How long would it take to fall through the center of the Earth?

450px-9_daughters_hole
We have a hole that leads straight through the center of the Earth. We neglect air resistance and assume that the Earth has uniform density ρ. How long would it take to fall through the center of the Earth and reach the other side of the planet?

Continue reading

Advertisements

Hooke’s Law and the Simple Harmonic Oscillator

2springsA mass m is attached to a spring S and oscillates with a period T.
(a) What would be the period of the oscillations on a planet with surface gravity 3g?
(b) What would be the period of the oscillation if two springs S are connected in series or in parallel?
Continue reading

A mass is attached to one end of the steel ruler

RulerA steel ruler is placed in a vertical position. A mass is attached to one end of the steel ruler and the other end fixed. When the mass is displaced slightly sideways and then released, the mass will begin to oscillate. In the first experiment, the mass is attached to the top of the ruler. In the second experiment, the mass is attached to the bottom of the ruler. In both experiments, the amplitude is nearly the same.

Consequently,

a) in the first experiment, the time period of oscillation is larger.
b) in the second experiment, the time period of oscillation is larger.
c) in both experiments, the time period of oscillation is the same.

Continue reading