Download Midterm Exam -- Review Problems 1. A 1,000 kg car starts from rest

Midterm Exam -- Review Problems
1. A 1,000 kg car starts from rest, and accelerates at a rate of +2 m/s2 for a period of 5 seconds.
a. what is the car’s final velocity? [kinematics]
b. what is the displacement of the car? [kinematics]
c. what is the Net Force acting on the car? [Newton’s 2nd Law]
d. what is the total work done to the car? [definition of work; work done by Net Force]
e. what is the change in the car’s kinetic energy? [work-energy theorem, or definition of
kinetic energy]
f.
what is the change in the car’s momentum? [definition of change in momentum]
g. what is the impulse delivered to the car. [impulse-momentum theorem, or definition of
impulse]
2. A 200 N/m spring is compressed a distance of 0.10 meters. A 0.2 kg mass is placed next to the
spring, and it is released from rest. Assume all surfaces are frictionless and horizontal.
a. When the spring reaches its relaxed length (xf = 0), what is the velocity of the mass?
[Conservation of Energy]
b. If the mass is accelerated over the 0.1 m distance of the spring’s compression, what is
the time required for the mass to achieve its velocity? [kinematics]
c. What is the acceleration of the mass? [kinematics]
d. What is the change in momentum of the mass? [definition of change in momentum]
3. [Continuation from #2] Now, assume that the 0.2 kg mass strikes an identical 0.2 kg mass that is
initially at rest. After the collision, assume that the first mass completely stops moving.
a. What is the final velocity of the second mass? [conservation of Momentum]
b. What is the final kinetic energy of the second mass? [definition of KE]
4. [Continuation from #3] Now, the 0.2 kg mass strikes a third identical 0.2 kg mass that is initially
at rest. This time, the two masses stick together.
a. What is the final velocity of the two masses? [Conservation of Momentum]
b. What is the final kinetic energy after the collision? [definition of KE]
c. *How much kinetic energy is lost in this collision? [definition of change in KE]
5. *[Continuation from #4] Assume the surface to the right of mass 3 is rough, and that the
coefficient of friction is 0.25. The two blocks slide together until they completely stop moving.
a. What is the magnitude of the force of friction? [definition of frictional force]
b. What is the change in kinetic energy of the two objects? [definition of change in KE]
c. How much work is done by the force of friction? [Work-Energy Theorem]
d. What is the distance the objects travel until they stop? [definition of Work]
e. How long does it take for the objects to stop moving? [kinematics]
6. A 1.0 kg coconut falls from rest from a point that is 10 meters above the ground.
a. What is its final velocity when it hits the ground? [Free-fall or Conservation of Energy]
b. What is the time required to reach the ground? [free-fall]
c. What is its momentum when it hits the ground? [definition of momentum]
d. What is its kinetic energy when it has fallen 5 meters? [Conservation of Energy]
e. What is its speed at this point? [definition of KE]
7. A 0.50 kg soccer ball is kicked off of the ground with an initial velocity of 10 m/s at an angle of
30 degrees. It follows the parabolic trajectory shown below.
a. What are the x- and y-components of the initial velocity? [vector components]
b. What are the x- and y-components of the velocity when the soccer ball reaches its
maximum height? [Projectile Motion]
c. How much time is required to reach the maximum height? [free-fall]
d. What is the maximum height to which the soccer ball rises? [free-fall]
e. How much total time is required for the soccer ball to return to the ground? [free-fall]
f. What is the horizontal displacement of the soccer ball when it lands on the ground?
[Projectile Motion]
g. What is the initial kinetic energy of the soccer ball? [definition of KE]
h. What is the gravitational PE of the ball at the maximum height? [definition of PEg]
i.
What is the speed of the soccer ball at the maximum height? [Conservation of Energy]
j.
What is the direction of the velocity vector at the maximum height?
8. A 100 kg object is at rest on a rough surface, where there is a coefficient of static friction μ s= 0.5;
the coefficient of kinetic friction is μk = 0.40. A horizontal force F is applied to the object.
a. What is the maximum amount of static friction that is exerted on the object? [definition
of static friction]
b. What is the acceleration of the object if F = 400 N? [Newton’s 2nd Law]
c. The force F is increased to 502 N. What is the acceleration of the object? [Newton’s
2nd Law]
d. This force F is held constant, and exerted for a time of 2.0 seconds. What is the final
velocity the object? [kinematics; or, Impulse-Momentum Theorem]
e. What is the change in the object’s kinetic energy? [definition of change in KE]
f. How far has the box moved over the 2.0 seconds? [kinematics; or, Work-Energy
Theorem]