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 106. The mean score was 81.3; the median was 83. The exam period was 90 minutes. 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.

Two objects of mass M (= 1 kg) each travel with identical speed (|v_{1}| = |v_{2}| = 3 m/s) making an angle of θ relative to the x-axis. After they collide with each other, they travel as one object of mass 2M and with a velocity v_{3} (|v_{3}| = 2 m/s) in the horizontal direction.

Is the collision elastic or inelastic?

(a) elastic (b) inelastic

(a) 2.5 J (b) 5 J (c) 10 J (d) 15 J (e) 20 J

(a) 0.50 radians (b) 0.84 radians (c) 1.37 radians (d) 1.51 radians (e) 1.60 radians

You have two balls of identical mass (m = 0.1 kg) but made of different materials. Let's call one the happy ball and the other the sad ball. When the happy ball is dropped and hits the floor at a speed of 2 m/s, it bounces back with the same speed. In contrast, the sad ball, when it is dropped and hits the floor at a speed of 2 m/s, it sticks to the floor without bouncing.

What is the magnitude of the impulse delivered to the floor by the happy ball?

(a) 0 kg m/s (b) 0.05 kg m/s (c) 0.1 kg m/s (d) 0.2 g m/s (e) 0.4 kg m/s

(a) the happy ball (b) the sad ball

A student is pushing a box of mass M (= 5 kg) by applying a force F (= 100 N) on a horizontal floor. The kinetic coefficient of friction between the box and the floor is 0.2. The box starts from rest and moves to the right over a distance of 2 m.

How much work is done by the student to the box?

(a) 0 J (b) -141 J (c) 141 J (d) -94 J (e) 94 J

(a) It is zero. (b) It is positive. (c) It is negative.

Kaushiki throws a ball straight up from an initial height of 1 m. The initial speed of the ball is 5 m/s. Ignore friction due to air for this problem. The mass of the ball is 0.3 kg.

What is the maximum height reached by the ball?

(a) 2.28 m (b) 3.56 m (c) 4.73 m (d) 5.88 m (e) 6.97 m

(a) 0 m/s (b) 10 m/s (c) 5 m/s

(a) 3.5 J (b) 6.7 J (c) 9.3 J (d) 11.1 J (e) 12.9 J

Fred (75 kg) and Jane (50 kg) are at rest on skates facing each other. Jane then pushes Fred with a constant force F = 45 N for a time Δt. Jane then moves at a speed of 1.35 m/s.

What can you say about Fred's motion after the push?

(a) He moves at the same speed as Jane's and in the opposite direction. (b) He moves at a speed higher than Jane's and in the opposite direction. (c) He moves at a speed lower than Jane's and in the opposite direction.

(a) 0.5 s (b) 1 s (c) 1.5 s (d) 2 s (e) 3 s

At one end of a light bar of length L is fixed a small ball of mass M. The other end of the bar is fixed to the ground at point P but can rotate freely around the point. A person supports the end of the bar where the ball is fixed with a force F that is perpendicular to the bar as noted in the figure. Initially, the bar makes an angle of 60° with the horizontal ground as illustrated below. You can ignore the mass of the bar.

To keep the bar stationary as shown in the figure, what force must the person exert? Give its magnitude. Here g is the acceleration of gravity.

(a) Mg / 4 (b) Mg / 2 (c) Mg

(a) nonzero and clockwise around Q (seen from you) (b) zero (c) nonzero and counterclockwise around Q (seen from you)

What is the magnitude of the angular acceleration α of the bar around point P immediately after the force F is gone?

(a) α = g / 2 (b) α = 3g / 4 (c) α = g / 4 (d) α = g / 2L (e) α = 3g / 4L

What can you say about the relation between the rotation kinetic energy K_{pulley} of the pulley and the translational energy K_{block} of the block after the block has dropped by a distance of L?

(a) K_{pulley} = K_{block} / 4 (b) K_{pulley} = K_{block} / 2 (c) K_{pulley} = K_{block} (d) K_{pulley} = 2K_{block} (e) K_{pulley} = 4K_{block}

You have invented a new recording device that uses a disk of radius 4.1 mm, similar to a DVD or CD (see figure). The outermost track is with radius 4 mm and the innermost track is with radius 1 mm. The reading speed (linear speed) is kept constant irrespective of the position on the disk by adjusting the angular velocity depending on which track is being read. The angular velocity of the disk when the outermost track is being read is 241 rad/s.

For the outermost track, what is the linear reading speed? (The linear reading speed is the constant tangential speed which is maintained while playing the disk.)

(a) 0.96 m/s (b) 1.08 m/s (c) 1.15 m/s (d) 1.52 m/s (e) 1.97 m/s

(a) 52 rad/s (b) 109 rad/s (c) 243 rad/s (d) 823 rad/s (e) 961 rad/s

(a) α = 246 rad/s (b) α = 246 rad/s^{2} (c) α = 385 rad/s (d) α = 385 rad/s^{2} (e) α = 454 rad/s

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

A puck of mass 0.2 kg slides in a circular path on a horizontal frictionless table at an angular speed ω of 10 rad/s. It is held at a constant radius of 1 meter by a string threaded through a frictionless hole at the center of the table. Then, you pull on the string such that the radius decreases by a factor of 3. What happens to the angular speed of rotation?

(a) It decreases by a factor of nine. (b) It decreases by a factor of three. (c) It does not change. (d) It increases by a factor of three. (e) It increases by a factor of nine.