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 96; the average score was 79.1; the median score was 82. The exam period was 90 minutes. Click here to see page1 page2 of the formula sheet that came with the exam.

A string is tied around a uniform disc of mass 7 kg and radius 0.3 m. The disc is held by a small rod that goes through its center. A vertical tension T is applied to the string. The angular acceleration of the disc is 20 rad/s^{2}.

Calculate the torque on the disc exerted by the tension T.

(a) 5.2 N m (b) 6.3 N m (c) 7.4 N m

(a) 1.0 s (b) 2.0 s (c) 3.0 s (d) 4.0 s (e) 5.0 s

(a) 80 rad/s (b) 85 rad/s (c) 95 rad/s

A composite disk of total mass 7 kg and radius 0.8 m is pulled on a horizontal surface by a string that is tied to its center. There is friction between the disk and the surface. The disk rolls without slipping. The acceleration of the disk is a = 4 m/s^{2} and the friction force is F = 23 N.

Calculate the moment of inertia of the disk.

(a) 2.54 kg m^{2} (b) 3.68 kg m^{2} (c) 4.77 kg m^{2} (d) 5.83 kg m^{2} (e) 6.49 kg m^{2}

(a) 21 N (b) 35 N (c) 44 N (d) 51 N (e) 72 N

(a) smaller than T. (b) equal to T. (c) larger than T.

A string is attached to a cube of wood of volume V = 0.1 m^{3} that is placed in fresh water with density 1000 kg/m^{3}, as shown in the figure below. The density of the wood is 750 kg/m^{3}.

Calculate the tension in the string.

(a) 131 N (b) 245 N (c) 377 N (d) 465 N (e) 526 N

(a) V_{s} = 0.030 m^{3} (b) V_{s} = 0.050 m^{3} (c) V_{s} = 0.075 m^{3}

Martha stands at the edge of the platform of a merry-go-round that is a uniform circular disk of radius 2 m and mass 250 kg. Martha can be treated as a point mass.

If the merry-go-round rotates at an angular velocity of 3 rad/s around its axis, and the angular momentum of the system consisting of Martha and the merry-go-round is equal to 2160 kg-m^{2}/s, what is the mass of Martha?

(a) 39 kg (b) 47 kg (c) 55 kg (d) 66 kg (e) 72 kg

(a) 1.0 rad/s (b) 2.1 rad/s (c) 3.2 rad/s (d) 4.3 rad/s (e) 5.4 rad/s

(a) KE_{initial} < KE_{final} (b) KE_{initial} = KE_{final} (c) KE_{initial} > KE_{final}

A 1.7 kg block is attached to the floor by a spring with force constant k = 23.1 N/m. At time t = 0, the block is observed to be at position y = 0 and traveling up with a velocity of 11.1 m/s.

What is the maximum force the spring exerts on the block?

(a) 70 N (b) 123 N (c) 154 N

(a) 1.7 s (b) 2.9 s (c) 5.4 s

(a) v(t) = -v_{max} sin(ωt) (b) v(t) = -v_{max} cos(ωt) (c) v(t) = +v_{max} cos(ωt)

(a) 105 J (b) 79 J (c) 53 J

Water (ρ = 1000 kg/m^{3} ) is flowing through a hose with radius 2.8 cm. There is a slight constriction in the hose in region b, such that the effective radius is only 2.1 cm. Water flows from left to right, region c is raised 0.4 meters above the ground, and the water is observed to flow out of region c with a velocity of 5 m/s.

How much time will it take to fill a tub of volume 0.8 m^{3}?

(a) 29 s (b) 53 s (c) 65 s

(a) v_{b} = 2.8 m/s (b) v_{b} = 6.5 m/s (c) v_{b} = 8.9 m/s

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

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

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

(a) d = 6 cm (b) d = 25 cm (c) d = 30 cm

(a) 10 m (b) 30 m (c) 50 m (d) 70 m (e) 90 m

A grandfather clock keeps time with a simple pendulum. Unfortunately the clock is running slow, (e.g. the period motion is 1.1 sec).

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

(a) Increase the mass 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.