Classical Mechanics
# Potential Energy

**in meters**?

**Details and assumptions**

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

$m=9\text{ kg}$ is released from rest at point $A,$ and slides down a long, frictionless, $h=60\text{ m}$ high slide. Then it enters the horizontal surface from point $B$ to $C,$ which is not frictionless, and comes to a complete stop at point $C.$ If the coefficient of kinetic friction between the object and the surface is $\mu=0.1,$ what is the horizontal distance $x$ between points $B$ and $C?$

An object of massThe 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 $g=10\text{ m/s}^2.$