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 98. The exam period was 90 minutes. The mean score was 67.7; 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 small projectile of mass M = 0.05 kg is connected to a rotating axis as shown in the figure. The length of the connecting rod is 5 cm. The projectile starts from rest and undergoes uniform angular acceleration. You should neglect gravity and the mass of the rod for all parts of this question.

The rod releases the projectile when the centripetal force reaches 40,000 N. What is the speed of the bullet at this point?

(a) 10 m/s (b) 50 m/s (c) 100 m/s (d) 150 m/s (e) 200 m/s

(a) -45° (b) 0° (c) 45°

(a) 1000 radians/s^{2} (b) 2000 radians/s^{2} (c) 3000 radians/s^{2} (d) 4000 radians/s^{2} (e) 5000 radians/s^{2}

(a) 100 J (b) 250 J (c) 500 J (d) 1000 J (e) 2000 J

Spacecraft A, which carriers a projectile (m_{P} = 10 kg), attacks spacecraft B (M_{B} = 200 kg), which does not have a projectile on board. The total mass of the spacecraft A, including the projectile, is M_{A} = 200 kg. A and B are initially at rest.

Spacecraft A shoots its projectile at spacecraft B with speed v_{P} = 50 m/s. What is the recoil speed of spacecraft A after shooting its projectile?

(a) 2.10 m/s (b) 2.63 m/s (c) 2.83 m/s

(a) 2.36 m/s (b) 2.38 m/s (c) 2.50 m/s

(a) 9000 J (b) 10900 J (c) 11900 J

A gun shoots pellets vertically at a rate of 1000 per second. Each pellet has mass of 1 g (0.001 kg). The pellets, traveling with a speed of 20 m/s, strike the left end of a horizontal plank, as shown in the figure. They bounce back with a speed of 15 m/s. Assume the plank is massless.

What is the impulse each pellet delivers to the plank?

(a) 0.035 kg m/s (b) 0.050 kg m/s (c) 0.065 kg m/s

(a) 0.035 Nm (b) 35 Nm (c) 50 Nm

(a) 61.8 cm (b) 81.8 cm (c) 91.8 cm

Assume that the coefficient of kinetic friction between the car and the road is μ = 0.294 and that the wheels lock up and the car skids in both cases. The car has mass 2500 kg.

Which one of the following statements is true?

(a) Braking uphill you needed a quarter of the distance to stop the car compared to braking downhill. (b) Braking uphill you needed half of the distance to stop the car compared to braking downhill. (c) Braking uphill you needed the same distance to stop the car compared to braking downhill. (d) Braking uphill you needed twice the distance to stop the car compared to braking downhill. (e) Braking uphill you needed four times the distance to stop the car compared to braking downhill.

Two masses approach one another, with m_{1} traveling along the x axis and m_{2} traveling along the y axis, as shown in the figure. They collide at the origin, stick together, and emerge as one mass with velocity v_{f}.

The total kinetic energy is conserved in this collision.

(T) True (F) False

(a) 0.93 m/s (b) 1.47 m/s (c) 2.45 m/s (d) 3.23 m/s (e) 4.84 m/s

(a) 14.2° (b) 21.8° (c) 34.4° (d) 41.7° (e) 52.6°

A hollow sphere and a solid cylinder, both with radius R and mass M, are released from rest at the top of an inclined plane. They roll without slipping.

Which mass reaches the bottom first?

(a) solid cylinder (b) hollow sphere (c) They reach the bottom at the same time.

(a) solid cylinder (b) hollow sphere (c) same

A wooden plank of length 6 m and mass m_{p} = 4 kg rests on two supports, denoted A and B. At the left end of the plank rests a weight with mass M_{L} = 25 kg. Another mass M_{R} is placed at the other end. The positions of the supports are as shown.

What is the smallest value of M_{R} required to keep the plank from tipping?

(a) 3.4 kg (b) 4.1 kg (c) 5.5 kg (d) 6.8 kg (e) 7.7 kg

(a) 5.7 kg (b) 9.2 kg (c) 11.5 kg (d) 13.8 kg (e) 15.1 kg

An annulus (cylinder with a hole in it) is free to rotate around its center axis, as shown. The annulus has an outer radius R_{o} = 1.5 m, total mass M = 4 kg, rotational inertia I = 10 kg m^{2}. A string is wrapped around the annulus, and is pulled by a force F = 4.5 N. The annulus is initially at rest. Note: moment of inertia (i.e. rotational inertia) for an annulus is I_{A} = M (R_{i}^{2}+R_{o}^{2}) / 2.

THIS QUESTION WAS DISCARDED. What is the inner radius of the annulus, R_{i}?

(a) 0.72 m (b) 0.98 m (c) 1.27 m (d) 1.66 m (e) 2.07 m

(a) 10.22 s (b) 13.64 s (c) 16.84 s (d) 19.61 s (e) 22.29 s

(a) 147 J (b) 266 J (c) 304 J (d) 392 J (e) 424 J

(a) clockwise (b) counterclockwise (c) Sally will not spin.

A Frisbee with rotational inertia of 2.2 kg m^{2} rotates with an angular frequency 15 cycles/sec.

What is the magnitude of the Frisbee's angular momentum?

(a) 116 kg m^{2}/s (b) 207 kg m^{2}/s (c) 274 kg m^{2}/s

(a) up (b) down (c) Angular momentum is a scalar so does not have a direction.