Spring 2011 Physics 101 Hour Exam 2(22 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 106. The mean score was 81.3; the median was 83. The exam period was 90 minutes. 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:

Two objects of mass M (= 1 kg) each travel with identical speed (|v1| = |v2| = 3 m/s) making an angle of θ relative to the x-axis. After they collide with each other, they travel as one object of mass 2M and with a velocity v3 (|v3| = 2 m/s) in the horizontal direction.

Is the collision elastic or inelastic?

(a)   elastic
(b)   inelastic

QUESTION 2*

How much kinetic energy is lost during the collision?

(a)   2.5 J
(b)   5 J
(c)   10 J
(d)   15 J
(e)   20 J

QUESTION 3**

What is the value for angle θ ?

QUESTION 4**

This question and the next one concern the same situation:

You have two balls of identical mass (m = 0.1 kg) but made of different materials. Let's call one the happy ball and the other the sad ball. When the happy ball is dropped and hits the floor at a speed of 2 m/s, it bounces back with the same speed. In contrast, the sad ball, when it is dropped and hits the floor at a speed of 2 m/s, it sticks to the floor without bouncing.

What is the magnitude of the impulse delivered to the floor by the happy ball?

(a)   0 kg m/s
(b)   0.05 kg m/s
(c)   0.1 kg m/s
(d)   0.2 g m/s
(e)   0.4 kg m/s

QUESTION 5**

Which of the two balls delivers a higher magnitude impulse to the floor?

(a)   the happy ball

QUESTION 6*

This question and the next two concern the same situation:

A student is pushing a box of mass M (= 5 kg) by applying a force F (= 100 N) on a horizontal floor. The kinetic coefficient of friction between the box and the floor is 0.2. The box starts from rest and moves to the right over a distance of 2 m.

How much work is done by the student to the box?

(a)   0 J
(b)   -141 J
(c)   141 J
(d)   -94 J
(e)   94 J

QUESTION 7*

What can you say about the work done by the normal force exerted by the floor?

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

QUESTION 8**

What is the work done by all of the forces acting on the box combined?

(a)   0 J
(b)   -141 J
(c)   141 J
(d)   -94 J
(e)   94 J

QUESTION 9*

This question and the next two concern the same situation:

Kaushiki throws a ball straight up from an initial height of 1 m. The initial speed of the ball is 5 m/s. Ignore friction due to air for this problem. The mass of the ball is 0.3 kg.

What is the maximum height reached by the ball?

(a)   2.28 m
(b)   3.56 m
(c)   4.73 m
(d)   5.88 m
(e)   6.97 m

QUESTION 10*

When the ball falls down back to the height of 1 m, what is the speed of the ball?

(a)   0 m/s
(b)   10 m/s
(c)   5 m/s

QUESTION 11*

What is the kinetic energy of the ball immediately before it hits the ground?

(a)   3.5 J
(b)   6.7 J
(c)   9.3 J
(d)   11.1 J
(e)   12.9 J

QUESTION 12*

This question and the next one concern the same situation:

Fred (75 kg) and Jane (50 kg) are at rest on skates facing each other. Jane then pushes Fred with a constant force F = 45 N for a time Δt. Jane then moves at a speed of 1.35 m/s.

What can you say about Fred's motion after the push?

(a)   He moves at the same speed as Jane's and in the opposite direction.
(b)   He moves at a speed higher than Jane's and in the opposite direction.
(c)   He moves at a speed lower than Jane's and in the opposite direction.

QUESTION 13*

What is the duration Δt of push?

(a)   0.5 s
(b)   1 s
(c)   1.5 s
(d)   2 s
(e)   3 s

QUESTION 14**

This question and the next two concern the same situation:

At one end of a light bar of length L is fixed a small ball of mass M. The other end of the bar is fixed to the ground at point P but can rotate freely around the point. A person supports the end of the bar where the ball is fixed with a force F that is perpendicular to the bar as noted in the figure. Initially, the bar makes an angle of 60° with the horizontal ground as illustrated below. You can ignore the mass of the bar.

To keep the bar stationary as shown in the figure, what force must the person exert? Give its magnitude. Here g is the acceleration of gravity.

(a)   Mg / 4
(b)   Mg / 2
(c)   Mg

QUESTION 15**

The bar with the small ball is stationary. What is the total torque acting on the bar around its mid point Q?

(a)   nonzero and clockwise around Q (seen from you)
(b)   zero
(c)   nonzero and counterclockwise around Q (seen from you)

QUESTION 16**

Now, the person stops holding the bar (of length L), so the force F is gone and the bar with the small ball (of mass M) starts to rotate around P. The situation immediately after the force is removed is illustrated below. You may ignore the size of the ball.

What is the magnitude of the angular acceleration α of the bar around point P immediately after the force F is gone?

(a)   α = g / 2
(b)   α = 3g / 4
(c)   α = g / 4
(d)   α = g / 2L
(e)   α = 3g / 4L

QUESTION 17**

A disk of radius R and mass M' is used as a frictionless pulley. There is a block of mass M with a massless string wound around it. Suppose M = M'. Initially, the system is stationary. Then, the mass is gently released, and it goes down by length L vertically as described in the figure below.

What can you say about the relation between the rotation kinetic energy Kpulley of the pulley and the translational energy Kblock of the block after the block has dropped by a distance of L?

(a)   Kpulley = Kblock / 4
(b)   Kpulley = Kblock / 2
(c)   Kpulley = Kblock
(d)   Kpulley = 2Kblock
(e)   Kpulley = 4Kblock

QUESTION 18*

This question and the next two concern the same situation:

You have invented a new recording device that uses a disk of radius 4.1 mm, similar to a DVD or CD (see figure). The outermost track is with radius 4 mm and the innermost track is with radius 1 mm. The reading speed (linear speed) is kept constant irrespective of the position on the disk by adjusting the angular velocity depending on which track is being read. The angular velocity of the disk when the outermost track is being read is 241 rad/s.

For the outermost track, what is the linear reading speed? (The linear reading speed is the constant tangential speed which is maintained while playing the disk.)

(a)   0.96 m/s
(b)   1.08 m/s
(c)   1.15 m/s
(d)   1.52 m/s
(e)   1.97 m/s

QUESTION 19*

What should be the angular velocity of the disk when the innermost track of radius 1 mm is being read to maintain the linear reading speed (tangential speed) of the track?

QUESTION 20*

After a recording is over, the disk must be stopped. The reading ends at the outermost track. What is the magnitude α of the uniform angular acceleration required to stop the disk rotating at 241 rad/s after 12 full rotations? (Pay attention to the units!)

QUESTION 21*

Two uniform objects of the same mass start to roll down an inclined plane without slip from the same height. One is a solid cylinder and the other is a hollow cylinder. Which gets to the bottom first?

(a)   solid cylinder
(b)   hollow cylinder
(c)   They arrive at the same time.

QUESTION 22**

A puck of mass 0.2 kg slides in a circular path on a horizontal frictionless table at an angular speed ω of 10 rad/s. It is held at a constant radius of 1 meter by a string threaded through a frictionless hole at the center of the table. Then, you pull on the string such that the radius decreases by a factor of 3. What happens to the angular speed of rotation?

(a)   It decreases by a factor of nine.
(b)   It decreases by a factor of three.
(c)   It does not change.
(d)   It increases by a factor of three.
(e)   It increases by a factor of nine.

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.