### Fall 2008 Physics 211 Hour Exam 2(25 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 115. The exam period was 90 minutes. The mean score was 86.2; the median was 89. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

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

A block m1 with mass 7 kg moves up an inclined plane with an initial velocity v0 = 4.7 m/s. The inclined plane is at an angle of θ = 45° from the horizontal. The coefficient of kinetic friction between the block and the incline is 0.25.

What is the block's velocity when it has traveled a distance D=1 meter up the incline?

(a)   0.10 m/s
(b)   0.31 m/s
(c)   0.57 m/s
(d)   1.59 m/s
(e)   2.18 m/s

### QUESTION 2*

Traveling up the incline, the work done on the block by friction is:

(a)   -mgDsinθ
(b)   μkmgDcosθ/2
(c)   μkmgD
(d)   -μkmgDcosθ
(e)   mgDsinθ

### QUESTION 3*

If mass m1 is cut in half, the speed of the block when it has traveled D = 1 meter up the incline

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

### QUESTION 4*

If the initial velocity is doubled, the speed when it has traveled D = 1 meter up the incline has also doubled.

(T)   True
(F)   False

### QUESTION 5**

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

A frictionless ramp of mass 3m is initially at rest on a horizontal frictionless floor. A small box of mass m is placed at the top of the ramp and then released from rest. After the box is released, it slides down the ramp and onto the horizontal floor, where it is measured to have a speed v, having fallen a total distance h.

What is the speed v of the box after it has left the ramp?

(a)
(b)
(c)
(d)
(e)

### QUESTION 6*

If there were kinetic friction between the box and the ramp, but none between the ramp or block and the floor, the speed v of the box after it has left the ramp, compared to its speed when both the ramp and the floor are frictionless, would be

(a)   less than in the previous question.
(b)   the same as in the previous question.
(c)   more than in the previous question

### QUESTION 7

If there were kinetic friction between the ramp and the floor, but none between the box and the ramp, the speed v of the box after it has left the ramp, compared to its speed when both the ramp and the floor are frictionless, would be

(a)   less.
(b)   the same.
(c)   more.

### QUESTION 8*

This and the next question refer to the following situation:

Two discs are free to move without friction on a horizontal table. The 0.4 kg disc is initially at the position (x = 0, y = 1.0) m, moving with velocity (vx = 3.0, vy = 0) m/s. The 0.6 kg disc is initially at (x = 1.5, y = 0) m, moving with velocity (vx =0, vy =2.0) m/s. The figure above displays the initial conditions for the two discs in the x-, y- coordinates.

The initial velocity of the center of mass of the two-disc system is:

(a)   (vx,vy) = (3.0,2.0) m/s
(b)   (vx,vy) = (2.0,3.0) m/s
(c)   (vx,vy) = (2.7,2.0) m/s
(d)   (vx,vy) = (1.8,1.8) m/s
(e)   (vx,vy) = (1.2,1.2) m/s

### QUESTION 9**

The two blocks collide at some point in the x-y plane. What is the velocity of the center of mass after the collision?

(a)   less than before the collision
(b)   the same as before the collision
(c)   It depends on whether the collision is elastic or inelastic.

### QUESTION 10*

"A force is conservative if the work done by the force is independent of the path that the object moves under the influence of the force". This statement is:

(T)   True
(F)   False

### QUESTION 11*

A ball of clay of mass m = 0.5 kg strikes a block of mass M = 8.0 kg which slides on a frictionless table as it compresses a spring with spring constant k = 60 N/m. The initial speed of the ball of clay is v = 12 m/s. The spring is initially at its relaxed length.

What is the maximum compression of the spring, d, after the collision (the clay sticks to the block)?

(a)   d = 0.034 m
(b)   d = 0.089 m
(c)   d = 0.108 m
(d)   d = 0.266 m
(e)   d = 0.437 m

### QUESTION 12*

This and the next question refer to the following situation:

Two eggs of mass m = 0.15 kg with initial velocity v = 3 m/s are incident on a trampoline and on an ordinary floor. One egg makes an elastic collision with the trampoline; the other makes a totally inelastic collision with the floor.

If the interaction time of the egg with the trampoline is tt = 0.1 s, what is the average force F on the egg during the collision?

(a)   F = 1.8 N
(b)   F = 2.0 N
(c)   F = 3.5 N
(d)   F = 6.0 N
(e)   F = 9.0 N

### QUESTION 13*

If the average force on the egg during the collision with the floor is 35 N, what is the interaction time, tf?

