Physics 141, Midterm Exam #2

Thursday November 2, 2006

8.00 am – 9.30 am

Do not turn the pages of the exam until you are instructed to do so.

You are responsible for reading the following rules carefully before beginning.

Exam rules: You may use only a writing instrument and your “cheat” sheet while taking this test. You may not consult any calculators, computers, books, nor each other.

Answer the multiple-choice questions (problems 1 – 10) by marking your answer on the scantron form. For each multiple-choice question (problems 1 – 10), select only one answer. Questions with more than one answer selected will be considered incorrect. Problems 11, 12, and 13 must be answered in the blue exam booklets and need to be well motivated and expressed in terms of the variables used in the problem. You will receive partial credit where appropriate, but only when we can read your solution. Answers that are not motivated will not receive any credit, even if correct.

At the end of the exam, you need to hand in your exam, the blue exam booklets, and the scantron form. All items must be clearly labeled with your name and student ID number. If any of these items are missing, we will not grade your exam, and you will receive a score of 0 points.

NOTE: If your student ID is not listed properly on the Scantron form, the form will not be processed and you loose points for all multiple-choice questions.

Name: __________________________________________________

ID number: ______________________________________________

Recitation Day/Time: ______________________________________

Useful Relations:

Problem 1 (2.5. points)

Two objects collide inelastically. Can all the initial kinetic energy in the collision be converted to other forms of energy?

1. Yes, but only for certain special initial speeds.

2. Yes, provided the objects are soft enough.

3. No, this violates a fundamental law of physics.

4. None of the above.

Problem 2 (2.5 points)

Two masses m₁ and m₂ sit on a table connected by a rope. A second rope is attached to the opposite side of m₂. Both masses are pulled along the table with the tension in the second rope equal to T₂. Let T₁ denote the tension in the first rope connecting the two masses. Which of the following statements is true?

1. T₁ = T₂

2. T₁ > T₂

3. T₁ < T₂

4. We need to know the relative values of m₁ and m₂ to answer this question.

Problem 3 (2.5 points)

A stone is launched upward into the air. In addition to the force of gravity, the stone is subject to a frictional force due to air resistance. The time the stone takes to reach the top of its flight path is

1. larger than

2. equal to

3. smaller than

the time it takes to return from the top to its original position.

Problem 4 (2.5 points)

A sports car accelerates from zero to 30 mph in 1.5 s. How long does it take for it to accelerate from zero to 60 mph, assuming the power of the engine to be independent of velocity and neglecting friction?

1. 2 s

2. 3 s

3. 4.5 s

4. 6 s

5. 9 s

6. 12 s

Problem 5 (2.5 points)

Some of the properties of the diatomic molecule NO can be described in terms of a simple model in which the two atoms are connected by a spring. Experiments show that the spacing between allowed vibrational energy levels in NO is 0.23 eV. Suppose you have a gas of 4 NO molecules. One molecule's vibrational energy is in the ground state (n = 0), the second molecule is in the first excited state (n = 1), the third molecule is in the second excited state (n = 2), and the fourth molecule is in the third excited state (n = 3). If we assume that all transitions from one excited states to lower-lying excited states occur with equal probability, what is the ratio of the intensities of 0.23 eV, 0.46 eV, and 0.69 eV photons?

1. 1:1:1.

2. 3:2:1.

3. 6:3:1.

4. 9:3:1.

Problem 6 (2.5 points)

When a small ball collides elastically with a more massive ball initially at rest, the massive ball tends to remain at rest, whereas the small ball bounces back at almost its original speed. Now consider a massive ball of inertial mass M moving at speed v and striking a small ball of inertial mass m initially at rest. The change in the small ball’s momentum is

1. Mv

2. 2Mv

3. mv

4. 2mv

5. none of the above

Problem 7 (2.5 points)

Two carts are put back-to-back on a track. Cart A has a spring-loaded piston; cart B, which has twice the inertial mass of cart A, is entirely passive. When the piston is released, cart A pushes against cart B, and the carts move apart. How do the magnitudes of the final momenta p and kinetic energies K compare?

1. p_A > p_B, K_A > K_B.

2. p_A > p_B, K_A = K_B.

3. p_A > p_B, K_A < K_B.

4. p_A = p_B, K_A > K_B.

5. p_A = p_B, K_A = K_B.

6. p_A = p_B, K_A < K_B.

7. p_A < p_B, K_A > K_B.

8. p_A < p_B, K_A = K_B.

9. p_A < p_B, K_A < K_B.

Problem 8 (2.5 points)

Two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has

1. as much kinetic energy as the lighter one.

2. twice as much kinetic energy as the lighter one.

3. half as much kinetic energy as the lighter one.

4. four times as much kinetic energy as the lighter one.

5. impossible to determine

Problem 9 (2.5 points)

A small rubber ball is put on top of a volleyball, and the combination is dropped from a certain height. Compared to the speed it has just before the volleyball hits the ground, the speed with which the rubber ball rebounds is

1. the same.

2. twice as large.

3. three times as large.

4. four times as large.

5. none of the above

Problem 10 (2.5 points)

I have marked my student ID number in the appropriate boxes on the scantron form, and I like to get credit for my answers on the multiple-choice questions.

1. Yes, please give me credit for these questions.

2. No, I do not need credit for these questions.

Problem 11 (25 points)

Consider and object consisting of two masses M connected by a low-mass spring of spring constant k_s. When you exert an upward force of 2Mg, the object remains at rest, as shown in the Figure below. In this situation, the spring is stretched by a distance s_i from its rest length.

At one point, a larger constant force is applied (F > 2Mg) and the object starts moving up. At some later time, the stretch of the spring has increased to s_f, and the object is located as shown in the Figure.

a. At this time, what is the speed of the center of mass of the object?

b. At this time, what is the vibrational kinetic energy of the object?

c. At this time, what is the acceleration of each block (they do not need to be the same)?

Express your answers in terms of the variables provided (F, M, y_1i, y_2i, y_1f, y_2f, k_s, s_i and s_f) and the gravitational acceleration g.

Problem 12 (25 points)

Two blocks with masses m₁ and m₂, shown in the figure below, are free to move. The coefficient of static friction between the blocks is m_s but the surface beneath m₂ is frictionless.

a. What is the minimum force F required to hold m₁ against m₂?

b. What is the acceleration of block m₂ when the minimum force F is applied to block m₁?

Express all your answers in terms of the variables provided (m₁, m₂, m_s) and the gravitational acceleration g.

Problem 13 (25 points)

Two nuclei with identical mass (M₁ = M₂ = M) are on a collision course, as indicated in the Figure below. Their initial velocities are v₁ and v₂. After the collision, they stick together.

a. What is the velocity of the center of mass of the system before the collision? Specify the magnitude and the direction of the velocity, or specify its components along the x and y axes.

b. What is velocity of the center of mass of the system after the collision? Specify the magnitude and the direction of the velocity, or specify its components along the x and y axes.

c. What fraction of the initial kinetic energy is lost in this collision? Assume that there is no rotational motion around the center of mass after the collision.

Express all your answers in terms of M, v₁, and v₂.