### Spring 2009 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 114. The exam period was 90 minutes. The mean score was 73.1; the median was 74. 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 question and the next two concern the same situation:

In the figure below, A is a circular cylinder of radius R with moment of inertia I (> 0). B is an identical cylinder except that a point mass of mass mp (> 0) is attached at the center.

We release the cylinders gently at the top of the slope in the figure without motion.

Suppose the slope is frictionless. After sliding down the slope for 1 m (see the figure), which has a faster translational motion??

(a)   A
(b)   B
(c)   A and B have the same speed.

### QUESTION 2***

Now, suppose the cylinders roll down the slope without slipping. After rolling down the slope for 1 m (see the figure), which has a faster translational motion?

(a)   A
(b)   B
(c)   A and B have the same speed.

### QUESTION 3***

Suppose the cylinder in B has a total mass m = 2.3 kg (= mass of the cylinder plus mass of the point-mass), a moment of inertia I = 0.1 kgm2 and R = 0.2 m. The slope is 30°. Given the angular acceleration is 11.7 rad/s2, what is the magnitude of the static frictional force between the cylinder and the slope?

(a)   5.85 N
(b)   8.90 N
(c)   11.7 N
(d)   15.8 N
(e)   21.3 N

### QUESTION 4**

This and the following question concern related physical situations:

Consider a pulley made of two connected cylinders of radius R and R/2 as shown in the figure. The moment of inertia of the pulley is I. Two blocks with the same mass M are hung with weightless strings that do not slip against the pulley.

The masses start to move and the pulley starts to rotate from the initial stationary condition. M = 1.2 kg and R = 1.5 m. When the right mass goes down by 1 m, what is the total kinetic energy of the system? Notice that the distance the left mass moves is just half of the right mass.

(a)   3.7 J
(b)   4.8 J
(c)   5.9 J
(d)   7.0 J
(e)   8.1 J

### QUESTION 5***

Suppose the speed of the right mass after descending by 1 m in the preceding problem is v0. Now, let us double the masses M to 2M and the moment of inertia I to 2I while keeping R as before. Then, what is the speed of the right mass after descending by 1 m as in the preceding problem in terms of v0?

(a)   0.5 v0
(b)   1.0 v0
(c)   1.1 v0
(d)   1.4 v0
(e)   none of the above

### QUESTION 6**

This and the next question concern the same situation:

There is a weightless bar of length 1 m. At one end A is a mass M = 30 kg and at the other end B is a mass m = 5 kg. The bar is at rest on the pivot P. (Note: Assume + is for counterclockwise rotation.)

What is the torque around B due to mass M?

(a)   +294 Nm
(b)   +187 Nm
(c)   0
(d)   -187 Nm
(e)   -294 Nm

### QUESTION 7***

What is the torque around A due to the force exerted by the pivot?

(a)   +98 Nm
(b)   +49 Nm
(c)   0
(d)   -49 Nm
(e)   -98 Nm

### QUESTION 8**

This and the next question concern the same situation:

There is a table whose top surface is frictionless and horizontal. A massive pulley is attached to its edge and two masses M1 and M2 are connected with a weightless string passing though the pulley as illustrated below. The block M1 has mass 1.3 kg and M2 = 5 kg. The string does not slip against the pulley whose radius R is 30 cm and whose moment of inertia is I= 1.2 kgm2.

The tension T1 is 11.9 N. Find the angular acceleration of the pulley.

(a)   1.1 rad/s2
(b)   2.2 rad/s2
(c)   3.3 rad/s2
(d)   4.4 rad/s2
(e)   5.5 rad/s2

### QUESTION 9**

Would the angular acceleration be larger, the same, or smaller, if the mass of the pulley were zero, but the radius was the same?

(a)   larger
(b)   smaller
(c)   not enough information

### QUESTION 10*

This and the next question concern the same situation:

A round horizontal table is turning freely. It has a moment of inertia I = 60 kgm2 with a radius R = 2 m. On the table stands a child of mass 15 kg. In the following you may ignore the size (cross section) of the child (i.e., you may regard her as a point mass).

From the initial position at the edge of the table the child moves to the center. What happens to the angular speed of the table?

(a)   It speeds up.
(b)   It slows down.
(c)   It stays the same speed.

### QUESTION 11***

To perform the motion in the preceding problem the child has to do W = +120 J of work. Find the angular momentum of the system.

