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Physics 141
Sample questions: Midterm 1
1. A 10 kg crate sits 10 meters up an incline that makes an angle of 30 degrees with
the horizontal direction.
10m
30°
a.)
b.)
c.)
d.)
Assuming that there is a coefficient of kinetic friction  k  0.25 , draw
a free body diagram for the 10 kg mass. Identify the source of each
force.
Find the friction force.
Find the work done by each of the forces as the mass slides to the
bottom of the ramp.
Find the speed of the mass when it reaches the bottom of the incline.
2. The gravitron produces a sort of weightlessness by rotating about its central axis
(represented by the vertical line on the right. The rider lays on the incline and is
represented by the box on the slope. Assume that the incline is frictionless. At the
location of the rider the velocity of the ride has speed v and is directed out of the
page. The rider is executing circular motion at constant speed.
R = 5m
45˚
The Gravitron
a. Draw a free body diagram for the rider. Identify the source of each force.
b. Using Newton’s Laws, construct the equations relating the forces and
accelerations for a passenger of mass m.
c. At what speed would the incline need to move so that the passenger would
not slide up or down on the frictionless ramp? Express the result as a
formula involving g and R.
d. Find a formula for the normal force.
3. A 1000 kg auto moving north at 6 m/s skids into an icy, frictionless intersection
and collides with a 2000 kg SUV skidding east at 4 m/s. The bumpers of the cars
lock together and they skid off together. What is the final velocity of the
wreckage?
4. Two identical particles collide and stick together as shown below.
a. Find the total momentum.
b. Find the final speed.
c. Find the total initial and final kinetic energy
d. How much energy is used to hold the particles together?
Initial
m1 = 1 g
v1 = 10 m/s
Final
45o
m2 = 1 g
v2 = 5 m/s
5. Find an approximate expression for the force of gravity that holds a planet on an
orbit about the Sun if the relationship between orbital period and orbital radius is
T2 ~ r3.
6. Consider a ramp of length 1 m and angle of incline 30 degrees. A block of mass 5
kg is released from rest from the bottom of the ramp. At the bottom of the ramp
is a spring with uncompressed length .1 m and spring constant k = 2x104 kgs-2.
0.05 m
1m
a. If the block begins with the spring compressed to .05m, what is the initial
energy of the block?
b. What is the speed of the block when it reaches the top of the incline?
Ignore friction.
c. Draw free body diagrams for the block when it is at the bottom and the top
of the ramp.
7. A 1 kg ball is released from a height of 1 m above a trampoline. After hitting the
trampoline surface, the ball rebounds to a height of 2 m. About how much energy
was added to the ball by the trampoline?
8. Show that a bullet fired from a gun with muzzle speed v and a bullet dropped
from the same height reach the ground at the same time.
9. Compare the gravitational force and the acceleration due to gravity between you
and the Earth, the Moon and you, and Jupiter and you. Feel free to comment on
astrological bullshit.
10. Problem 3.65
Newton’s first law of motion states that
1.
a.
the total momentum of a system is conserved in the absence of any external
forces.
the force applied to an object is proportional to the acceleration it causes.
an object moves in a straight line at constant speed or remains motionless
unless acted upon by a force
a robot may not harm, nor through inaction cause harm, to a human.
b.
c.
d.
2.
Consider the plot below of a particle’s 1-D acceleration with respect to time:
Acc.
time
Which of the plots below shows the particle’s velocity as a function of time?
a)
b)
c)
d)
3.
Consider the case of a skydiver in free fall. Eventually, she reaches a constant
velocity due to air resistance. Which of the following is then true?
a.
b.
c.
d.
4.
Which of the following requires the LEAST amount of work on the brakes of a
car?
a.
b.
c.
d.
5.
Slowing down from 150 kph to 100 kph.
Slowing down from 100 kph to 50 kph.
Slowing down from 50 kph to 0 kph.
All the above require the same amount of work.
What are the SI units for momentum?
a.
b.
c.
d.
e.
6.
The gravitational force is zero.
The force due to air resistance is zero.
The net force on the diver is zero.
The gravitational force is greater than the air resistance force.
kg-m2/s
kg-m/s
kg-s/m
N-J
Liar! Momentum is unitless.
Captain Kirk boldly lands on a strange, new world in which the gravitational
acceleration near the surface is half as large as on the Earth: |gp|= 1/2|g|.
Neglecting air resistance, how would this affect the time it would take Kirk to fall
a certain distance (naturally ripping his shirt in the process)?
a.
b.
c.
d.
e.
tPlanet = tEarth.
tPlanet = 2tEarth.
tPlanet = (1/2)tEarth.
tPlanet = √2tEarth.
tPlanet = (1/√2)tEarth.
7. A mass is supported by two identical, massless wires as shown. Which wire has
the smallest tension?
a) Wire A
A
B
b) Wire B
c) Both wires have
the same tension
d) Not enough information is
given to answer this
problem.
8. Two hockey pucks glide across a frictionless, horizontal surface and collide
elastically. Which of the following quantities is conserved in the collision?
a.
b.
c.
d.
Momentum
Kinetic Energy
Both of the above are conserved.
None of the above is conserved.
9. The Sun has about 1 million times the mass of the Earth. About how many atoms
comprise the Sun?
a.
b.
c.
d.
e.
10100
1033
10-3
1057
1039
10. Suppose the frictional force between a car’s tires and the road is responsible for
the inward radial force that the car experiences as it makes a turn of radius R at
constant speed v. Which of the following expressions would be true?
a.
b.
c.
d.
N = W.
R = mv2/(mg).
R = v2/m
v = mg/N