### Spring 2004 Physics 101 Hour Exam 2(26 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 86. When the exam was given, the mean was 61.2; the median was 62. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1**

This and the next three questions concern the same situation:

Two balls with equal mass are dropped from a height of 2 meters above the floor. They both bounce back up to a maximum height of 1.8 meters above the floor. The first ball is made of steel, and is in contact with the floor for 0.04 seconds. The second ball is made of rubber and is in contact with the floor for 0.09 seconds.

Which ball has a greater impulse on the floor?

(a)   steel
(b)   rubber
(c)   same

### QUESTION 2**

Which ball has a greater average force on the floor during the collision?

(a)   steel
(b)   rubber
(c)   same

### QUESTION 3*

What is the speed of the steel ball just before it hits the floor?

(a)   3.13 m/s
(b)   5.94 m/s
(c)   6.26 m/s

### QUESTION 4*

What is the maximum speed of the steel ball after it bounces off the floor?

(a)   3.13 m/s
(b)   5.94 m/s
(c)   6.26 m/s

### QUESTION 5**

This and the next three questions concern the same situation:

A 0.05 kg ball travels horizontally with initial velocity vi, before colliding with, and sticking to a 0.13 kg block attached to an uncompressed massless spring (k = 150 N/m). Immediately after the collision, the block and ball are traveling at 15 m/s to the right. (You may assume the collision takes place in a negligible amount of time. Ignore gravity.)

During the collision of the ball with the block

(a)   the total momentum of the ball and block and spring are conserved.
(b)   the total mechanical energy (potential plus kinetic) of the ball, block and spring are conserved.
(c)   Both are correct.

### QUESTION 6***

After the collision, and as the spring compresses,

(a)   the total momentum of the ball and block and spring are conserved.
(b)   the total mechanical energy of the ball, block and spring are conserved.
(c)   Both are correct.

### QUESTION 7*

Calculate vi the initial velocity of the ball before sticking to the block.

(a)   15 m/s
(b)   39 m/s
(c)   54 m/s

### QUESTION 8**

Calculate x, the maximum compression of the spring attached to the block after the collision.

(a)   0.35 m
(b)   0.52 m
(c)   0.73 m

### QUESTION 9*

This and the next question concern the same situation:

A 3 kg ball is dropped from the top of a 30 meter building.

The work done be gravity as the ball falls down is

(a)   positive.
(b)   zero.
(c)   negative.

### QUESTION 10*

The speed of the ball just before it hits the ground is measured to be 20 m/s. How much work was done by non-conservative forces (e.g. air resistance) in slowing the ball down as it fell?

(a)   282 J
(b)   312 J
(c)   339 J

### QUESTION 11*

In the figure below the result of an explosion is depicted. The object was originally at rest and split in three parts. The arrows show the velocity of these parts after the explosion. Which one of these proposed scenarios could have a physical sense?

(a)
(b)
(c)

### QUESTION 12*

This and the next question concern the same situation:

A 4 kg cart is sliding across a frictionless table at 3 m/s to the right. It collides and sticks to a 3 kg cart that was initially at rest.

What is the speed of the carts after they collide?

(a)   1.71 m/s
(b)   2.51 m/s
(c)   5.23 m/s

### QUESTION 13*

Calculate the total mechanical energy (of both carts) lost during the collision.

(a)   7.7 J
(b)   12.3 J
(c)   22.5 J

### QUESTION 14**

This and the next question concern the same situation:

A 3-kg block is pulled up a frictionless ramp as shown in the diagram to the right. Calculate the work done by the 30 N force as the block moves a distance of 3m along the ramp.

(a)   50 J
(b)   60 J
(c)   90 J

### QUESTION 15***

As the block is pulled up, its speed

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

### QUESTION 16*

This and the next two questions concern the same situation:

In the scale depicted below, the mass of the uniform beam is 50 g. The mass of the object you want to weigh is equal to 610 g. The mass of the sliding weight is M. The position of the pivot under the beam is shown in the picture.

What is the position of the center of mass of the beam?

(a)   5.34 cm to the right of the pivot
(b)   6.57 cm to the right of the pivot
(c)   7.75 cm to the right of the pivot

### QUESTION 17*

What is the smallest mass M that can be used to balance this scale?

(a)   M = 127 g
(b)   M = 163 g
(c)   M = 198 g
(d)   M = 221 g
(e)   M = 257 g

### QUESTION 18*

Let M be the answer to the previous question. If you were doing the same experiment on the Moon, where gravity is 6 times smaller than on Earth, what would be the smallest mass that can be used to balance this scale?

(a)   M / 6
(b)   M
(c)   6 M

### QUESTION 19*

This and the next two questions concern the same situation:

Four point-like objects of equal mass m = 1.5 kg are located in four corners of a square of side 1.1 m as shown in the figure below.

What is the moment of inertia of this system about the axis A?

(a)   1.1 kg m2
(b)   1.8 kg m2
(c)   2.9 kg m2

### QUESTION 20***

Compare the moments of inertia of this system about the axis A and B?

(a)   IA < IB
(b)   IA > IB
(c)   IA = IB

### QUESTION 21*

Let IC be the moment of inertia around axis C, which is perpendicular to the plane of the page and crosses it at the center of the square. If the mass of the objects were doubled to 3 kg, the moment of inertia around axis C of this new system would be equal to

(a)   IC / 2
(b)   IC
(c)   2 IC

### QUESTION 22***

This and the next two questions concern the same situation:

A cylinder rotates about the axis OO’. The radius of the cylinder is 15 cm. A handle is attached to the cylinder and this system can be used to lift heavy objects attached to the cylinder by a rope, as shown in the figure below. The length of the handle is 80 cm.

What is the minimum force that must be applied to the handle to keep the 50-kg box in equilibrium?

(a)   49 N
(b)   92 N
(c)   234 N
(d)   490 N
(e)   527 N

### QUESTION 23*

What is the minimum amount of work needed to lift up the box of 50 kg by 1.5 m?

(a)   735 J
(b)   544 J
(c)   321 J

### QUESTION 24**

Let W be the answer to the previous question. If you were to lift the box of 50 kg by 1.5 m by directly pulling the rope with your hands, without using the cylinder, the minimum amount of work you would need to produce would be

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

### QUESTION 25***

This and the next question concern the same situation:

A cord passes over a pulley and suspends two blocks of different masses as shown in the figure below. The mass of the pulley is 4 kg and its radius is equal to 25 cm. The mass of the object on the left is m1 = 2 kg. The mass of the object on the right is m2 = 3 kg.

The blocks are initially at rest and they start to move. What is the speed of the second block after it has moved down by Δh = 3m . (Moment of inertia of the pulley I = ½ MpRp2).

(a)   2.9 m/s
(b)   3.3 m/s
(c)   4.8 m/s
(d)   5.4 m/s
(e)   6.8 m/s

### QUESTION 26*

If m1 = m2 and the blocks start at rest, can the blocks start to move by themselves?

(a)   Yes
(b)   No

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.