### Fall 2009 Physics 211 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 110. The exam period was 90 minutes. The mean score was 85.1; the median was 89. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

This and the next question refer to the following situation:

A puck of mass 1 kg collides with a wall. The puck will explode if hit with a force greater than 15 N. Before the collision the puck's velocity is 10 m/s. After the collision the puck's velocity is -10 m/s. Assume a constant force is applied to the puck during the collision.

What is the shortest time interval over which this puck could have been hit such that it did not explode?

(a)   2.33 s
(b)   1.33 s
(c)   0.33 s
(d)   0.033 s
(e)   0.0033 s

### QUESTION 2*

The mass of the puck is doubled. The initial and final velocity are the same as given above. The puck will explode if hit with a force greater than 15 N, as above. The time interval over which the puck is hit is the same as given for the answer in the previous question. Which one of the following statements is accurate?

(a)   The puck doesn't explode.
(b)   The puck explodes.
(c)   Not enough information is given to determine if the puck explodes.

### QUESTION 3**

This and the next question refer to the following situation:

A 0.001 kg bullet is fired from a gun and lodges inside a wooden block of mass 0.2 kg. The block and bullet then slide on a rough floor with a coefficient of kinetic friction μk = 0.4 before coming to rest after sliding a distance of 3 m.

Compare KEi, the initial kinetic energy of the bullet, with Wf, the macroscopic work done by the frictional force between the block and the floor in stopping the block.

(a)   KEi < Wf
(b)   KEi = Wf
(c)   KEi > Wf

### QUESTION 4*

The initial velocity of the bullet was:

(a)   440 m/s
(b)   680 m/s
(c)   975 m/s
(d)   1175 m/s
(e)   1600 m/s

### QUESTION 5*

This and the next two questions refer to the following situation:

A 5 kg block slides on a horizontal, frictionless surface with a velocity of 2 m/s. It collides with an ideal, massless spring which is attached to a 15 kg block which is initially at rest. The spring has a spring constant of k = 50 N/m.

At the instant the spring is maximally compressed, both masses will be traveling with a common velocity of:

(a)   0.25 m/s
(b)   0.5 m/s
(c)   1 m/s
(d)   1.5 m/s
(e)   2 m/s

### QUESTION 6**

When the spring is maximally compressed, how do the magnitudes of the acceleration of the two blocks compare?

(a)   The acceleration of the 5 kg block is 3 times the acceleration of the 15 kg block.
(b)   The acceleration of the 15 kg block is 3 times the acceleration of the 5 kg block.
(c)   The acceleration of the 5 kg block equals the acceleration of the 15 kg block.

### QUESTION 7*

What is the maximum compression of the spring during the collision?

(a)   0.24 m
(b)   0.55 m
(c)   0.74 m
(d)   0.94 m
(e)   1.32 m

### QUESTION 8*

This and the next two questions refer to the following situation:

A small block having a mass of 2 kg is in contact with an ideal spring of relaxed length 1 m and spring constant k = 100 N/m . The spring is compressed to a length of 0.5 m. The block is released from rest at x = 0.5 m. At x = 1 m the mass leaves the spring and comes to rest at x = 2 m. Throughout its entire motion the block slides on a rough surface with a coefficient of kinetic friction μk .

The maximum acceleration of the block occurs the instant the block begins to move.

(T)   True
(F)   False

### QUESTION 9***

Which statement correctly describes the position xfast where the block is traveling the fastest?

(a)   xfast = 1 m
(b)   xfast < 1m
(c)   xfast > 1m

### QUESTION 10**

What is the coefficient of kinetic friction of the surface?

(a)   0.12
(b)   0.42
(c)   0.36
(d)   0.53
(e)   0.62

### QUESTION 11*

This and the next two questions refer to the following situation:

A small box of mass M = 10 kg is released from rest at a height of 2 meters on a frictionless incline as shown. At the bottom of the ramp, it encounters a 1 meter long rough surface with μk = 0.25, and then a frictionless circular rise.

At what height h does the box stop on the circular rise?

(a)   2 meters
(b)   1.75 meters
(c)   1.50 meters
(d)   1.25 meters
(e)   1.0 meters

### QUESTION 12**

Compare the magnitude of the work done on the box by gravity to the magnitude of the work done on the box by friction from the time it is released to the time it reaches its maximum height h on the circular rise.

