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 mean score was 101.1; the median was 106. 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 solid sphere and a solid cylinder, both with mass M and radius R, are released from rest simultaneously at the top of a ramp.

Which reaches the bottom of the ramp first?

(a) cylinder (b) sphere (c) They arrive at the same time.

(a) cylinder (b) sphere (c) They have the same kinetic energy.

A box of mass m = 2.2 kg is suspended from a thin wire which is wound around a solid, cylindrical frictionless pulley with mass M = 5.6 kg and radius R = 0.2 m. The box is released from rest at a height h = 0.8 m off the ground.

What is the acceleration of the box?

(a) 1.27 m/s^{2} (b) 2.66 m/s^{2} (c) 3.05 m/s^{2} (d) 4.31 m/s^{2} (e) 5.07 m/s^{2}

(a) 6.77 J (b) 9.66 J (c) 12.8 J (d) 15.02 J (e) 17.25 J

Two masses are suspended from a massless rod, which is supported at a pivot point, as shown. In this figure L_{A} = 3 m, L_{1} = 1 m, L_{2} = 2.5 m, m_{1} = 1 kg, and m_{2} = 5 kg. Note that the figure is not drawn to scale.

What mass would have to be placed at the point A to balance the rod?

(a) 0.22 kg (b) 1.91 kg (c) 2.86 kg (d) 3.83 kg (e) 4.07 kg

(a) 5.5 kg (b) 8.6 kg (c) 12.5 kg (d) 13.7 kg (e) 14.2 kg

(a) 1.57 N (b) 2.08 N (c) 3.36 N (d) 4.78 N (e) 5.12 N

(a) 4.32 J (b) 6.00 J (c) 17.28 J

A hoop of radius R = 0.4 m and mass M = 0.4 kg is released from rest at the top of an inclined plane with height h = 0.8 m. The angle between the plane and the horizontal is 20°. The hoop rolls without slipping.

What is the ratio of the hoop's rotational kinetic energy to its translational kinetic energy?

(a) K_{rot} / K_{trans} = 1/3 (b) K_{rot} / K_{trans} = 1/2 (c) K_{rot} / K_{trans} = 1 (d) K_{rot} / K_{trans} = 3/2 (e) K_{rot} / K_{trans} = 2

(a) 2.8 m/s (b) 3.6 m/s (c) 4.2 m/s (d) 5.7 m/s (e) 6.6 m/s

Two solid disks with mass m_{1} = 3.5 kg and m_{2} = 0.8 kg and radius R_{1} = R_{2} = 0.2 m both slide and rotate without friction on a vertical axis. Initially, the upper disk m_{1} is rotating with angular velocity ω_{1} and the lower disk is at rest. The upper then disk falls, sticks to the lower disk, after which they are observed rotate together at angular velocity ω_{2} = 23 rad/s.

What was the initial angular velocity of the upper disk, ω_{1}?

(a) 4.71 rad/s (b) 28.26 rad/s (c) 51.80 rad/s (d) 75.35 rad/s (e) 98.90 rad/s

(a) 0.064 kg m^{2} (b) 0.075 kg m^{2} (c) 0.086 kg m^{2}

A girl on a sled slides from the top of a hill of height h_{0} (point A) starting from rest. The girl and the sled have a combined mass of 30 kg. The sled (with the girl) slides down on a frictionless hill to point B. Then it slides up another hill to point C and down again to point D which is at the same height as point B. The sled's speed at point B at the bottom of the hill is v_{0} = 19.8 m/s.

What is the height of point A, h_{0}, that the sled started from?

(a) 16 m (b) 18 m (c) 20 m

(a) 5 m/s (b) 8 m/s (c) 12 m/s (d) 14 m/s (e) 16 m/s

(a) -5240 J (b) -5520 J (c) -5880 J

(a) 0.75 (b) 1.00 (c) 1.25 (d) 1.50 (e) 1.75

(a) 7 m (b) 10 m (c) 20 m

A block of mass M_{1}= 3 kg slides without friction down a ramp, starting from rest at height h_{1}. At the bottom, it runs into another block of mass M_{2} = 8 kg which is at rest before the collision. The two blocks stick together and slide up the second ramp (see the drawing below). They reach a maximum height h_{2} before sliding back down. (Note: the drawing is not to scale.) Immediately after sticking together, the two blocks move with the velocity v = 6 m/s.

What was the velocity of the 3 kg block immediately before the collision?

(a) 5 m/s (b) 13 m/s (c) 19 m/s (d) 22 m/s (e) 33 m/s

(a) 1.66 m (b) 1.84 m (c) 2.10 m (d) 2.45 m (e) 2.75 m

An object of mass 8 kg moves horizontally in a straight line at speed v_{0} on a frictionless surface. A force F = 100 N slows it down to 11 m/s in 2 seconds.

What was the starting speed v_{0}?

(a) 12 m/s (b) 16 m/s (c) 31 m/s (d) 36 m/s (e) 38 m/s

(a) -2100 J (b) -3500 J (c) -4700 J (d) -5100 J (e) -5900 J

Three objects collide. Two of them have equal mass m_{1} = m_{2} = 5 kg and equal and opposite velocities in the x-direction, v_{1} = -v_{2} = 5 m/s. The third object, whose mass m_{3} = 2 kg, has velocity 10 m/s in the +y direction (see the figure below.) After the objects collide, they stick together and move with a final velocity v_{total} .

What is the magnitude of the momentum after the collision?

(a) 20 kg m/s (b) 70 kg m/s (c) 120 kg m/s

(a) 1.15 m/s (b) 1.30 m/s (c) 1.67 m/s (d) 1.90 m/s (e) 2.00 m/s

(a) along the +x direction (b) along the -x direction (c) along the +y direction (d) along the -y direction (e) v_{total} has components in both the x and y directions.