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 115. The exam period was 90 minutes. The mean score was 86.2; the median was 89. Click here to see the formula sheet that came with the exam.

A block m_{1} with mass 7 kg moves up an inclined plane with an initial velocity v_{0} = 4.7 m/s. The inclined plane is at an angle of θ = 45° from the horizontal. The coefficient of kinetic friction between the block and the incline is 0.25.

What is the block's velocity when it has traveled a distance D=1 meter up the incline?

(a) 0.10 m/s (b) 0.31 m/s (c) 0.57 m/s (d) 1.59 m/s (e) 2.18 m/s

(a) -mgDsinθ (b) μ_{k}mgDcosθ/2 (c) μ_{k}mgD (d) -μ_{k}mgDcosθ (e) mgDsinθ

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

(T) True (F) False

A frictionless ramp of mass 3m is initially at rest on a horizontal frictionless floor. A small box of mass m is placed at the top of the ramp and then released from rest. After the box is released, it slides down the ramp and onto the horizontal floor, where it is measured to have a speed v, having fallen a total distance h.

What is the speed v of the box after it has left the ramp?

(a) (b) (c) (d) (e)

(a) less than in the previous question. (b) the same as in the previous question. (c) more than in the previous question

If there were kinetic friction between the ramp and the floor, but none between the box and the ramp, the speed v of the box after it has left the ramp, compared to its speed when both the ramp and the floor are frictionless, would be

(a) less. (b) the same. (c) more.

Two discs are free to move without friction on a horizontal table. The 0.4 kg disc is initially at the position (x = 0, y = 1.0) m, moving with velocity (v_{x} = 3.0, v_{y} = 0) m/s. The 0.6 kg disc is initially at (x = 1.5, y = 0) m, moving with velocity (v_{x} =0, v_{y} =2.0) m/s. The figure above displays the initial conditions for the two discs in the x-, y- coordinates.

The initial velocity of the center of mass of the two-disc system is:

(a) (v_{x},v_{y}) = (3.0,2.0) m/s (b) (v_{x},v_{y}) = (2.0,3.0) m/s (c) (v_{x},v_{y}) = (2.7,2.0) m/s (d) (v_{x},v_{y}) = (1.8,1.8) m/s (e) (v_{x},v_{y}) = (1.2,1.2) m/s

(a) less than before the collision (b) the same as before the collision (c) It depends on whether the collision is elastic or inelastic.

What is the maximum compression of the spring, d, after the collision (the clay sticks to the block)?

(a) d = 0.034 m (b) d = 0.089 m (c) d = 0.108 m (d) d = 0.266 m (e) d = 0.437 m

Two eggs of mass m = 0.15 kg with initial velocity v = 3 m/s are incident on a trampoline and on an ordinary floor. One egg makes an elastic collision with the trampoline; the other makes a totally inelastic collision with the floor.

If the interaction time of the egg with the trampoline is t_{t} = 0.1 s, what is the average force F on the egg during the collision?

(a) F = 1.8 N (b) F = 2.0 N (c) F = 3.5 N (d) F = 6.0 N (e) F = 9.0 N

(a) t_{f} = 0.00038 s (b) t_{f} = 0.0024 s (c) t_{f} = 0.0086 s (d) t_{f} = 0.0129 s (e) t_{f} = 0.153 s

(a) 1/3 m (b) 2/3 m (c) 1 m (d) 4/3 m (e) 5/3 m

A space capsule of mass m is launched from the surface of the earth with a speed V_{E} = 6.0 × 10^{3} m/s. The radius and mass of the earth are R_{E} = 6.37 × 10^{6} m and M_{E} = 5.97 × 10^{24} kg respectively. Newton's gravitational constant is G = 6.67 × 10^{-11} N-m^{2}/kg^{2}. Neglect air resistance.

What is the maximum height R_{max} measured from the center of the earth, reached by the space capsule?

(a) R_{max} = 5.73 × 10^{6} m (b) R_{max} = 7.00 × 10^{6} m (c) R_{max} = 8.95 × 10^{6} m (d) R_{max} = 1.27 × 10^{7} m (e) R_{max} = 1.72 × 10^{7} m

(a) larger. (b) smaller. (c) the same.

(a) about 2V_{E}. (b) about 0.01V_{E}. (c) about the same as V_{E}.

Two identical masses are suspended from massless strings of equal length. One mass is released from a height h as depicted in the figure below. When the first mass hits the second, the two masses stick together.

What is the maximum height H reached by the two masses together?

(a) H = h / 4 (b) H = h / 2 (c) H = h (d) H = 2 h (e) H = 4 h

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

A massless spring of spring constant k = 30 N/m hangs vertically in the earth's gravitational field. A 1 kg mass is attached to the spring.

Measuring from the unstretched length of the spring, how much has the gravitational potential energy of the mass changed when the spring reaches its equilibrium length with the mass attached?

(a) 0 N-m (b) +1.27 N-m (c) -1.27 N-m (d) +3.21 N-m (e) -3.21 N-m

(a) 0 m/s (b) 0.55 m/s (c) 0.72 m/s (d) 1.10 m/s (e) 2.73 m/s

If the weight is to move up a distance h, through what distance, D, must you pull the free end of the rope?

(a) D = h (b) D = h/2 (c) D = 2h (d) D = 4h (e) D = 3h/2

Two identical blocks initially have the same velocity V at the bottom of two ramps. The first ramp inclined at a shallower angle (θ_{1}) with respect to the horizontal than the second ramp (θ_{2}). The maximum heights reached by the blocks are h_{1} and h_{2} respectively.

Assume that both ramps are frictionless. Which one of these statements is correct concerning the maximum heights reached by the blocks?

(a) h_{2} = h_{1} (b) h_{2} > h_{1} (c) h_{2} < h_{1}

If the speeds after the collision are v_{1f} = +3 m/s and v_{2f} = -2 m/s, what were their speeds v_{1i} and v_{2i} before the collision?

(a) v_{1i} = -3.00 m/s, v_{2i} = +2.00 m/s (b) v_{1i} = -4.50 m/s, v_{2i} = +1.50 m/s (c) v_{1i} = +2.75 m/s, v_{2i} = -1.75 m/s (d) v_{1i} = -3.25 m/s, v_{2i} = +1.75 m/s (e) v_{1i} = +3.25 m/s, v_{2i} = -2.25 m/s