- #1

SeventeenForever

## Homework Statement

[/B]A block of mass, m, is dropped from height, h (above the plate), onto a plate of mass, M, which is attached to a spring with spring constant, k. The block sticks to the plate and the system starts to oscillate. What is the amplitude of the oscillations.

## Homework Equations

E

_{total}=K + U

_{gravitational}+ U

_{spring}

U

_{spring}=0.5kx

^{2}

K=0.5mv

^{2}

U

_{gravitational}=mgh

Conservation of Energy

## The Attempt at a Solution

I decided to approach this problem from an energy perspective, setting the equilibrium position of the spring (w/ plate) as 0 gravitational potential energy.

The initial gravitational potential energy is U

_{g}=mgh. Just before it hits the plate, all of this gravitational PE is converted to KE.

mgh = 0.5mv

^{2}

v= (2gh)

_{0.5}

The problem specifically states that the block "sticks" to the plate, suggesting a completely inelastic collision. I can use the conservation of momentum to find the velocity after the collision; after the collision, the velocity of the plate and block is:

v

_{f}= m(2gh)

^{0.5}/ (m+M)

The kinetic energy of the system is now:

0.5(m+M)v

_{f}

^{2}= K

_{f}

The spring will then be compressed from its equilibrium position until the velocity of the plate/block becomes zero, which is the max compression/amplitude. At this point, all of the kinetic energy has been converted to elastic potential energy.

0.5(m+M)v

_{f}

^{2}= 0.5kx

^{2}

I can then plug in my equation for v

_{f}and solve for x, which is the maximum compression/amplitude.

Is this approach okay? Did I make any incorrect assumptions?

Thaaaaaanks!