Spring 2008 Physics 101 Hour Exam 2
(24 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

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/s2 downward and ignore any effects due to air resistance.


QUESTION 1*

This and the next three questions concern the same situation:

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


QUESTION 2**

At the moment the projectile is released, the rod is horizontal, as shown in the figure. Which direction will the projectile fly? The angle is defined clockwise from the vertical arrow in the figure.

(a)   -45°
(b)   0°
(c)   45°


QUESTION 3*

Suppose it takes 2 seconds to accelerate the projectile from rest to v = 100 m/s. What is the average angular acceleration?

(a)   1000 radians/s2
(b)   2000 radians/s2
(c)   3000 radians/s2
(d)   4000 radians/s2
(e)   5000 radians/s2


QUESTION 4*

When the projectile reaches v = 100 m/s, what was the net work done on the projectile during its acceleration?

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


QUESTION 5*

This and the next two questions concern the same situation:

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

Spacecraft A shoots its projectile at spacecraft B with speed vP = 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


QUESTION 6*

The projectile hits spacecraft B and gets stuck (i.e. the collision is completely inelastic). What is B's speed after the collision?

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


QUESTION 7*

How much kinetic energy is lost in the collision?

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


QUESTION 8*

This and the next two questions concern the same situation:

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


QUESTION 9**

The plank is attached to a pivot at its right end, P. What is the average torque exerted around this pivot?

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


QUESTION 10**

Suppose the average torque (the previous answer) were 45 Nm. You now place a mass M = 5 kg on top of the plank as shown. At what distance x from the pivot must you place the mass so that the system is in rotational equilibrium?

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


QUESTION 11***

You travel on a straight road in a car at 100 km/h and hit the brakes to avoid an obstacle. The road is going uphill at an angle of 10°. The next day you travel on a different road at the same speed and you need to brake again. This road is going downhill at an angle of -10°.

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.


QUESTION 12**

This and the following two questions concern the same situation:

Two masses approach one another, with m1 traveling along the x axis and m2 traveling along the y axis, as shown in the figure. They collide at the origin, stick together, and emerge as one mass with velocity vf.

The total kinetic energy is conserved in this collision.

(T)   True
(F)   False


QUESTION 13**

What is the magnitude of the velocity of the combined mass, vf?

(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


QUESTION 14*

What is the angle θ defined as shown in the figure above?

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


QUESTION 15**

This and the following question concern the same situation:

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.


QUESTION 16**

Which object has the larger rotational kinetic energy when it reaches the bottom?

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


QUESTION 17**

This and the following question concern the same situation:

A wooden plank of length 6 m and mass mp = 4 kg rests on two supports, denoted A and B. At the left end of the plank rests a weight with mass ML = 25 kg. Another mass MR is placed at the other end. The positions of the supports are as shown.

What is the smallest value of MR 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


QUESTION 18**

What is the largest mass, MR, that can be added to the right end without tipping the plank?

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


QUESTION 19

This and the following two questions concern the same situation:

An annulus (cylinder with a hole in it) is free to rotate around its center axis, as shown. The annulus has an outer radius Ro = 1.5 m, total mass M = 4 kg, rotational inertia I = 10 kg m2. 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 IA = M (Ri2+Ro2) / 2.

THIS QUESTION WAS DISCARDED.
What is the inner radius of the annulus, Ri?

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


QUESTION 20**

Because of the force F the string unwinds and the annulus begins to rotate. Assuming it starts at rest, how long does it take for the annulus to make ten rotations?

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


QUESTION 21**

How much work is done by F after the ten turns are completed?

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


QUESTION 22**

Sally sits on a frictionless, rotatable bar stool. Initially the stool is stationary, i.e. not rotating. She holds horizontally a bicycle wheel that is spinning counterclockwise (when viewed from above). Sally then flips the bicycle wheel 180°, i.e. so that it is again horizontal but spins in the opposite direction (i.e. clockwise). After flipping the wheel, which direction does Sally spin?

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


QUESTION 23*

This and the following question concern the same situation:

A Frisbee with rotational inertia of 2.2 kg m2 rotates with an angular frequency 15 cycles/sec.

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

(a)   116 kg m2/s
(b)   207 kg m2/s
(c)   274 kg m2/s


QUESTION 24**

If the Frisbee rotates as shown, what is the direction of its angular momentum?

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