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 111. The exam period was 90 minutes; the average score was 78.3; the median score was 81. Click here to see page1 page2 page3 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.

There is a massless rod of length 3 m. A balloon is attached at the right end B, which pulls the rod upward with a force of 105 N. At C, which is 1 m from the right end B of the rod, hangs a block of mass M. Also, a force is applied at A to keep the rod horizontal and stationary.

What is the mass M of the block?

(a) 7.2 kg (b) 9.4 kg (c) 11.6 kg (d) 16.1 kg (e) 17.3 kg

(a) positive (counterclockwise). (b) negative (clockwise). (c) not decidable due to insufficient information

A solid homogeneous cylindrical roller of mass M_{1} and radius 30 cm is connected via a massless pulley and with a massless wire to a block of mass M_{2}, as shown in the figure below. M_{1} is 40 kg and M_{2} is 10 kg. The roller does not slip. The roller is placed on the slope of 30° from horizontal. At t = 0, the block M_{2} is going down, pulling the roller M_{1} along the slope -- that is, the mass M_{1} is climbing up the slope due to the initial push. The total kinetic energy of the system is 300 J.

What is the kinetic energy of the block M_{2}?

(a) 31.8 J (b) 42.9 J (c) 54.0 J (d) 65.1 J (e) 76.2 J

(a) 3.2 rad/s^{2} (b) 4.3 rad/s^{2} (c) 4.7 rad/s^{2} (d) 6.5 rad/s^{2} (e) 7.6 rad/s^{2}

(a) unchanged. (b) multiplied by square root of 2. (c) halved.

A person is standing at the center of a rotating disk. She holds a horizontal weightless stick with two identical small masses attached to its ends, as shown in the figure.

Initially, she holds one end of the stick as in figure A.

(a) It increases. (b) It stays the same. (c) It decreases.

(a) yes (b) no (c) not necessarily

A cylindrical container filled with water having cross section 0.04 m^{2} is placed on a scale as illustrated in figure A below. The scale reads 24 kg. Now, a uniform ball is put into the container as shown in figure B. The ball floats on the water, and the reading of the scale becomes 27.3 kg. The density of water is 1000 kg/m^{3}.

How much larger is the pressure at the bottom of the container in B than in A?

(a) 123.8 Pa (b) 209.4 Pa (c) 351.0 Pa (d) 563.4 Pa (e) 808.5 Pa

(a) 2.5 cm (b) 3.6 cm (c) 5.8 cm (d) 6.6 cm (e) 8.3 cm

(a) 615 kg/m^{3} (b) 713 kg/m^{3} (c) 815 kg/m^{3} (d) 889 kg/m^{3} (e) 921 kg/m^{3}

(a) the same as in B. (b) lower than in B. (c) higher than in B.

(a) 0.33 mm (b) 0.44 mm (c) 0.55 mm (d) 0.66 mm (e) 0.77 mm

Consider blood (density 1025 kg/m^{3}) flowing through an artery with circular cross section that looks like this:

Ignore viscosity. Assume that the change in height is negligible between regions A, B, and C.

What is the mass flow rate through region A?

(a) 0.011 kg/s (b) 0.024 kg/s (c) 0.039 kg/s (d) 0.052 kg/s (e) 0.128 kg/s

(a) +46 Pa (b) +13 Pa (c) 0 Pa (d) -13 Pa (e) -46 Pa

(a) 0.19 m (b) 0.38 m (c) 0.75 m (d) 1.5 m (e) 3.1 m

Consider a spring with spring constant k = 30 N/m suspended vertically from a hook. A block of mass 1.0 kg is attached to the bottom of the spring.

How much longer is the spring after the mass is attached?

(a) 0.16 m (b) 0.24 m (c) 0.33 m

(a) a_{y} = 0.06 ω^{2} cos ωt (b) a_{y} = 0.06 ω^{2} sin ωt (c) a_{y} = -0.06 ω^{2} cos ωt

(a) 0.15 m/s (b) 0.24 m/ (c) s 0.33 m/s (d) 1.22 m/s (e) 2.43 m/s

(a) 0.23 s (b) 0.49 s (c) 1.15 s (d) 2.30 s (e) 5.86 s

(a) increase. (b) stay the same. (c) decrease.

The motion of the human leg during walking can be modeled (very roughly) as a simple pendulum; while one leg is on the ground, the other leg is off the ground and swinging forward with a pendulum-like motion. One period of the pendulum corresponds to two steps, and each step involves rotating the leg through a fixed angle (which is the same for everyone) about the hip.

Following this model, if you are walking next to a child who is half your height, you expect the child's walking speed to be

(a) the same as yours. (b) 1/sqrt(2) times yours. (c) 1/2 of yours.

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

(a) 1.1 m (b) 4.7 m (c) 5.9 m

(a) 9.8 N (b) 122 N (c) 385 N (d) 980 N (e) 1752 N