Classical Mechanics
# Potential Energy

**Details and assumptions**

- The acceleration due to gravity is \(9.8~m/s^2\).
- Treat the grandfather clock as a simple pendulum.

The gravitational acceleration is \(g=10\text{ m/s}^2.\)

An object of mass \(4\text{ kg}\) initially at rest falls freely towards a huge spring that is \(100\text{ m}\) below. If the spring constant is \(k=16\text{ N/m},\) what is the maximum change in the spring's length?

Air resistance is negligible and gravitational acceleration is \(g=10\text{ m/s}^2.\)

A meteor of mass \(m=800\text{ kg}\) enters the earth's atmosphere with a velocity of \(500\text{ m/s},\) and falls vertically toward the ground. The meteor burns while falling, and its mass decreases at a rate of \(5\text{ kg/s}.\)

If the meteor falls with a constant velocity, how much gravitational potential energy will it lose in \(16\) seconds?

**Note**

- The height of the meteor when it enters the atmosphere is \(1000\text{ km},\)
- The gravitational acceleration is \(g=10\text{ m/s}^2.\)

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