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 120. The exam period was 90 minutes; the average score was 93.3; the median score was 98. 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 piston of area A = 0.3 m^{2} sits on top the water in a tank (ρ = 1000 kg/m^{3}), in which a block of mass m = 0.2 kg that is tethered by a string floats. Ssee figure.

Another mass M = 30 kg is placed on top of the piston. By how much does the pressure increase at the position marked X?

(a) 980 Pa (b) 1100 Pa (c) 1730 Pa (d) 2000 Pa (e) 5010 Pa

(a) smaller magnitude. (b) the same magnitude. (c) greater magnitude.

(a) 344 kg/m^{3} (b) 419 kg/m^{3} (c) 501 kg/m^{3} (d) 699 kg/m^{3} (e) 797 kg/m^{3}

(a) 980 Pa (b) 1402 Pa (c) 3870 Pa (d) 8880 Pa (e) 12740 Pa

(a) 39 N (b) 120 N (c) 190 N (d) 250 N (e) 380 N

(a) 0.6 cm (b) 1.2 cm (c) 6.0 cm (d) 12 cm (e) 21 cm

Oil (density = 800 kg/m^{3}) flows through a cylindrical pipe, then through a narrower valve with circular cross section, and finally emerges into an open, cylindrical tank of radius 15 m where the pressure is 10^{5} Pa (i.e. equals atmospheric pressure). See diagram. The speed of fluid in the pipe is 1.59 m/s. The speed of fluid in the valve is 25.5 m/s.

What is the ratio of the radius r_{p} of the pipe to the radius r_{v} of the valve?

(a) r_{p} / r_{v} = 4 (b) r_{p} / r_{v} = 2 (c) r_{p} / r_{v} = 1 (d) r_{p} / r_{v} = 0.5 (e) r_{p} / r_{v} = 0.063

(a) F_{p} > F_{v} (b) F_{p} = F_{v} (c) F_{p} < F_{v}

(a) 0.01 m (b) 0.05 m (c) 0.2 m (d) 0.8 m (e) 1.6 m

(a) 240000 Pa (b) 360000 Pa (c) 480000 Pa (d) 600000 Pa (e) 720000 Pa

A mass M = 2 kg is suspended by a spring with spring constant k = 8 N/m. Initially the mass is at its resting position, y = 0. At t = 0 it is struck sharply from below by a hammer so that the mass begins to move with speed 0.1 m/s.

What is the period with which the mass oscillates?

(a) 1.1 s (b) 2.1 s (c) 3.1 s (d) 4.1 s (e) 5.1 s

(a) smaller. (b) larger. (c) the same.

(a) y = 0.05 sin(2t) m (b) y = 0.05 cos(2t) m (c) y = 0.1 sin(2t) m (d) y = 0.1 cos(2t) m (e) y = 0.1 cos(4t) m

(a) 0.1 m/s^{2} (b) 0.2 m/s^{2} (c) 0.3 m/s^{2} (d) 0.4 m/s^{2} (e) 0.5 m/s^{2}

A spring with a block of mass 3.8 kg attached at one end is fixed to the wall. A leftward force of F = 35 N is applied on the mass, compressing the spring (Fig. A). The mass is then released with zero initial velocity and starts to oscillate (Fig. B). The spring constant is k = 150 N/m.

What is the maximum kinetic energy of the mass?

(a) 4 J (b) 8 J (c) 10 J (d) 11 J (e) 15 J

(a) It is halved. (b) It is doubled. (c) It remains the same.

A pendulum consists of a point mass M = 7.3 kg suspended at the end of a string of length L = 1.3 m.

The maximum speed of the point mass is v = 0.75 m/s. What is the difference in the height Δh of the mass between its highest and lowest positions while oscillating?

(a) Δh = 1.2 cm (b) Δh = 2.1 cm (c) Δh = 2.9 cm (d) Δh = 3.7 cm (e) Δh = 4.1 cm

(a) 1.2 s (b) 2.3 s (c) 3.4 s (d) 4.5 s (e) 5.6

A sound wave with frequency 520 Hz hits a balloon containing a mixture of gases. Inside the balloon the wavelength is increased by 30% compared with that in the air (in which the sound speed is 340 m/s).

What is the speed of sound inside the balloon?

(a) 200 m/s (b) 260 m/s (c) 340 m/s (d) 440 m/s (e) 570 m/s

(a) 400 Hz (b) 520 Hz (c) 680 Hz

What is the ratio of the frequencies (where f_{A} is from plane A and f_{B} is from plane B)?

(a) f_{B} / f_{A} = 1/9 (b) f_{B} / f_{A} = 1/3 (c) f_{B} / f_{A} = 1 (d) f_{B} / f_{A} = 3 (e) f_{B} / f_{A} = 9

How many trumpeters at distance 10 m must play in unison to increase the loudness to 100 dB?

(a) 10 players (b) 20 players (c) 50 players (d) 100 players (e) 200 players

(a) 0.5 (b) 0.33 (c) 0.11