(a)   |Wgravity| > |Wfriction|
(b)   |Wgravity| < |Wfriction|
(c)   |Wgravity| = |Wfriction|

### QUESTION 13**

An explosion occurs which splits a bomb, initially at rest in outer space, into a chunk of mass M1 and a chunk of mass M2. The ratio of their kinetic energies after the explosion is given by:

(a)   KE1 / KE2  =  M1 / M2
(b)   KE1 / KE2  =  M2 / M1
(c)   KE1 / KE2  =  1

### QUESTION 14**

A rocket sled with a mass of 100 kg starts from rest on a frictionless track, inclined at 30°. The rocket engine provides a constant horizontal thrust of 12,000 N until the sled reaches the end of the 50 m ramp and the engine is shut off. The sled then falls under the influence of gravity until it strikes the ground. Find the speed at which the sled hits the ground.

(a)   3.13 m/s
(b)   77 m/s
(c)   102 m/s
(d)   151 m/s
(e)   204 m/s

### QUESTION 15*

This and the next question refer to the following situation:

A small steel ball of mass M is attached to the end of a massless string of length L which is fixed at the opposite end. The string is pulled taut and held horizontally, as shown above. The ball is then released from rest. At the bottom of the path, the ball strikes a steel block of mass 3M initially at rest on a horizontal frictionless surface.

What is the speed of the steel ball just before the collision?

(a)   sqrt(2gL)
(b)   sqrt(gL)
(c)   sqrt(L/g)

### QUESTION 16*

In the x-direction, if the velocity of the ball just before the collision is v and the velocity of the ball just after the collision is -v/3, what is the velocity of the block just after the collision?

(a)   4 v / 9
(b)   2 v / 3
(c)   3 v / 4
(d)   3 v / 2
(e)   v

### QUESTION 17*

This and the next question refer to the following situation:

A 6 kg box is pulled across a rough floor by a rope. There is friction between the box and the floor. The tension in the rope is T = 5 N. Consider a time interval during which the box moves a distance of 2 m, and its velocity decreases from 1.5 m/s to 0.8 m/s.

How much work is done on the box by the rope?

(a)   0 J
(b)   10 J
(c)   -10 J

### QUESTION 18**

Calculate the work done on the box by friction?

(a)   -4.83 J
(b)   -6.91 J
(c)   -8.11 J
(d)   -9.25 J
(e)   -14.83 J

### QUESTION 19*

This and the next question refer to the following situation:

A glider of mass m1 slides on a frictionless track with initial velocity v1i = 2 m/s. It hits a stationary glider of mass m2. A spring attached to the first glider compresses and relaxes during the collision so that mechanical energy is conserved and the collision is elastic. The velocity of the center of mass of the system is VCM = 0.3 m/s.

How does m1 compare to m2?

(a)   m1 > m2
(b)   m1 = m2
(c)   m1 < m2

### QUESTION 20**

What is the final velocity of the first glider after the collision?

(a)   v1f = -0.6 m/s
(b)   v1f = -1.2 m/s
(c)   v1f = -1.4 m/s
(d)   v1f = -1.6 m/s
(e)   v1f = -2.0 m/s

### QUESTION 21**

A car of mass m slides on frictionless ice with velocity 2v. It collides with a truck of mass 2m that slides on the same ice with velocity v directed in the opposite direction. The car and the truck stick together after the collision. How much kinetic energy is lost in the collision

(a)   m v2 / 2
(b)   m v2
(c)   2 m v2
(d)   3 m v2
(e)   5 m v2

### QUESTION 22*

This and the next question refer to the following situation:

A hunter with a mass of 80 kg stands on a frictionless horizontal ice surface and fires a 12 gram bullet in the horizontal direction from a 5 kg rifle. The hunter, still holding the rifle, recoils with a velocity of 0.15 m/s with respect to the ice. What must be the horizontal component of the speed of the bullet with respect to the ice?

(a)   304 m/s
(b)   531 m/s
(c)   1062 m/s
(d)   1220 m/s
(e)   1500 m/s

### QUESTION 23*

What is the average force on the bullet, if it reaches this final velocity in 0.001 seconds.

(a)   12.5 N
(b)   1290 N
(c)   12750 N

### QUESTION 24**

A fisherman has docked his boat on the shore as shown, but has not tied the boat to the shore. He is initially in the middle of the boat as shown when he starts to walk on the boat towards the shore. The boat is 20 meters long with its center of mass in the middle, and the mass of the boat is the same as the mass of the man.

When he reaches the end of the boat (the end towards shore), how far is he from the shoreline? (Assume that there are no horizontal forces applied by the water on the boat.)

(a)   He is exactly at the shoreline, where he wanted to be.
(b)   He is 5 meters away from the shoreline.
(c)   He is 10 meters away from the shoreline.
(d)   He is 15 meters away from the shoreline.
(e)   There is no unique answer because when he reaches the end of the boat, he is travelling away from the shoreline with a constant velocity.

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.