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 mean score was 80.2; the median was 81. 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 mass (m = 2 kg), initially at rest, slides down a ramp with height h, emerging with velocity v = 9 m/s. The mass slides up a second ramp of height 2 m and then passes through a loop-the-loop of radius R = 0.6 m. Assume the entire surface is frictionless and g = 9.8 m/s^{2}.

What is the height h?

(a) 2.05 m (b) 4.13 m (c) 6.67 m (d) 7.45 m (e) 8.27 m

(a) 3.72 m/s (b) 4.65 m/s (c) 5.02 m/s (d) 6.47 m/s (e) 7.55 m/s

(a) 68 N (b) 41 N (c) 22 N (d) 11 N (e) The mass does not have enough energy to reach P_{2}.

(a) 8.16 rad/s (b) 6.04 rad/s (c) 3.76 rad/s (d) 2.21 rad/s (e) 1.08 rad/s

(a) 14.7 J (b) 19.2 J (c) 24.6 J (d) 31.0 J (e) 39.5 J

A box of mass M = 5 kg is pushed at constant speed a distance 5 m across a floor with coefficient of kinetic friction μ_{K} = 0.2. The force F is acting horizontally, as shown.

How much work was done by the force F ?

(a) 32 J (b) 49 J (c) 106 J

(a) The total mechanical energy of the box increased. (b) The total mechanical energy of the box decreased. (c) The total mechanical energy of the box was unchanged.

A block with mass m = 3 kg, initially at rest, is released at the top of a frictionless inclined plane of height h = 1.8 m. The angle θ = 15°.

What is the block's velocity when it reaches the bottom?

(a) 3.36 m/s (b) 4.68 m/s (c) 5.94 m/s

(a) 26.2 J (b) 39.5 J (c) 52.9 J (d) 62.4 J (e) 78.1 J

(a) 20 kg m/s (b) 60 kg m/s (c) 80 kg m/s

(a) 0.15 m/s (b) 0.28 m/s (c) 5.1 m/s (d) 23 m/s (e) 40 m/s

(a) 0.667 m/s (b) 1.33 m/s (c) 2.5 m/s

(a) V_{x} = -4.3 m/s (b) V_{x} = -0.67 m/s (c) V_{x} = 0.13 m/s (d) V_{x} = 0.67 m/s (e) V_{x} = 4.3 m/s

(a) τ_{A} > τ_{B} (b) τ_{A} = τ_{B} (c) τ_{A} < τ_{B}

(a) 26 radians/second (b) 56 radians/second (c) 82 radians/second

A 4 kg, 3 kg and 2 kg mass are attached to a massless meter stick as shown in the figure.

Calculate the distance from the left edge of the meter stick to the center of mass of these 3 masses.

(a) x = 0.51 m (b) x = 0.61 m (c) x = 0.71 m

(a) I = 0.48 kg m^{2} (b) I = 2.25 kg m^{2} (c) I = 3.73 kg m^{2}

A solid cylinder with radius 0.85 meters is pulled across a horizontal floor, such that it rolls without slipping. The cylinder starts from rest and is observed to accelerate at a constant rate of 2.8 m/s^{2} to the right. The moment of inertia of the cylinder is 3.25 kg m^{2}.

Calculate the mass of the cylinder.

(a) M = 7 kg (b) M = 8 kg (c) M = 9 kg

(a) f = 9.1 N (b) f = 11.4 N (c) f = 12.6 N (d) f = 18.1 N (e) f = 23.1 N

(a) F = 25.1 N (b) F = 31.4 N (c) F = 37.8 N

(a) K_{tot} = 68.2 J (b) K_{tot} = 75.3 J (c) K_{tot} = 94.4 J (d) K_{tot} = 113 J (e) K_{tot} = 143 J

A 60 cm massless rod is suspended from the ceiling by two wires as shown. A 1.5 kg mass is suspended from the left edge of the rod, and a 2.0 kg mass is suspended from the right end of the rod.

Calculate T_{L} the tension in the left string.

(a) 1.5 N (b) 2.5 N (c) 3.5 N (d) 4.5 N (e) 5.5 N

(a) 2.0 kg (b) 2.8 kg (c) 3.8 kg

Two masses are suspended over a massive pulley (I = 0.192 kg m^{2}, R = 0.4 m, M = 3 kg). The 3.5 kg mass is released from rest 0.8 meters above the ground.

Assuming a uniform mass distribution, which shape best describes the pulley?

(a) spherical (b) cylindrical (c) hoop

(a) 1.48 m/s (b) 2.13 m/s (c) 3.24 m/s (d) 3.95 m/s (e) 4.60 m/s