Homework 11 Problems – Simple Harmonic Motion

Homework 11 Problems – Simple Harmonic Motion
1. [10 points] A grandfather clock depends on the period of a pendulum to keep correct
time. Suppose such a clock is calibrated correctly and then the temperature of the room in
which it resides increases.
a. Does the clock run slow, fast, or correctly? [Hint: A material expands when its
temperature increases.]
b. How could we adjust the length of the pendulum to correct the time?
2. [10 points] A block of mass
is attached to a spring of force constant
that lies on a horizontal surface as shown below. The block is
pulled to a position
to the right of the equilibrium and released from rest.
a. Find the work required to stretch the spring.
b. Find the speed the block as it passes through equilibrium.
3. [10 points] A 2.00-kg object on a frictionless track is attached to the end of a horizontal
spring whose force constant is 5.00 N/m. The object is displaced 3.00 m to the right from
its equilibrium position, initiating simple harmonic motion.
a. What is the force (magnitude and direction) acting on the object 3.50 s after it is
released.
b. How many times does the object oscillate in 3.50 s?
4. [10 points] The position of a 0.30-kg object attached to a spring is described by
(
)
(
)
a. Find the amplitude of the motion and the spring constant
b. Find the position of the object and the force exerted on the object at
c. Find the object’s speed and acceleration at
d. Determine the kinetic energy, potential energy, and total energy at
5. [10 points] A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and
passes through a 1.00-kg block, as shown below. The block, initially at rest on a
frictionless horizontal surface, is connected to a spring with a spring constant of 900 N/m.
If the block moves 5.00 cm to the right after impact,
a. Find the speed at which the bullet emerges from the block and
b. Find the mechanical energy lost in the collision.
Bonus: [6 points] A large block P executes simple harmonic motion as it slides across a
frictionless surface with a frequency
. Block B rests on it, as shown below, and the
coefficient of static friction between the two is
. What maximum amplitude of
oscillation can the system have if block B is not to slip?