(a)   tf = 0.00038 s
(b)   tf = 0.0024 s
(c)   tf = 0.0086 s
(d)   tf = 0.0129 s
(e)   tf = 0.153 s

### QUESTION 14*

A 1000 kg horse trailer with frictionless wheels is sitting in a level parking lot. The trailer is 4 m long, and its center of mass is at its center. Its passenger, a 500 kg horse, breaks free from its stall at one end of the trailer and walks to the other end. How far does the trailer move relative to the ground? Treat the horse as a point particle. The mass of the trailer above does not include the 500 kg horse.

(a)   1/3 m
(b)   2/3 m
(c)   1 m
(d)   4/3 m
(e)   5/3 m

### QUESTION 15**

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

A space capsule of mass m is launched from the surface of the earth with a speed VE = 6.0 × 103 m/s. The radius and mass of the earth are RE = 6.37 × 106 m and ME = 5.97 × 1024 kg respectively. Newton's gravitational constant is G = 6.67 × 10-11 N-m2/kg2. Neglect air resistance.

What is the maximum height Rmax measured from the center of the earth, reached by the space capsule?

(a)   Rmax = 5.73 × 106 m
(b)   Rmax = 7.00 × 106 m
(c)   Rmax = 8.95 × 106 m
(d)   Rmax = 1.27 × 107 m
(e)   Rmax = 1.72 × 107 m

### QUESTION 16*

Compared to the previous problem, if the mass of the capsule were doubled, its maximum radius, compared to that in the previous question, would be

(a)   larger.
(b)   smaller.
(c)   the same.

### QUESTION 17**

If it is to escape completely from the earth's gravity, the capsule's minimum speed at the moment of launch would be

(c)   about the same as VE.

### QUESTION 18**

This and the next question refer to the following situation:

Two identical masses are suspended from massless strings of equal length. One mass is released from a height h as depicted in the figure below. When the first mass hits the second, the two masses stick together.

What is the maximum height H reached by the two masses together?

(a)   H = h / 4
(b)   H = h / 2
(c)   H = h
(d)   H = 2 h
(e)   H = 4 h

### QUESTION 19***

If the collision between the two masses was elastic, the maximum height reached by the mass on the right would be

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

### QUESTION 20**

This and the next question refer to the following situation:

A massless spring of spring constant k = 30 N/m hangs vertically in the earth's gravitational field. A 1 kg mass is attached to the spring.

Measuring from the unstretched length of the spring, how much has the gravitational potential energy of the mass changed when the spring reaches its equilibrium length with the mass attached?

(a)   0 N-m
(b)   +1.27 N-m
(c)   -1.27 N-m
(d)   +3.21 N-m
(e)   -3.21 N-m

### QUESTION 21*

Suppose now that the mass is pulled down from the equilibrium position a distance of 0.1 m and released. What is the speed of the mass when it returns to the equilibrium position?

(a)   0 m/s
(b)   0.55 m/s
(c)   0.72 m/s
(d)   1.10 m/s
(e)   2.73 m/s

### QUESTION 22**

Two pulleys arranged to help lift a heavy mass, M, which hangs from one of the pulleys as shown. A massless rope runs around the two pulleys (which are massless and frictionless). You exert a force F on the free end of the rope.

If the weight is to move up a distance h, through what distance, D, must you pull the free end of the rope?

(a)   D = h
(b)   D = h/2
(c)   D = 2h
(d)   D = 4h
(e)   D = 3h/2

### QUESTION 23*

This and the next question refer to the following situation:

Two identical blocks initially have the same velocity V at the bottom of two ramps. The first ramp inclined at a shallower angle (θ1) with respect to the horizontal than the second ramp (θ2). The maximum heights reached by the blocks are h1 and h2 respectively.

Assume that both ramps are frictionless. Which one of these statements is correct concerning the maximum heights reached by the blocks?

(a)   h2 = h1
(b)   h2 > h1
(c)   h2 < h1

### QUESTION 24**

Now assume instead that in both cases there is the same (non-zero) coefficient of kinetic friction between the blocks and the ramps. Which statement is correct concerning the maximum heights reached by the blocks?

(a)   h2 = h1
(b)   h2 > h1
(c)   h2 < h1

### QUESTION 25**

A 1-dimensional elastic collision occurs between two masses m1 = 3 kg and m2 = 5 kg.

If the speeds after the collision are v1f = +3 m/s and v2f = -2 m/s, what were their speeds v1i and v2i before the collision?

(a)   v1i = -3.00 m/s, v2i = +2.00 m/s
(b)   v1i = -4.50 m/s, v2i = +1.50 m/s
(c)   v1i = +2.75 m/s, v2i = -1.75 m/s
(d)   v1i = -3.25 m/s, v2i = +1.75 m/s
(e)   v1i = +3.25 m/s, v2i = -2.25 m/s

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.