### Spring 2010 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 108. The exam period was 90 minutes. The mean score was 78.1; the median was 79. Click here to see the formula sheet that came with the exam.

### QUESTION 1*

A 12 kg block moves in the x-direction at 28 m/s, and a 24 kg block moves in the y-direction at 8.0 m/s. Find the velocity of their center of mass.

(a)   (Vx, Vy) = (6.3 m/s, 1.6 m/s)
(b)   (Vx, Vy) = (2.8 m/s, 4.9 m/s)
(c)   (Vx, Vy) = (8.6 m/s, 2.6 m/s)
(d)   (Vx, Vy) = (9.3 m/s, 5.3 m/s)
(e)   (Vx, Vy) = (4.6 m/s, 1.4 m/s)

### QUESTION 2**

A light automobile has a speed of 45 miles per hour in the +x direction and a heavy truck has a speed of 30 miles per hour in the -x direction. What is the relative speed scm at which they approach one another in the center-of-mass system?

(a)   |scm| < 75 mph
(b)   |scm| = 75 mph
(c)   |scm| > 75 mph

### QUESTION 3**

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

A 4.0 kg circular disk slides in the x-direction on a frictionless horizontal surface with a speed of 5.0 m/s. It collides with an identical disk that is at rest before the collision. The collision is elastic. Disk 1 goes off at an angle of 60° with respect to the x-direction. Disk 2 goes off at an angle of 30° with respect to the x-direction. Treat the disks as point objects and ignore the possible rotations of the disks.

Which one of the following statements is correct?

(a)   Disk 1 has the greater kinetic energy after the collision.
(b)   Disk 2 has the greater kinetic energy after the collision.
(c)   The kinetic energies of the two disks are equal after the collision.

### QUESTION 4***

Find the speed of disk 2.

(a)   2.5 m/s
(b)   2.8 m/s
(c)   3.3 m/s
(d)   3.9 m/s
(e)   4.3 m/s

### QUESTION 5*

Find the sum of the kinetic energies of disk 1 and disk 2 after the collision.

(a)   0 J
(b)   25 J
(c)   50 J
(d)   75 J
(e)   100 J

### QUESTION 6*

This and the next question refer to the following situation:

In a Physics 211 laboratory experiment one end of a string is tied to a cart. The other end of the string is tied to a force probe that is fixed to the track. The cart is free to move on the track. Initially the string is slack. The cart is given a velocity vo and the magnitude of the momentum of the cart is 0.42 kg m/s. The experimental setup is shown below.

The string becomes taut, and a force is exerted on the cart by the string. The string then becomes slack again. The force on the cart is measured as a function of time by the force probe. The data from the force probe are shown below. The integral of force on the cart with respect to time is 0.66 kg m/s.

Find how long the string exerted a force on the cart.

(a)   0.2 s
(b)   1.1 s
(c)   2.4 s

### QUESTION 7**

Find the magnitude of the momentum of the cart after the string again becomes slack.

(a)   0.24 kg m/s
(b)   0.42 kg m/s
(c)   0.66 kg m/s
(d)   0.90 kg m/s
(e)   1.24 kg m/s

### QUESTION 8*

This and the next question refer to the following situation:

Ricardo (R) and Maria (M) are in a canoe that is stationary and floating on a calm lake. They are 4.0 m apart, symmetrically located about the center of the canoe as shown in the figure on the left. Ricardo has mass 80 kg Maria has a mass of 62 kg. The canoe is massless and is free to move in the water without friction.

If Ricardo and Maria both move to the center of the canoe what distance d will the canoe move relative to a rock that is stationary in the water?

(a)   d = 0 (The canoe will not move.)
(b)   d = 0.15 m
(c)   d = 0.25 m
(d)   d = 0.35 m
(e)   d = 0.55 m

### QUESTION 9***

While Ricardo and Maria are moving to the center of the canoe, the momentum of the system (Maria+Ricardo)

(a)   is to the right.
(b)   is to the left.
(c)   is zero.

### QUESTION 10**

This and the next question refer to the following situation:

A ballistic pendulum like the one demonstrated in lecture has mass M = 2 kg. The ballistic pendulum begins at rest and is struck by a ball of mass m = 0.25 kg, which sticks to the pendulum. The pendulum is observed to rise a maximum height h above its equilibrium position.

During which of the following intervals is the total horizontal momentum of the ball plus pendulum system conserved?

(a)   while the ball is travelling through the air (before the collision)
(b)   while the ball is hitting the pendulum (during the collision)
(c)   while the pendulum is swinging up to its maximum height (after the collision)
(d)   both a. and b.
(e)   both b. and c.

### QUESTION 11*

Immediately after the collision, both the ball and the pendulum are observed to be moving horizontally with a speed of 3 m/s. What was the horizontal speed of the ball just before it hit the pendulum?

(a)   9 m/s
(b)   24 m/s
(c)   27 m/s

### QUESTION 12**

As shown in lecture, two pucks of equal mass M are being pulled at different points by massless strings in which there are equal tensions across a frictionless surface. Puck (1) is pulled by tension T1 through its center of mass and has acceleration A1 while puck (2) is pulled by tension T2 at its outer edge and has acceleration A2. The configuration is such that T1 = T2. The string is wrapped around puck (2) and the puck is free to rotate.

How do the accelerations A1 and A2 compare?

