Block dropped onto spring: finding maximum compression

[dorkymichelle]

Homework Statement

A block of mass m = 3.5 kg is dropped from height h = 81 cm onto a spring of spring constant k = 2220 N/m (Fig. 8-37). Find the maximum distance the spring is compressed.

Homework Equations

Pe(spring) = 1/2kx²
Pe(gravity)=mgh
Ke = 1/2mv²

The Attempt at a Solution

so far, i got mgh+1/2mv_i² =1/2mv_f² = 1/2kx²

because the energy used to compress the spring is the amount of energy from the end of the drop.
but I don't have initial velocity or final velocity. or can i use 0 as final velocity at the point that the object hits the spring..

 

[PhanthomJay]

Homework Statement

A block of mass m = 3.5 kg is dropped from height h = 81 cm onto a spring of spring constant k = 2220 N/m (Fig. 8-37). Find the maximum distance the spring is compressed.

Homework Equations

Pe(spring) = 1/2kx²
Pe(gravity)=mgh
Ke = 1/2mv²

The Attempt at a Solution

so far, i got mgh+1/2mv_i² =1/2mv_f² + 1/2kx²

because the energy used to compress the spring is the amount of energy from the end of the drop.
but I don't have initial velocity or final velocity. or can i use 0 as final velocity at the point that the object hits the spring..

The block is dropped from rest, and it ends up momentarily at rest when the spring is fully compressed, not when it first hits the spring. You need to change your PE term to account for the extra height due to the spring displacement in its fully compressed position.

 

[dorkymichelle]

so kinetic initial and kinetic final would both be 0
changing my PE(gravity) term to include the compressed spring,
would the equation I need be mg(h+x) = 1/2kx^2 ? and solve for x to be the length the spring compresses?

 

[PhanthomJay]

Yes, exactly.