Physics 121, Midterm Exam #1

Tuesday February 28, 2008

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 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 attached pages. 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. **Answer questions 11 and 12 in booklet # 1 and question 13
in booklet # 2.** 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 your scantron form. 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:
______________________________________________

Workshop Day/Time: ______________________________________

__ __

__Useful Relations:__

A planet has the same mass as the Earth, but
its surface gravitational acceleration is *g*/2. What
is the radius of the planet?

- 2
×
*r*_{E} - Ã2
×
*r*_{E} - 4
×
*r*_{E} *r*_{E}/2

__Problem 2__ (2.5 points)

At which point is the gravitational force zero
between two masses separated by a distance *d* when one mass has a mass *m* and the other has a mass 4*m*?

- (1/3)
*d*away from the mass*m* - (1/3)
*d*away from the mass 4*m* - (1/4)
*d*away from the mass*m* - (1/4)
*d*away from the mass 4*m*

__Problem 3__ (2.5 points)

A satellite is in a circular orbit of radius *r* about a planet of mass *m*. Its
orbital period is *T*. What is the period of an orbit with the
same radius *r* about a planet
of mass 2*m*?

- 2
*T* *T*/2*T*/Ã2*T*/4

__Problem 4__ (2.5 points)

Three projectiles A, B, and C are launched with
the same initial velocities at angles of 30¡, 45¡, and 60¡, respectively. Their launch position and their points
of impact are located at sea level.
What is the relation between their flight times?

*t*_{A}=*t*_{C}>*t*_{B}*t*_{B}>*t*_{A}=*t*_{C}*t*_{A}>*t*_{B}>*t*_{C}*t*_{C}>*t*_{B}>*t*_{A}

__Problem 5__ (2.5 points)

Observer B is moving with a constant velocity
relative to observer A. Observer A
sees an object accelerate with an acceleration . What does
observer B see as the acceleration of the object?

- Zero.
- Depends
on the direction of the relative velocity of B to A.

__Problem 6__ (2.5 points)

An object starts from rest and travels a
distance *d* in time *t* when a constant force *F* acts on the object. What constant force must act on the object in order for it
to start from rest and travel the same distance in a time *t*/2?

- 4
*F* *F*/4- 2
*F* *F*/2

__Problem 7__ (2.5 points)

When a person with a mass of 98.4 kg stands on
a spring scale in an elevator, the scale reads 0 N. Which statement about the elevator is true?

- The
elevator is stationary.
- The
elevator is moving downward with a velocity of 9.8 m/s.
- The
elevator is accelerating upward with an acceleration of 9.8 m/s
^{2}. - The
elevator is accelerating downward with an acceleration of 9.8 m/s
^{2}.

__Problem 8__ (2.5 points)

A car travels around a curve of radius *r* at constant speed *v*. Its
acceleration has a magnitude *a*. If the
car rounds the same curve so that its acceleration is 2*a*, what will its speed be?

*v*/2- 2
*v* - 4
*v*

__Problem 9__ (2.5 points)

A car travels around a curve of radius *r* at constant speed *v*. Its
acceleration has a magnitude *a*. If the
car rounds a different curve at the same speed such that its acceleration is 2*a*, what will the radius of the curve be?

- 2
*r* *r*/2- 4
*r*

__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?

- The
Yankees.
- The
Yankees.
- The
Yankees.
- I do
not know.

__Problem
11__ (25 points) **Answer
in Exam Booklet 1**

A block with mass *m* is pushed along a horizontal floor by a force *P* that makes an angle *q* with the horizontal, as
shown in Figure a. The
coefficients of kinetic and static friction between the block and the floor are
µ_{k} and µ_{s}, respectively.

a)
Calculate the maximum force
that can be applied without moving the block.

b)
The applied force *P* is larger than the maximum force calculated in a). As a consequence, the block will start
to move. Calculate the
acceleration of the block.

Instead of pushing the block with
a force *P*, we can pull the block with
the same force *P* (see Figure b).

c)
Calculate the maximum force
that can be applied without moving the block. Is this force larger or smaller than the maximum force
calculated in a)?

d)
Calculate the acceleration of
the block.

e)
In which situation (block
being pulled or pushed) will the block have the highest kinetic energy when it
has been displaced over a distance *d*? Your answer needs to be well motivated.

Express all you answers in terms
of *g*, *m*, *P*, *d*, µ_{k}, µ_{s}, and *q*.

__Problem
12__ (25 points) **Answer
in Exam Booklet 1**

A projectile of mass *m* is fired from ground level with an initial speed *v*_{0} at an angle *q* above the
horizontal (see Figure).

a)
Calculate the time at which
the projectile hits the ground again.

b)
Calculate the range *R* of the projectile (note: you will not receive any credit
if you just write down the formula of the range presented in the text book).

c)
Find a relation between the
maximum height *H* and the range *R* in terms of *q*.

d)
Find a relation between the
elevation angle *f* of the highest point, as seen from the launch point, and
the firing angle *q* (see Figure).

Express all your answers in terms
of *g, m*, *v*_{0}, and *q*.

__Problem
13__ (25 points) **Answer
in Exam Booklet 2**

A ball of mass m is attached to a
rigid vertical rod by means of two massless strings with length *L*. The strings
are attached to the rod at points a distance *L* apart (see Figure).
The system is rotating about the axis of the rod, both strings being
taut and forming an equilateral triangle.
The tension in the upper string is *T*_{1}.

a)
Draw a free-body diagram,
showing all forces acting on the ball.

b)
What is the tension in the
lower string?

c)
What is the net force on the
ball at the instant shown in the Figure?
You need to specify both the magnitude and the direction of the force in
terms of the variable provided.

d)
What is the speed of the ball?

Express all your answers in terms of *g*, *L*, *m*, and *T*_{1}.