This document contains a physics test with multiple choice and free response questions covering topics like special relativity, forces, friction, circular motion, and differential equations. The test has two parts, with the first part containing 6 shorter free response questions and the second part containing 3 longer free response questions. Some of the questions involve calculating distances, velocities, times, and tensions using concepts like relativistic velocity addition and Newton's laws of motion. The test requires showing all work to receive credit and indicates which questions are to be graded and which can be done as a bonus.

1. Physics 125 Test 2 Apr. 2, 2020 Name:
Part 1: Below are 6 short work out questions. Answer any 5 of
the 6 questions. YOU
MUST SHOW ALL YOUR WORK TO RECEIVE ANY
CREDIT. You may do the
remaining question as a bonus. Indicate which questions are to
be graded and which is the
bonus.
1. a) A bomb is moving to the right at 0.3 c. Ship A is chasing
the bomb at 0.5 c to the right
while ship B is chasing the bomb at 0.5 c to the left. Which
ship, A or B, will measure the
largest dilated time for the bomb to explode? Explain your
reasoning.
b) Three equal mass objects are each acted upon by different
forces acting in the x-direction.
The x-velocity as a function of time for each mass is shown
below. Rank the forces in the x-
direction acting on each of the masses from smallest to largest.
Note any ties.

2. c) Mass m is at rest on an inclined plane. The coefficient of
static friction between the
mass and the inclined plane is �". Student A claims that the
static frictional force acting
on m is equal to �"�. Student B claims that the static frictional
force acting on m is
equal to ������. Student C claims that the static frictional
force acting on m must
exceed the x-component of the weight. Which student is
correct? Explain your
reasoning.
d) Mass m is swung in a vertical circle of radius R. Rank the
tensions in the string at
points A, B, and C from least to greatest assuming that the
speed is a constant.
Do not neglect gravity.
2. Find an expression for the acceleration of the masses. Your
answer should only
contain �*, �+, �, and various constants.

3. a =
3. Masses �* and �+ are connected by a string, which passes
over a frictionless and massless
pulley. Mass �* is at rest on an inclined plane. The coefficient
of static friction between mass
�* and the inclined plane is �". What is maximum value that
�+ can have before �* starts

4. to move? Your answer will be in the form of an expression.
�+-./ =
4. A car of mass m is traveling over a series of hills and
valleys. The hills and valleys can be
viewed as hemispheres of radius R.
a) If the car on top of the hill, point A, just loses contact with
the road, what must be the car’s
speeds. You answer will be in the form of an equation.
b) If the car’s speed does not change from part a), what will be
the normal force acting on the
car at point B? You answer will be in the form of an equation.

5. v at point A =
N =
5. You are traveling in space ship A. You measure the length of
ship A to be 200 m.
You see space ship B coming towards you with a speed of
0.99c. You measure the
length of B’s ship to also be 200 m.
a) What is the length of ship B according to someone traveling
on ship B?

6. b) What is the length of ship A as measured by someone on ship
B?

7. 6. A ball is thrown straight upwards with an initial velocity of
�2. Assuming that the
air resistance is given by �.4 = �� where � is a constant,
prove that the velocity of the
ball as a function of time is given by
�(�) = :-;
<
+ �2>�
@AB
C − -;
<
.
Take up to be positive. Hint: Start with the free body diagram.
Also, how do you think that
you are going to write the acceleration?
Part 2: Below are 3 longer work out questions. YOU MUST
SHOW ALL YOUR

8. WORK TO RECEIVE ANY CREDIT. Answer all 3 questions.
1. An astronomer on earth discovers planet X 100 ly away from
the earth. Earth sends out a
ship, which travels at 0.85 c, towards the planet. The
inhabitants of planet X shoot a missile at
the earth ship. The speed of the missile is 0.9 c.
a) What is the distance between earth and planet X according to
someone on the earth
ship? What is the distance between earth and planet X according
to someone riding on
the missile?
distance according to
someone on the earth =
ship
distance according to
someone on the missile =

9. b) What is the velocity of the missile according to someone on
the ship from earth?
velocity of the missile according
to someone of the earth ship =
c) Someone on the earth ship sees that the missile self
destructs in 2 hours. How long
would it take the missile to self destruct according to someone
on the missile?

