Physics 141, Midterm Exam #1

Thursday October 8, 2009

8.00 am – 9.30 am

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

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

1. 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. If your student ID is not listed properly on the Scantron form (in the bubbles on the top-left corner), the form will not be processed and you loose points for all multiple-choice questions.

2. Problems 11, 12, and 13 must be answered in the blue exam booklets (answer questions 11 and 12 in booklet 1 and question 13 in booklet 2.) The answers 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, your student ID number, and the day/time of your recitation. If any of these items are missing, we will not grade your exam, and you will receive a score of 0 points.

Name: __________________________________________________

ID number: ______________________________________________

Recitation Day/Time: ______________________________________

Useful Relations:

Problem 1 (2.5 points)

The z-component of the linear momentum of a ball is observed to change with time in the following way:

at t = 0 s, p_z = 12 kg m/s

at t = 1 s, p_z = 7 kg m/s

at t = 2 s, p_z = 2 kg m/s

at t = 3 s, p_z = −3 kg m/s

Which of the following statements about the z component of the net force acting on the ball during the time the ball is observed is true?

1. The z component of the net force on the ball is zero.

2. The z component of the net force on the ball is constant.

3. The z component of the net force on the ball is changing with time.

4. Not enough information is given to determine the z component of the net force on the ball.

Problem 2 (2.5 points)

A spring-loaded dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring?

1. 96 m

2. 48 m

3. 24 m

4. 12 m

5. 6 m

6. 3 m

7. Impossible to determine.

Problem 3 (2.5 points)

A ball is dropped from the edge of a cliff. Soon after, a second ball is dropped. As a function of time, the separation between the two balls

1. stays the same.

2. increases.

3. decreases.

4. it depends on the time specified.

Problem 4 (2.5 points)

Consider the distribution of 11 equal-mass spheres, located on the circumference of a circle, as shown in the Figure. If we place another mass at the center of the circle, in what direction will the net gravitational force acting on this mass point?

1. Towards the East.

2. Towards the South.

3. Towards the West.

4. Towards the North.

Problem 5 (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 6 (2.5 points)

Which of the following statements is false

1. The tension force in a wire or string is due to the stretching of the inter-atomic bonds in the object.

2. The normal force between two objects is a result of the compression of the atoms in the contact region between the two objects.

3. The tension force in a wire or string is always constant.

4. A measurement of the Young's modulus can be used to determine the inter-atomic "spring constant".

Problem 7 (2.5 points)

Two blocks of mass m₁ and m₃, connected by a rod of mass m₂, are sitting on a frictionless surface. You push to the left on the right block with a constant force F. What is the compression force in the rod near its right end?

1. m₁F/(m₁ + m₂ + m₃)

2. m₂F/(m₁ + m₂ + m₃)

3. m₃F/(m₁ + m₂ + m₃)

4. (m₁ + m₂)F/m₁

5. (m₁ + m₃)F/m₂

6. (m₂ + m₃)F/m₃

7. (m₁ + m₂)F/(m₁ + m₂ + m₃)

8. (m₁ + m₃)F/(m₁ + m₂ + m₃)

9. (m₂ + m₃)F/(m₁ + m₂ + m₃)

Problem 8 (2.5 points)

Consider an object carrying out circular motion at constant speed. What is the direction of the net force on the object?

1. Tangent to the path.

2. In the radial direction away from the center of the circle.

3. In the radial direction toward the center of the circle.

Problem 9 (2.5 points)

What is the best baseball team in the USA?

1. The Yankees.

2. The Red Sox.

3. I do not know.

4. I do not care.

Note: there is only one correct answer (see hint).

Problem 10 (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 11 (25 points) Answer in Exam Booklet 1

A spring, with spring constant k and negligible mass, is hanging from the ceiling. The rest length of the spring is L. A block of mass M is connected to the end of the spring, as shown in the Figure below.

a. What is the increase in the length of the spring, y, when the block is attached?

b. Starting from the equilibrium position shown in the Figure, we pull the block down before releasing it. Calculate the angular frequency of the resulting harmonic motion.

c. We observe that when the block moves past its equilibrium position, its speed is v₀. What is the amplitude of the harmonic motion the block is carrying out?

Express all your answers in terms of the variables provided. Your answers must be well motivated.

Problem 12 (25 points) Answer in Exam Booklet 1

There is no general analytical solution for the motion of a gravitational system consisting of more than two bodies. However, there do exist analytical solutions for multiple-body systems with very special initial conditions. Consider the four-star system shown in the Figure below.

The system consists of four stars, each of mass m, moving with the same speed in the plane of the page along a circle of radius r.

a. Calculate the magnitude of the gravitational force exerted on one star by the other three stars.

b. Calculate how long it takes one star to make one complete revolution.

Express all your answers in terms of the variables provided in the problem, and assume that v « c. Your answers must be well motivated.

Problem 13 (25 points) Answer in Exam Booklet 2

A robot spacecraft lands on an asteroid, picks up a sample, and blasts off to return to Earth. The total mass of the spacecraft is m. When the spacecraft is at a distance d from the center of the asteroid, its rockets are turned off. At that point, its velocity is v₁. When the spacecraft has coasted to a distance 2d, its velocity has decreased to v₂. Assume v₁ « c and v₂ « c.

What is the mass of the asteroid?

Express your answer in terms of the variables provided. Your answers must be well motivated.

SCRATCH PAPER