Calculating the Maximum Compression of a Spring

[soul5]

Homework Statement

A block of mass m = 3.4 kg is dropped from height h = 44 cm onto a spring of spring constant k = 1920 N/m (Fig. 8-38). Find the maximum distance the spring is compressed.

[PLAIN]http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c08/fig08_36.gif

Homework Equations

Ep=mgh

Ep=1/2kx^2

The Attempt at a Solution

Ok so I found the Potential Energy Ep=mgh. That energy should equal to 1/2kx^2.

So I set mgh = 1/2kx^2 to solve for x but my answer was wrong?

 

[swraman]

Your choice to use kinetic and potential energy is correct, but you are missing one small thing.

The distance the block moves down along the spring (that is, the distance the spring is displaced x) still counts as gravitational potential energy for the block. So modifying the equation you have to take this into account will yield:

mg(h+x) = .5kx^2

From here you can solve for x, the displacement of the spring. Since it is a quadratic, you will get 2 different answers, but it should be clear which one is the correct answer.

 

[Gorz]

What was your answer for x, I got 0.1236m.

 

[soul5]

What was your answer for x, I got 0.1236m.

that's what I got to the first time, but it was wrong...

 

[swraman]

if you try what I mentioned you will get x=.142m which I believe is the correct answer.