(a)   A1 > A2
(b)   A1 = A2
(c)   A1 < A2

### QUESTION 13*

This and the next question refer to the following situation:

A young boy of mass m = 25 kg sits on a coiled spring that has been compressed to a length 0.4 m shorter than its uncompressed length and then held at this length. Suddenly the spring is released, and the boy flies vertically into the air. He reaches a maximum distance 0.5 m above his initial position. The spring is ideal and massless and we ignore the air friction.

What is the spring constant k of the spring?

(a)   766.4 N/m
(b)   1532.8 N/m
(c)   613.1 N/m

### QUESTION 14**

What is the speed of the boy when he is 0.4 meters above his starting position?

(a)   1.1 m/s
(b)   1.4 m/s
(c)   1.7 m/s
(d)   1.9 m/s
(e)   2.1 m/s

### QUESTION 15***

An asteroid with mass 250 kg is travelling directly toward the earth. When it is 25,000 km from the surface of the earth, it has a speed of 10 km/s. What is its speed when it hits the surface of the earth?

(The mass and radius of the earth are ME = 5.98 × 1024 kg and RE = 6,380 km respectively, and Newton's gravitational constant is G = 6.67300 × 10-11 m3 kg-1 s-2. You should ignore any effects due to air resistance and the rotation of the Earth)

(a)   6 km/s
(b)   11 km/s
(c)   14 km/s
(d)   21 km/s
(e)   25 km/s

### QUESTION 16*

This and the next question refer to the following situation:

Here is a graph from Physics 211 Lab 4. The basketball of mass m = 0.62 kg was released from the height h and it started bouncing. The numbers on the graph correspond to the maxima of its kinetic energy.

From what height h was the ball released? Ignore air friction.

(a)   1.01 m
(b)   1.82 m
(c)   2.23 m

### QUESTION 17*

The data for the graph of "Total" energy was computed as a sum of Gravitational Potential Energy of the ball and its Kinetic Energy. It is clear from the graph that after each bounce, the "Total" energy decreases. The numbers on the graph represent the mean values of "Total" energy before each bounce.

Which one of the following statements is correct?

(a)   The step-like dependence of the "Total" energy on time demonstrates the violation of the energy conservation law.

(b)   The graph demonstrates that the "Total" energy is conserved throughout the entire four-second interval.

(c)   The step-like dependence of the "Total" energy on time corresponds to the mechanical energy dissipation via its transformation into other forms.

### QUESTION 18*

A pendulum consists of a ball attached to the end of a string of length l = 100 cm. The other end of the string is attached at point O1. The ball is released from rest from a horizontal position as shown in the picture. At the bottom of its swing the string hits a peg O2 a distance d = 80 cm below O1 and the pendulum continues swinging around O2 as shown by the dashed line. Treat the ball as a point object.

What is the speed V2 of the ball when it reaches a point in its swing which is level with O2?

(a)   2.21 m/s
(b)   3.96 m/s
(c)   4.29 m/s
(d)   4.83 m/s
(e)   5.11 m/s

### QUESTION 19*

You just discovered a peculiar spring which follows the force law F = -Kx3. K is a constant and x = l - l0, where l is the stretched or compressed length of the spring and l0 is the unstretched and uncompressed length of the spring.

How much work W is done on this spring when it is stretched by an amount x from its relaxed position?

(a)   W = (1/2)Kx2
(b)   W = (1/3)Kx3
(c)   W = (1/4)Kx4

### QUESTION 20**

A block of mass M slides with a constant speed V down a plane inclined at an angle θ to the horizontal.

During a time interval Δt the magnitude of the work W done by the frictional force is

(a)   |W| = Mg tanθ (VΔt)
(b)   |W| = Mg sinθ (VΔt)
(c)   unknown, since the coefficient of kinetic friction is not given.

### QUESTION 21*

This and the next question refer to the following situation:

A box of mass M slides on a horizontal floor with initial speed V0. The kinetic coefficient of friction between the box and the floor is μk.

After sliding a distance D the speed of the box is ¾V0. What is the magnitude of the macroscopic work W done by the frictional force on the box during this motion?

(a)   |W| = (1/4) MV02
(b)   |W| = (7/32) MV02
(c)   |W| = (3/4) MV02
(d)   |W| = (3/4) MgμkD
(e)   |W| = Mgμk / D

### QUESTION 22**

If the experiment was repeated with a box that had mass 2M but had the same initial speed V0 and the same coefficient of friction μk, what would its speed be after sliding the same distance D?

(a)   V1 < ¾ V0
(b)   V1 = ¾ V0
(c)   V1 > ¾ V0

### QUESTION 23*

This and the next question refer to the following situation:

Identical constant forces push two blocks A and B over identical horizontal surfaces for identical periods of time. The masses are initially at rest. The mass of A is twice the mass of B.

Which block ends up with the biggest momentum?

(a)   block A
(b)   block B
(c)   Both blocks end up with the same momentum.

### QUESTION 24*

Which block ends up with the biggest kinetic energy?

(a)   block A
(b)   block B
(c)   Both blocks end up with the same kinetic energy.

### QUESTION 25*

A 2.4 kg block with a kinetic energy of 48 J slides on a frictionless horizontal table and collides with a second block. The second block is made of a different material and is initially at rest. The two blocks stick together and after the collision have a kinetic energy of 36 J. Find the mass of the second block.

(a)   0.6 kg
(b)   0.8 kg
(c)   1.2 kg
(d)   1.8 kg
(e)   2.4 kg

Scoring of True-False (T,F) Questions:
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• If you mark the wrong answer or if you mark neither answer, you get 0 points.
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• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
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• 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.
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