The body of a car is suspended above its wheels by four stro

The body of a car is suspended above its wheels by four strong springs. These springs allow the wheels to respond quickly to bumps in the road without having the entire body respond, too. However, the wheels are also connected to the body by shock absorbers. Unlike the springs, which store energy when work is done on them, the shock absorbers use frictionlike effects to convert work into thermal energy.

a. You remove the shock absorbers from your parked car and then jump into the driver’s seat. The body bounces up and down for a long time. Explain this behavior.

b. If the car’s first bounce takes 1 s, how long does its second bounce take? its tenth bounce?

c. You then drive the car off a high curb and onto the road. Describe the body’s motion for the next ten seconds.

d. You reinstall the shock absorbers. Now every time the car body moves toward or away from the wheels, it does work on the shock absorbers and this work becomes thermal energy. You jump back into the driver’s seat of the parked car. How does it respond?

e. You again drive the car off the high curb and onto the road. The shock absorbers make a difference. Describe the body’s motion for the next ten seconds.

Solution

(a) Since there is small or amount little of energy dissipation (no shocks or damping) the oscillations will continue because the energy is not leaving the system.

(b) Each consecutive bounce takes 1 second, the car bounces according to it\'s natural frequency which is what happened when you applied a force

(c) Since the car has mass m, and the springs are under compression, when the tire leaves the concrete momentarily they will extend, until the wheel hits the ground, then the car will bounce, since the potential energy of the car was higher while on the curb than when it is lower, this results in oscillations because the spring is now dealing with the energy transfer.
It will continue to oscillate until the energy is dissipated through air resistance and friction, and the small damping in the spring itself

(d) Since the shock absorbers provide a way for energy to be dissipated out of the system faster, the car will bounce much less. Same thing for part (e)