Physics 141, Midterm Exam #1

Tuesday October 10, 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)

How many times did the Yankees win the world series?

1. 22

2. 24

3. 26

4. 28

Unfortunately, this number will not change this year.

Problem 2 (2.5 points)

List the four basic forces in order of strength (start with the strongest force and end with the weakest force).

1. Strong > Electromagnetic > Gravitational > Weak.

2. Electromagnetic > Strong > Weak > Gravitational.

3. Strong > Electromagnetic > Weak > Gravitational.

4. Strong > Electromagnetic > Gravitational > Weak.

Problem 3 (2.5 points)

Which of the following statements is false?

1. The buoyant force in liquid is much larger than the buoyant force in air.

2. The buoyant force is a result of small differences in molecular density of the air/liquid across the surface of the object.

3. The buoyant force is a result of differences in the average molecular velocity of the air/liquid molecules across the surface of the object.

4. The magnitude of the buoyant force increases with increasing temperature, due to the corresponding increase in the average molecular velocities.

Problem 4 (2.5 points)

The only force acting on a body as it moves along the x axis varies as shown in the following Figure. The body has a positive velocity when it is located at x = 0 m.

At what x position between x = 0 m and x = 8 m will the kinetic energy of the body reach a maximum value?

1. x = 0 m

2. x = 1 m

3. x = 2 m

4. x = 3 m

5. x = 8 m.

Problem 5 (2.5 points)

Which of the following statements is correct?

1. Sound propagation requires a medium; light propagation requires a medium.

2. Sound propagation does not require a medium; light propagation requires a medium.

3. Sound propagation requires a medium; light propagation does not require a medium.

4. Sound propagation does not require a medium; light propagation does not require a medium.

Problem 6 (2.5 points)

A constant force is exerted on a cart that is initially at rest on an air track. Friction between the cart and the track is negligible. The force acts for a short time interval and gives the cart a certain speed. To reach the same final speed with a force that is only half as big, the force must be exerted on the cart for a time interval

1. four times as long as

2. twice as long as

3. equal to

4. half as long as

5. a quarter of

that for the stronger force.

Problem 7 (2.5 points)

The Figure on the right shows various possible trajectories of an object launched from the surface of the earth. What can you say about the total energy of the object for the various trajectories shown in the Figure?

1. E_{elliptical trajectory} > 0 J, E_{hyperbolic trajectory} = 0 J, and E_{parabolic trajectory} < 0 J.

2. E_{elliptical trajectory} > 0 J, E_{hyperbolic trajectory} < 0 J, and E_{parabolic trajectory} = 0 J.

3. E_{elliptical trajectory} = 0 J, E_{hyperbolic trajectory} > 0 J, and E_{parabolic trajectory} < 0 J.

4. E_{elliptical trajectory} = 0 J, E_{hyperbolic trajectory} < 0 J, and E_{parabolic trajectory} > 0 J.

5. E_{elliptical trajectory} < 0 J, E_{hyperbolic trajectory} = 0 J, and E_{parabolic trajectory} > 0 J.

6. E_{elliptical trajectory} < 0 J, E_{hyperbolic trajectory} > 0 J, and E_{parabolic trajectory} = 0 J.

Problem 8 (2.5 points)

In part (a) of the figure, an air track cart attached to a spring rests on the track at the position x_equilibrium and the spring is relaxed. In part (b), the cart is pulled to a position x_start and released. It then oscillates about x_equilibrium. Which of the six graphs correctly represents the potential energy of the spring as a function of the position of the cart?

Problem 9 (2.5 points)

A mass attached to a spring oscillates back and forth as indicated in the position vs. time plot below. What is the velocity and the acceleration of the mass at point P?

1. Positive velocity and positive acceleration.

2. Positive velocity and negative acceleration.

3. Positive velocity and zero acceleration.

4. Negative velocity and positive acceleration.

5. Negative velocity and negative acceleration.

6. Negative velocity and zero acceleration.

7. Zero velocity and non-zero acceleration (positive or negative).

8. Zero velocity and zero acceleration.

Problem 10 (2.5 points)

Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the centripetal force acting on B to that acting on A?

1. 1/8

2. 1/4

3. 1/2

4. 1/√2

5. 1

Problem 11 (25 points)

Consider a cube of side d. A spherical mass m is located at each corner of the cube. The cube is positioned such that its center is located at the origin of the coordinate system and its sides are parallel to the coordinate axes.

a. What is the net force that acts on a spherical mass M (M > m) located at the origin of the coordinate system (specify magnitude and direction)?

Now consider what happens when we replace the mass m located at position (d/2, d/2, d/2) with a sphere of mass M (see Figure below).

b. What is now the net force that acts on a spherical mass M (M > m) located at the origin of the coordinate system (specify magnitude and direction)?

Express your answers in terms of the variables provided (m, M, and d) and the gravitational constant G.

Problem 12 (25 points)

Two springs, with spring constants k₁ and k₂ and with negligible mass, are connected as shown in the Figure below. The length of the double spring system is L. When a mass m is connected to the bottom spring, the equilibrium length of the two springs is increased by ∆L.

a. Determine the increase in length ∆L of the two springs.

b. What is the total energy of the system (the two springs and the mass) when it is in equilibrium? The gravitational potential energy is 0 J at the position indicated in the Figure.

When the mass is in its equilibrium position, the mass is given a velocity v₀ (directed upwards) and the system will start to carry out harmonic motion.

c. What is the amplitude of the harmonic motion?

d. What is the period of the harmonic motion?

Express all your answers in terms of the variables provided (L, k₁, k₂, m, and v₀) and the gravitational acceleration g.

Problem 13 (25 points)

The Stanford Linear Accelerator Center (SLAC), located at Stanford University in Palo Alto, California, accelerates electrons through a vacuum tube of length L.

Electrons of mass m, which are initially at rest, are subjected to a continuous force F along the entire length of the tube and reach speeds very close to the speed of light.

a. Calculate the final energy of the electrons.

b. Calculate the final momentum of the electrons.

c. Calculate the final speed of the electrons.

d. Calculate the time required travel the distance L.

Express all your answers in terms of the variables provided (m, F, and L) and the speed of light c.