### Fall 2010 Physics 211 Hour Exam 2(23 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 99. The exam period was 90 minutes. The mean score was 81.2; the median was 84. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

This and the next question refer to the following situation:

Two ice skaters of mass 70 kg and 50 kg, each having an initial velocity of 10 m/s in the directions shown, collide and fall and slide across the ice together. The ice surface is horizontal and frictionless.

What is the speed of the skaters after the collision?

(a)   V = 0 m/s
(b)   V = 1.7 m/s
(c)   V = 2.7 m/s
(d)   V = 10 m/s
(e)   V = 20 m/s

### QUESTION 2*

What is the angle θ relative to the x axis that the two skaters travel after the collision?

(a)   θ; = 41°
(b)   θ = 28°
(c)   θ = 25°

### QUESTION 3*

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

A cart of mass M = 9 kg rolls without friction on a horizontal surface. It is attached through a freely pivoting initially-horizontal massless rod of length L to a ball of mass m = 3 kg. The system is initially at rest when the ball is released. The pendulum swings down and to the left, and at the bottom of its swing the ball is observed to have a velocity of 3.5 m/sec to the left.

Which one of the following remain constant as the pendulum swings down?

(a)   horizontal component of the momentum of the ball
(b)   horizontal component of the momentum of the cart
(c)   horizontal component of the momentum of the ball + cart

### QUESTION 4*

What is the speed of the cart when the ball is at the bottom?

(a)   Vcart = 1.17 m/s
(b)   Vcart = 1.75 m/s
(c)   Vcart = 2.44 m/s
(d)   Vcart = 2.91 m/s
(e)   Vcart = 3.37 m/s

### QUESTION 5**

What is the length L of the pendulum?

(a)   0.59 m
(b)   0.83 m
(c)   1.18 m

### QUESTION 6**

How far to the right has the cart moved, when the ball is at the bottom?

(a)   L / 2
(b)   L / 3
(c)   L / 4

### QUESTION 7**

A comet of mass 109 kg is observed at a distance from the sun of 8 × 1011 m (mass of sun = 2 × 1030 kg) at a speed of 17000 m/s. Assuming no forces on it other than the sun's gravity, how fast will it be going when it is a distance of 2.25 × 1011 m from the sun? (The universal gravitational constant is G = 6.67 × 10-11 Nm2/kg2)

(a)   12,900 m/s
(b)   18,300 m/s
(c)   23,700 m/s
(d)   29,200 m/s
(e)   33,800 m/s

### QUESTION 8*

Two fishermen, of masses 70 and 90 kg stand at opposite ends of their 20 meter boat. The boat (without fishermen) has a mass of 400 kg. There is no wind or current and the boat can move without friction on the water's surface. The 90 kg fisherman walks to the left end of the boat. How far has the boat moved when the fisherman reaches the left end?

(a)   5.8 m to the right
(b)   3.2 m to the right
(c)   The boat does not move.
(d)   3.2 m to left
(e)   5.8 m to left

### QUESTION 9*

The centers of three spheres having masses 1 kg, 2 kg and 3 kg are placed at the corners of an equilateral triangle whose sides are each 1 meter long, as shown below. What is the horizontal position of the center of mass?

(a)   xcm = 0.50 m
(b)   xcm = 0.58 m
(c)   xcm = 0.76 m

### QUESTION 10**

This and the next question refer to the following situation:

An artillery shell of mass 20 kg is fired from a rail car which is initially at rest on a horizontal frictionless track. The combined mass of the car and cannon is 2000 kg. As viewed by someone on the ground the shell moves with an initial speed of 300 m/s at an angle of 27° above the horizontal and the rail car recoils to the right.

Relative to the ground, what is the speed of the rail car after the shell is fired?

(a)   1.36 m/s
(b)   2.67 m/s
(c)   3.00 m/s

### QUESTION 11*

If the shell was accelerated through the cannon for a time of 0.03 seconds, what was the average force on the shell during this time?

(a)   200 N
(b)   2,300 N
(c)   15,000 N
(d)   90,000 N
(e)   200,000 N

### QUESTION 12*

This and the next question refer to the following situation:

A block of mass m = 1.8 kg starts at rest on a rough inclined plane a height H = 8 m above the ground. It slides down the plane, across a frictionless horizontal floor, and then around a frictionless loop-the-loop of radius R = 2.0 m. On the floor the speed of the block is observed to be 11 m/s.

What is the work done by friction on the block as it slides down the inclined plane?

(a)   -49 J
(b)   -28 J
(c)   -78 J
(d)   -23 J
(e)   -32 J

### QUESTION 13**

What is the magnitude of the normal force exerted on the block at the top of the loop?

(a)   0 N
(b)   5.1 N
(c)   9.8 N
(d)   17.6 N
(e)   20.6 N

### QUESTION 14*

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

A 2.5 kg box is held released from rest 1.5 meters above the ground and slides down a frictionless ramp. It slides across a floor that is frictionless, except for a small section 0.5 meters wide that has a coefficient of kinetic friction of 0.4. At the left end, is a spring with spring constant 250 N/m. The box compresses the spring, and is accelerated back to the right.

What is the speed of the box at the bottom of the ramp?

(a)   5.4 m/s
(b)   3.7 m/s
(c)   2.8 m/s

### QUESTION 15*

What is the maximum distance the spring is compressed by the box?

(a)   0.50 m
(b)   0.66 m
(c)   0.83 m
(d)   0.94 m
(e)   1.21 m

### QUESTION 16*

What is the maximum height to which the box returns on the ramp?

(a)   1.1 m
(b)   1.3 m
(c)   1.5 m

### QUESTION 17*

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

Consider the following two cases:

In case 1 a ball of mass m is thrown horizontally with speed v0 at a stationary box of mass M. The ball bounces off the box and after the collision the box is moving to the right with V1 and the ball is moving to the left with speed vf .

In case 2 a ball of mass m is thrown horizontally with speed v0 at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is moving to the right with speed V2. In both cases the box slides without friction. Assume all motion is horizontal.

In which case is the change in momentum of the ball the biggest?

(a)   Case 1
(b)   Case 2
(c)   The change in momentum of the ball is the same in both cases.

### QUESTION 18*

Which one of the following statements best describes V1 and V2?

(a)   V1 < V2
(b)   V1 = V2
(c)   V1 > V2

### QUESTION 19*

In case 2 it is observed that V2 = v0/3. What is the ratio of masses M/m ?

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

### QUESTION 20**

In Case 1 it is observed that vf = v0/2. What V1/v0?

(a)   V1/v0 = 3M / 2m
(b)   V1/v0 = 2M / 3m
(c)   V1/v0 = 3m / 2M
(d)   V1/v0 = 2m / 3M
(e)   V1/v0 = m / 2M

### QUESTION 21*

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

Two blocks of mass mA and mB are placed side by side on a frictionless horizontal table. At time t0 both blocks are at rest and a constant force of the same magnitude is applied to each of the blocks. Block A has a smaller mass than block B (mA < mB).

How do the momenta of the two blocks compare 5 seconds after t0?

(a)   pA < pB
(b)   pA > pB
(c)   pA = pB

### QUESTION 22**

How do the kinetic energies of the two blocks compare 5 seconds after t0?

(a)   KA < KB
(b)   KA > KB
(c)   KA = KB

### QUESTION 23***

After each block has traveled the distance of 1 m, which is correct?

(a)   pA = pB
(b)   KA = KB
(c)   both of the above

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.