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Physics 150
Sample questions: Midterm 1
1. A mass m = 1 kg is connected to a spring of spring constant k = 100 N/m.
Neglect the mass of the spring and assume that the mass can slide without friction
in the horizontal direction. The mass is moved so that the spring is compressed by
1.0 meter and then released from rest.
a. Find the frequency of oscillation of the mass.
b. What is the total mechanical energy of the spring and mass? Is it
conserved?
c. Develop a formula that gives the speed v of the mass as a function of the
displacement x of the mass.
2. 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. Choose x- and y-axes parallel and perpendicular to the ramp
surface, respectively.
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.
3. 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.
4. 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?
5. A mass m is suspended from a string that is wound around the circumference of a
hollow cylinder of mass M, radius R, and moment of inertia I  MR 2 . The mass
starts from rest and accelerates downward through a distance h. Assume that the
cylinder can rotate without friction and that the mass of the string can be
neglected.
a. Draw a free body diagram for the suspended mass at its initial location. .
b. Find an equation for the tension in the string in terms of the mass m and its
acceleration.
c. Find the torque exerted on the cylinder by the string.
d. Find the magnitude of the downward acceleration of the mass in terms of
the acceleration of gravity and the other parameters given in the problem.
e. Find the rotational kinetic energy and angular momentum of the cylinder
about its axis of rotation after the hanging mass falls a distance h.
6. A Lunar Landing Module approaches the surface of the Moon. Lunar surface
gravity acceleration is 1/6 that of the Earth’s.
a. The retro-rockets of the LM shut down at a height of 5 m. If the downward
speed of the LM is 1.0 m/s at the time of retro-rocket cutoff, what is the
speed of the LM when it touches down? How long does the LM require to
reach the surface from the point of retro engine cutoff?
b. The mass of the LM is 50,000 kg. What is the force of impact at the
moment that the LM lands?
7. An elevator has a total mass of 2500 kg and cables that can withstand a maximum
tension of 30,000 N.
a. Draw the free-body diagram for the elevator.
b. What is the net force on the elevator if it is moving upward with a constant
velocity of 5 m/s? What is the net force if the elevator is moving
downward with a constant velocity of 5 m/s?
c. What is the maximum acceleration that the elevator can take before the
cables snap?
8. 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
9. Write an expression for the final translational velocity of a cylinder that moves
down an inclined plane assuming a) hollow vs. solid cylinders and b) sliding vs.
rolling without slipping.
10. 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.