(a)   170 kg m2/s
(b)   245 kg m2/s
(c)   420 kg m2/s
(d)   560 kg m2/s
(e)   720 kg m2/s

### QUESTION 12*

This question and the next three concern the same situation:

Two blocks moving in a straight line, along the x-axis, on a frictionless, horizontal surface collide in a completely elastic collision (no energy is lost in the collision).

Block 1 has m1 = 2 kg, v1 = 3.3 m/s, Block 2 has m2 = 0.1 kg, v2 = -3.3 m/s.

What is the magnitude of the total momentum of the blocks after the collision?

(a)   less than it was before the collision
(b)   the same as it was before the collision
(c)   more than it was before the collision

### QUESTION 13**

The energy of block 2 will

(a)   increase.
(b)   decrease.
(c)   stay the same.

### QUESTION 14*

Suppose that the blocks had a partially inelastic collision instead. Would it be possible for block 1 to have a speed of 4 m/s after the collision?

(a)   yes
(b)   no
(c)   It is impossible to tell from the information given.

### QUESTION 15**

Block 2 then undergoes another collision so that its velocity is now vx = -18 m/s, vy = 0 m/s. Then it explodes into two pieces 2a and 2b of mass m2a = 0.03 and m2b = 0.07 kg; block m2a moves with velocity vx = -20 m/s, vy = 3 m/s. What is the velocity of block 2b?

(a)   vx = +16 m/s, vy = -2 m/s
(b)   vx = -17 m/s, vy = +1.3 m/s
(c)   vx = -24 m/s, vy = -4 m/s
(d)   vx = -17 m/s, vy = -1.3 m/s
(e)   vx = -25 m/s, vy = +2 m/s

### QUESTION 16**

This question and the next two concern the same situation:

A car of mass M = 1000 kg is moving in a straight line on level ground at 70 m/s. It applies its brakes and slides (skids) to a halt. Which one of the following forces does nonzero work?

(a)   normal force
(b)   gravitational force
(c)   kinetic friction
(d)   static friction
(e)   centripetal force

### QUESTION 17***

Suppose that the car starts up again and drives up a hill of height h = 300 m (obviously this is not in Champaign-Urbana) at constant speed v = 30 m/s, and that the wheels turn without slipping. What is the net work done (sum of the work done by all external forces), on the car, as it climbs the hill?

(a)   M g h
(b)   0
(c)   (1/2) M v2

### QUESTION 18*

At the top of the hill the car turns around, stops, and rolls freely, without air resistance or any other kind of friction, back to the bottom of the hill. What is its kinetic energy at the bottom of the hill?

(a)   300,000 J
(b)   2,940,000 J
(c)   4,400,000 J
(d)   10,100,000 J
(e)   39,000,000 J

### QUESTION 19*

This question and the next two concern the same situation:

A box sits on the floor. A force F = 200 N is then applied to the right but slightly upward at an angle of 30° from the horizontal (see diagram) such that the box moves 5 meters horizontally to the right. How much work is done by the force?

(a)   50 J
(b)   866 J
(c)   1900 J
(d)   2430 J
(e)   3230 J

### QUESTION 20*

Suppose that the force (of magnitude 200 N) is applied horizontally instead. How much work is done by the force?

(a)   less than when the force was applied at an angle
(b)   the same as when the force was applied at an angle
(c)   more than when the force was applied at an angle

### QUESTION 21*

Suppose that the force is applied horizontally still, and the box moves with a speed of 0.2 m/s. What power is supplied by the force?

(a)   10 W
(b)   18 W
(c)   30 W
(d)   40 W
(e)   44 W

### QUESTION 22***

A Hooke's law spring with spring constant 2 kg/s2 (= 2 N/m) is initially at its resting position (x = 0). A time-variable force F is applied so that the spring is compressed by 0.1 m (x = -0. 1m), then it expands past its resting position to 0.1 m (x = +0.1 m). How much work is done by the force F?

(a)   0
(b)   0.01 J
(c)   It is impossible to tell from the information given.

### QUESTION 23***

A ball of mass 0.1 kg is falling straight down with speed 10 m/s just before it bounces off the floor. It then rises (straight up) to a height of 4 m. What is the impulse delivered to the ball by the floor?

(a)   0.98 kg m/s
(b)   1.2 kg m/s
(c)   1.9 kg m/s
(d)   2.0 kg m/s
(e)   4.7 kg m/s

### QUESTION 24*

A system of 3 identical masses is arranged as shown in the figure. What is the x-coordinate of the center of mass?

(a)   0
(b)   2
(c)   3
(d)   3.5
(e)   4

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.