Physics 121, Midterm Exam #2

Tuesday March 23, 2004

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, notes, or each other.

**Procedure:** 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 booklet 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 must
hand in the blue exam booklet 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:** You are not
allowed to use a cheat sheet on this exam. Please refer to the formula sheet at the end of this package
for important equations.

Suppose the radius of the Earth was doubled while its density was kept fixed. The value of the gravitational acceleration at the surface would

c increase by a factor of 2.

c decrease by a factor of 2.

c remain the same.

The weight of an object in a cavern below the EarthÕs surface is

c greater than its weight at the surface.

c less than its weight at the surface.

c equal to its weight at the surface.

Two objects, each of mass *m*, are placed on the *x* axis, one at *x* = *d* and the other at *x* = -*d*. The
gravitational force due to these two objects on an object located on the *y* axis takes on its maximum magnitude at

c *y* = 0

c *y* = ´

c *y
*= ±*d*

c *y
*= ±*d*/Ã2

A box (mass 5 kg) is accelerated by a force *F* across the floor with an acceleration of 2 m/s^{2}
for 10 s. The work done by
the force is

c 50 J

c 100 J

c 1000 J

c 1500 J

The work done by a force *F* = *k* |*x*| on an object moving along the *x* axis directly from *x* = -2 m to *x* = +2 m is

c 0 J

c 2*k*

c 4*k*

c 8*k*

What is the force that corresponds to the
potential energy function *U*(*x*, *y*) = 3*xy* + 5*x*^{2} + 6*y*^{3}?

c ** F** = 5

c ** F** =

c ** F** = (-3

c ** F** = (3

A ball is dropped from a height *h* and hits the ground with speed *v*. To
have the ball hit the ground with a speed 2*v* it should be dropped from a height

c *h*

c 2*h*

c 3*h*

c 4*h*

Three uniform spheres of radii 2*R*, *R*, and 3*R* are placed in contact next to each other on the *x* axis in this order (the smallest sphere is in the
center, the 2*R* sphere is
located to the left, and the 3*R* sphere is located to the right). The centers of the spheres are located
on the *x* axis. What is the distance from the center of
mass of this system from the center of the smallest sphere, assuming that each
sphere has the same density?

c (7/3)*R*

c (1/3)*R*

c (3/7)*R*

c (65/36)*R*

If the kinetic energy of an auto triples because of a speed change, its linear momentum

c increases by a factor of 3.

c remains the same.

c increases by a factor 9.

c increases by a factor of Ã3.

A tennis ball moving with a speed of 10 m/s collides elastically in a head-on collision with a massive locomotive engine moving with a speed of 10 m/s towards the ball. After bouncing directly back, the ball has a speed of

c 20 m/s.

c 30 m/s.

c 40 m/s.

__Problem 11__ (25 points)

Several planets (Jupiter, Uranus, Saturn) possess nearly
circular surrounding rings, perhaps composed of material that failed to form a
satellite. In addition, many
galaxies contain ring-like structures.
Consider a homogeneous ring of mass *M* and radius *R*.

a.
What is the direction of the gravitational force exerted by
the ring on a particle of mass *m* located
a distance *x*
from the center of the ring along its axis (see Figure)?

b.
What is the magnitude of the gravitational force exerted by
the ring on the particle when it is located a distance *x* from the center of the ring along its axis?

c.
What is the potential energy of mass *m* as a function of the distance *x*?

d.
Suppose the particle falls from rest from its current distance
*x* as a result of the attraction of the
ring of matter. Find an expression
for the speed with which it passes through the center of the ring. Note: assume that the ring remains
stationary at all times.

Express all your answers in terms of *x*, *R*, *m* and *M*.

__Problem 12__ (25 points)

A bullet of mass *m* is
fired horizontally at two blocks resting on a smooth frictionless table top, as
shown in the Figure. The bullet
passes through the first block of mass *M*_{1}, and embeds itself in a second block of mass *M*_{2}.
Speeds equal to *v*_{1}
and *v*_{2}, respectively,
are thereby imparted on the blocks, as shown in the Figure. The mass removed from the first block
by the bullet can be neglected.

a. Find the speed of the bullet immediately after emerging from the first block.

b.
Find the original speed *v*_{0}
of the bullet.

Express your answers in term of *M*_{1}, *M*_{2}, *v*_{1},
*v*_{2}, and *m*.

__Problem 13__ (25 points)