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 86. When the exam was given, the mean was 61.2; the median was 62. Click here to see page1 page2 of the formula sheet that came with the exam.

Two balls with equal mass are dropped from a height of 2 meters above the floor. They both bounce back up to a maximum height of 1.8 meters above the floor. The first ball is made of steel, and is in contact with the floor for 0.04 seconds. The second ball is made of rubber and is in contact with the floor for 0.09 seconds.

Which ball has a greater impulse on the floor?

(a) steel (b) rubber (c) same

(a) 3.13 m/s (b) 5.94 m/s (c) 6.26 m/s

A 0.05 kg ball travels horizontally with initial velocity v_{i}, before colliding with, and sticking to a 0.13 kg block attached to an uncompressed massless spring (k = 150 N/m). Immediately after the collision, the block and ball are traveling at 15 m/s to the right. (You may assume the collision takes place in a negligible amount of time. Ignore gravity.)

During the collision of the ball with the block

(a) the total momentum of the ball and block and spring are conserved. (b) the total mechanical energy (potential plus kinetic) of the ball, block and spring are conserved. (c) Both are correct.

(a) the total momentum of the ball and block and spring are conserved. (b) the total mechanical energy of the ball, block and spring are conserved. (c) Both are correct.

(a) 15 m/s (b) 39 m/s (c) 54 m/s

(a) 0.35 m (b) 0.52 m (c) 0.73 m

A 3 kg ball is dropped from the top of a 30 meter building.

The work done be gravity as the ball falls down is

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

(a) 282 J (b) 312 J (c) 339 J

(a) (b) (c)

A 4 kg cart is sliding across a frictionless table at 3 m/s to the right. It collides and sticks to a 3 kg cart that was initially at rest.

What is the speed of the carts after they collide?

(a) 1.71 m/s (b) 2.51 m/s (c) 5.23 m/s

(a) 7.7 J (b) 12.3 J (c) 22.5 J

A 3-kg block is pulled up a frictionless ramp as shown in the diagram to the right. Calculate the work done by the 30 N force as the block moves a distance of 3m along the ramp.

(a) 50 J (b) 60 J (c) 90 J

(a) increases. (b) remains the same. (c) decreases.

In the scale depicted below, the mass of the uniform beam is 50 g. The mass of the object you want to weigh is equal to 610 g. The mass of the sliding weight is M. The position of the pivot under the beam is shown in the picture.

What is the position of the center of mass of the beam?

(a) 5.34 cm to the right of the pivot (b) 6.57 cm to the right of the pivot (c) 7.75 cm to the right of the pivot

(a) M = 127 g (b) M = 163 g (c) M = 198 g (d) M = 221 g (e) M = 257 g

(a) M / 6 (b) M (c) 6 M

Four point-like objects of equal mass m = 1.5 kg are located in four corners of a square of side 1.1 m as shown in the figure below.

What is the moment of inertia of this system about the axis A?

(a) 1.1 kg m^{2} (b) 1.8 kg m^{2} (c) 2.9 kg m^{2}

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

(a) I_{C} / 2 (b) I_{C} (c) 2 I_{C}

A cylinder rotates about the axis OO’. The radius of the cylinder is 15 cm. A handle is attached to the cylinder and this system can be used to lift heavy objects attached to the cylinder by a rope, as shown in the figure below. The length of the handle is 80 cm.

What is the minimum force that must be applied to the handle to keep the 50-kg box in equilibrium?

(a) 49 N (b) 92 N (c) 234 N (d) 490 N (e) 527 N

(a) 735 J (b) 544 J (c) 321 J

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

A cord passes over a pulley and suspends two blocks of different masses as shown in the figure below. The mass of the pulley is 4 kg and its radius is equal to 25 cm. The mass of the object on the left is m_{1} = 2 kg. The mass of the object on the right is m_{2} = 3 kg.

The blocks are initially at rest and they start to move. What is the speed of the second block after it has moved down by Δh = 3m . (Moment of inertia of the pulley I = ½ M_{p}R_{p}^{2}).

(a) 2.9 m/s (b) 3.3 m/s (c) 4.8 m/s (d) 5.4 m/s (e) 6.8 m/s

(a) Yes (b) No