Physics 141, Midterm Exam #1

Tuesday October 9, 2007

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 and the equation sheet 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, the form will not be processed and you loose points for all multiple-choice questions.

2.     The analytical problems (11 – 13) must be answered in the blue exam booklet.

3.     The answer to each analytical problem must 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.

4.     At the end of the exam, you must hand in the blue exam booklets, the scantron form, and the exam.  All items must be clearly labeled with your name and student ID number.  If any of these items is 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)

Consider a 0.1-kg hockey puck, moving with a velocity that can be specified by the vector <10, 0, 0> m/s.  A hockey player strikes the puck with a stick, and exerts a force on it during a 1 ms time interval.  Afterwards, the puck moves with a velocity that can be specified by the vector <10, 20, 0> m/s.  What is magnitude of the force exerted by the stick on the puck?

1.     20000 N

2.     2000 N

3.     200 N

4.     20 N

 

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)

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 4 (2.5 points)

A planet is in a circular orbit of radius r around a massive star.  The planet has a momentum p and a period T.  The gravitational force exerted on the planet by the star is equal to

1.     , in the direction of the momentum.

2.     , at a right angle to the momentum.

3.     , in the direction of the momentum.

4.     , at a right angle to the momentum.

 

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 billiard ball on a billiard table has a momentum <3, 0, 4> kg m/s.  When a stick strikes the ball, a net force of <10, 4, -3> N acts on the billiard ball for 0.1 s.  What is the final momentum of the ball after it is struck?

1.     <4, 0.4, 3.7> kg m/s

2.     <0.1, 0.4, -0.3> kg m/s

3.     <0.3, 0.0, 0.4> kg m/s

4.     <7, 0, -7> kg m/s

5.     <13, 4, 1> kg m/s

 

Problem 7 (2.5 points)

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

á      At t = 0 s, pz = 12 kg m/s.

á      At t = 1 s, pz = 7 kg m/s.

á      At t = 2 s, pz = 2 kg m/s.

á      At t = 3 s, pz = -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 8 (2.5 points)

Which of the following is not conclusive evidence of an interaction?

1.     A change of velocity, either a change of direction or a change of speed.

2.     A change of shape or configuration without a change of velocity.

3.     A change of position without a change of velocity.

4.     A change of identity without a change of velocity.

 

Problem 9 (2.5 points)

Suppose that in a Star Trek episode, an enemy space ship is approaching the USS Enterprise at a speed of 0.95c and turns on a laser.  The speed of the laser light in the reference frame of the enemy spaceship is c.  Captain Picard on the Enterprise measures the speed of the laser light as

1.     0.05c

2.     0.95c

3.     less than c, but not 0.05c or 0.95c

4.     greater than c

5.     c

 

Problem 10 (2.5 points)

The following graph shows the cumulative World Series wins of the Yankees and of the Red Sox, as function of Year.  After careful examination of these scientific data, which is the better team?

1.     The Yankees.

2.     The Yankees.

3.     The Yankees.

4.     I do not know.

Problem 11 (25 points)

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 Ç c.  Your answers must be well motivated.

Problem 12 (25 points)

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 13 (25 points)

In the photograph you see New York YankeesÕ Shelley Duncan hit a two-run homerun against the Baltimore Orioles on Saturday, September 29, 2007.  Shelley hits the ball at a height h above the ground.  The ball flies of the bat with a speed v0 and with an angle q above the horizon.

 

 

To solve this problem, we will assume that there are no stands behind the wall of the baseball field.

a.     How long after Shelley Duncan hits the ball will it hit the ground?

b.     How far from the battersÕ box will the ball hit the ground?

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