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 102. The exam period was 90 minutes. The mean score was 67.6; the median was 69. 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 sled starts downhill from rest, from the height h =100 meters above the finish line. The total mass of the sled and people is M = 200 kg.

What is the final speed of the sled, v_{F}, when it arrives (with the people) at the finish line?

(a) v_{F} = 40.1 m/s (b) v_{F} = 44.3 m/s (c) v_{F} = 50.6 m/s

(a) μ = 0.21 (b) μ = 0.44 (c) μ = 1.20

(a) v_{F2} = 44.1 m/s (b) v_{F2} = 44.3 m/s (c) v_{F2} = 44.6 m/s (d) v_{F2} = 44.8 m/s (e) v_{F2} = 45.0 m/s

A block of mass M_{1}= 2 kg slides without friction down the ramp, starting from rest at height h_{1}= 16 m. At the bottom, it runs into another block of mass M_{2} = 6 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.)

How much kinetic energy, ΔKE = KE_{initial} - KE_{final}, was lost in the collision?

(a) ΔKE = 0 J (b) ΔKE = 45 J (c) ΔKE = 125.J (d) ΔKE = 235 J (e) ΔKE = 270 J

(a) h_{2} = 1.0 m (b) h_{2} = 3.0 m (c) h_{2} = 4.0 m (d) h_{2} = 16.0 m (e) h_{2} = 27.0 m

An object of mass M = 50 kg slides on a frictionless horizontal surface with velocity v_{0} = 50 m/s to the right. It explodes into two pieces of masses M_{1} = 20 kg and M_{2} = 30 kg which continue to slide on the frictionless horizontal surface. The 20 kg piece goes off at 60° with velocity v_{1} = 100 m/s as shown in the drawing. (Note everything happens on a horizontal surface, so you do not need to worry about gravity.)

Calculate v_{2y}, the y component of the velocity of the 30 kg piece?

(a) v_{2y} = -50.0 m/s (b) v_{2y} = -57.7 m/s (c) v_{2y} = -66.6 m/s

(a) β = 45° (b) β = 49° (c) β = 60°

(a) KE_{f} = 0.0 J (b) KE_{f} = 62.6 kJ (c) KE_{f} = 125.0 kJ (d) KE_{f} = 187.5 kJ (e) KE_{f} = 250.0 kJ

A car with mass M = 3000 kg is traveling 50 m/s when its brakes are applied bringing it to a stop in 85 meters on a flat horizontal road.

How much work, W_{1}, does it take to stop the car?

(a) W_{1} = -3500 kJ (b) W_{1} = -3750 kJ (c) W_{1} = -6000 kJ

(a) 0.5 W_{1} (b) W_{1} (c) 2 W_{1}

An object of mass M = 10 kg is moving horizontally in a straight line at a speed of 15 m/s on a frictionless surface. A force of 50 N slows down the object to 12 m/s.

How long was the force applied?

(a) 0.3 s (b) 0.6 s (c) 0.9 s

(a) -405 J (b) -252 J (c) 0 J (d) +252 J (e) +405 J

A massless beam is placed on a fulcrum as shown in the figure (not to scale) below. A 3 kg box is placed 1.25 m to the left of the fulcrum. A force of 15 N is applied at an unknown distance x to the right of the fulcrum (see the figure), so the beam is balanced.

What is the force of the fulcrum on the beam?

(a) 15 N (b) 29 N (c) 44 N

(a) x = 1.25 m (b) x = 2.0 m (c) x = 2.45 m

(a) 38 Nm (b) 33 Nm (c) 16 Nm

A solid sphere rolls downs a ramp of height h. The sphere has a radius of 0.38 m and a moment of inertia of 0.14 kg m^{2} and its acceleration as it rolls down the ramp is 0.4 m/s^{2}. When it reaches the bottom of the ramp, the sphere is traveling at 7 m/s.

What is the mass of the sphere?

(a) m = 2.42 kg (b) m = 3.62 kg (c) m = 4.37 kg

(a) h = 2.5 m (b) h = 3.0 m (c) h = 3.5 m (d) h = 4.0 m (e) h = 4.5 m

(a) 0 (b) 0.29 N (c) 0.39 N (d) 0.98 N (e) 1.3 N

(a) < 7 m/s (b) = 7 m/s (c) > 7 m/s

A 65 kg person is standing 0.5 meters from the center of a merry-go-round that is spinning with angular frequency ω = 1.7 radians/second. When no one is on it, the merry-go-round has moment of inertia of 150 kg m^{2}.

What is the speed of the person standing 0.5 m from the center of the merry-go-round?

(a) v = 0.85 m/s (b) v = 1.35 m/s (c) v = 2.17 m/s

(a) 94 N (b) 235 N (c) 637 N

(a) ω = 0.95 rad/s (b) ω = 1.4 rad/s (c) ω = 1.7 rad/s (d) ω = 2.3 rad/s (e) ω = 3.4 rad/s

(a) KE_{0.5} < KE_{1.5} (b) KE_{0.5} = KE_{1.5} (c) KE_{0.5} > KE_{1.5}

Two identical blocks with mass M are connected by a string that runs over a disk pulley (I = 1/2 MR^{2}) that also has mass M as shown. The top block is on a horizontal frictionless table. The blocks are released from rest.

How fast are the blocks moving after the vertical block has dropped 0.4 meters?

(a) 1.53 m/s (b) 1.77 m/s (c) 1.98 m/s (d) 2.87 m/s (e) 3.21 m/s

(a) faster than (b) the same rate as (c) slower than