_{ }= 0.6 (c) V_{2} / V_{ }= 0.8

(a) M = 155 kg (b) M = 205 kg (c) M = 255 kg

A hydraulic lift is filled with oil (ρ = 700 kg/m^{3}). The cross section area of the large piston in the cylinder on the right is A_{2} = 180 cm^{2}. The area of the small piston in the cylinder on the left is A_{1} = 0.4 cm^{2}.

What force F_{1} do we need to apply to the small piston to lift a 20000 N weight so the bottom of both pistons is at the same height?

(a) F_{1} = 4.44 N (b) F_{1} = 44.44 N (c) F_{1} = 444.44 N

(a) 0.055 cm (b) 0.075 cm (c) 103.0 cm

(a) 0.027 N (b) 0.225 N (c) 314.0 N

Water flows through a pipe with the cross section area A_{1}. The pipe is connected to a wider pipe with the cross section area A_{2} = 20 cm^{2}. The velocity of water_{ }in the narrow pipe is v_{1} = 3.00 m/s, and in the wider pipe it is v_{2} = 0.6 m/s. The density of water is 1000 kg/m^{3}.

Define P_{1} = the water pressure in the narrow pipe, and P_{2} = the water pressure in the wider pipe. Which one of these statements is correct?

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

(a) A_{1} = 3.00 cm^{2} (b) A_{1} = 3.75 cm^{2} (c) A_{1} = 4.00 cm^{2}

(a) |ΔP| = 0 (b) |ΔP| = 173 Pa (c) |ΔP| = 208 Pa (d) |ΔP| = 503 Pa (e) |ΔP| = 4320 Pa

The submersible Alvin, which has been in service since 1964, has been used for biological research as well as for dives to the Titanic. It can dive down to the depth of about 4500 m.

On an average dive, Alvin dives to the depth of 2000 meters. What is the pressure at this depth, P_{2000}? The density of the seawater, ρ_{seawater }= 1030 kg/m^{3}.

(a) P_{2000} = 1.8 10^{6} Pa (b) P_{2000} = 1.0 10^{7} Pa (c) P_{2000} = 2.0 10^{7} Pa (d) P_{2000} = 3.5 10^{7} Pa (e) P_{2000} = 4.0 10^{7} Pa

(a) 0.5 × 10^{5} N (b) 1.0 × 10^{5} N (c) 7.5 × 10^{5} N (d) 1.5 × 10^{6} N (e) 2.0 × 10^{7} N