A 5 kg mass is thrown down with a velocity of 10 m/s from a height of 20 m onto an upright spring with a relaxed length of 10 m, and a constant of 50 N/m. What will the maximum compression of the spring be? What will the speed of the object be when the spring is compressed 0.2 m?
Here's what I have so far:
INITIAL HEIGHT = 20 meters
FINAL HEIGHT = 10 meters
MASS = 5 kilograms
ACCELERATION = 9.8 meters per second squared
INITIAL VELOCITY = 10 meters per second
SPRING CONSTANT = 50 Newtons per meter
ENERGY OF GRAVITY = mgh
KINETIC ENERGY = 0.5mv^2
SPRING ENERGY = 0.5kx^2
TOTAL ENERGY = The sum of those 3 energies
I need to find the final velocity and then how much the spring gets compressed. Then I have to find the speed of the object when the compression of the spring is 0.2 meters.
The spring in compressed until the initial sum of kinetic and potential energy equals the final stored energy in the spring, MINUS the decrease in PE during compression.
Let x be the maximum compression
(1/2) M Vo^2 + M g H = (1/2) kx^2 - M g x
Solve for maximum x deflection. When the spring is compressed x = 0.2 m, you can energy conservation to solve for v
(1/2) M Vo^2 + M g H = (1/2) kx^2 - M g x + (1/2) M v^2