1.
Crazy
Jumpers Incorporated wants to test the elasticity of a new bungee cord without
endangering anyoneÕs life. While
the clients are busy jumping from a bridge (using the older cords), the owner
(M = 100 kg) is attached to a 10-meter length of the new cord and slowly
lowered until he is hanging motionlessly.
At that time it is noted that the cord has stretched to a new length of
20 meters.

Make a FBD for the owner as he dangles
(motionlessly) from the bungee cord.

Using NewtonÕs 2nd Law, determine the
spring constant for this bungee cord.

Now that the spring constant of the new cord is
known, the owner (who recently completed a physics course) performs a few quick
calculations and then decides to do a trial jump using a 40 m length
(unstretched) of the new cord. He
jumps from the 90 m tall bridge as his assistants (who unfortunately never
learned physics) watch with a mixture of fascination and morbid curiosity. Your goal in this problem is to
recreate the ownerÕs calculations to determine whether it was safe for him to
jump.

2.
A car is stopped by a
constant friction force that is independent of the car's speed. By what factor is the stopping distance
changed if the car's initial speed is doubled? Hint: think
about work and energy conservation.

3.
Consider a mass
sandwiched between two collinear springs that are arranged along the x-axis
such that there is no force on the mass when it is centered at x = 0 m. Assume the mass slides on a
frictionless surface and that both springs have a spring constant k.

(a)
What is the force on the
mass as a function of x and k (for reasonable x that is smaller than the spring
length)?

(b)
Qualitatively graph the
potential energy function of the system as a function of x.

4.
Consider a 2 kg mass
stacked on top of at 7 kg mass as shown below. The two masses are attached to a spring (which is attached
to the wall) and can move back and forth on a frictionless surface. The coefficient of static friction
between the bottom surface of the top mass and the top surface of the bottom
mass is 0.45. The spring constant
is 200 N/m.

a)
What is the maximum
amplitude of the simple harmonic motion
(maximum amount the spring is compressed and stretched) of the system
shown below such that the top mass does not slip during the oscillation?

b)
In a system that
undergoes this limiting motion:
What is the total energy of the system?