10. time it takes the missile to self
destruct according to someone =
on the missile
2. Consider the three masses connected as shown below. The
inclined plane make an angle q
with the horizontal. The coefficient of kinetic friction on all
surfaces is �,. The pulleys are
massless and frictionless. The masses move as shown below.
a) Draw the free body diagrams for each mass.
b) Apply Newton's second law to each of the masses. DO NOT
solve the equations yet. Just

11. set them up.
c) Using your equations, derive an expression for the
acceleration. Your answer should only
contain �*, �+, �E, �,, , and various constants.
3. Two equal mass 1 kg balls are connected by strings and
swung in horizontal circles.
The radii of the circles and the angles that the strings make with
the vertical are shown
below. Answer the following questions. Do not neglect gravity.

12. a) Draw the free body diagram of mass 1 and find the tension
in string 1.
b) What is the velocity of mass 1?
c) Draw the free body diagram of mass 2 and find the tension
in the string 2.

13. b) What is the velocity of mass 2?
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Physics 125 HW5 Assigned Feb.
26; Due Mar. 4, 2020
1. Consider the threemasses connected as
shown below. The inclined plane makes
an
angle q with the horizontal and the coefficient of
kinetic friction for all surfaces is µk. The
pullies are massless and frictionless. The mass

16. m1 moves downwardas shown. Answer
the following questions.
a) Draw the free body diagrams for each of
the masses.
b) Apply Newton's second law to each of
the masses. DO NOT solve the equations
yet.
Just set them up.
c) Solve your equations in part b) for the
acceleration of the system. Yourexpression
for the acceleration should only contain m1 ,
m2, m3, q, µk, and various constants.
2. Three blocks are being pulled to the
right by a 100 N force. Find the tensions in
each
string connecting the masses. Assume that the
surface is frictionless. You may find it
easiest to start by drawing the free body diagram of
the entire system.
3. Massm is held against a wall by the
force
€
Fpush . Massm does not slide along the wall.

17. The coefficient of static friction between the
wall and mass m is
€
µS . What is the smallest
value of
€
Fpush that can be applied so that mass m remains
at rest? Youranswer will be in
the form of an expression.
€
100 N
€
3 kg
€
4 kg
€
5 kg
€
Wall

18. €
m
€
Fpush
4. A circular curve of highway is designed
for traffic traveling at 60 km/h (37 mi/h).
a) If the radius is 150 m (490 ft), what is
the correct angle of banking of the road?
b) If the road was not banked, what would be
the minimum coefficient of static
friction between the tires and the road to keep the
cars from sliding using the
speeds in part a)?
5. A 150 lb student has an apparent weight
of 110 lb at the top of a Ferris wheel
that is rotating at a constant angular velocity.
(The apparent weight is the normal.)
a) What is the student’s apparent weight at
the bottom of the Ferris wheel?
b) If the speed of the Ferris wheel were
doubled, what would be the student’s
apparent weight at the top of the Ferris wheel?

19. 6. If the coefficient of static friction
for the tires on a road of 0.25,at what
maximum
speed can a car travel around a horizontal
circular road of radius 48 m?
7. Two masses are connected by strings. Each string
is 1 m long.Each mass, which is
10 kg, is rotated in a vertical circle. The
speed of the top mass is 8 m/s while
the
speed of the lower mass is 4 m/s. Find the
tension in each string. Do not neglect
gravity.
€
1 m
€
8 m/s
€
4 m/s
€

20. 1 m
8. A 5 kg mass is swung in a vertical
circle of radius 2 m. Assume for
simplicity that
the speed is a constant and equal to 10
m/s. Draw and find the magnitude of
the
TOTAL, i.e. not just radial, acceleration vector at
points A, B, and C.
€
R
€
v
€
θ
€
A
€
B

21. €
C
Physics 125 HW6 Assigned Mar.
19; Due Mar. 27, 2020
1. Solve the following differential equation without
a calculator
−1= 2
dy
dt
+ y when t = 0, y = 8.
2. An object of mass m initially at x =
2, and traveling with an initial velocity of 1
m/s
and is acted upon by the forceF = 2+4v .
Assuming the mass only moves along the x-
axis, find v(t) and x(t).
3. An object of mass m initially at x =
1, and traveling with an initial velocity of 1
m/s and is acted upon by the forceF = 2+5t .
Assuming the mass only moves along

22. the x-axis, find v(t) and x(t).