Block attached to spring - calculate how far it will move

[jcjc16]

Homework Statement

A spring with spring constant 200 N/m is suspended vertically with its upper end fixed to the ceiling and its lower end at position y = 0. A block of weight 20 N is attached to the lower end, held still for a moment, and then released. How far will the block move before coming momentarily to a stop?

Homework Equations

mg = -kx
mg = 0.5kx^2

The Attempt at a Solution

I tried using the first equation and got x = 0.1m as my ans. which was wrong. I then tried using the second equation instead and still got an incorrect answer. Where am I going wrong? The ans. is 0.2 m.

Thanks in advance!

 

[lewando]

You need to look at this problem from an energy conservation standpoint.

 

[QED Andrew]

The block comes to a stop when its speed is zero. Your approach is invalid because the speed of the block is not necessarily zero when the net force acting on the block is zero.

 

[jcjc16]

Hmm ok would it be something like this? mgh = 0.5kx^2 and the x and the h are the same? Cuz then solving for h I get (2mg)/k and when I subbed in the number I got 0.2. Is this the right way of doing this problem?

 

[lewando]

Looks like a good way to get the answer!

 

[QED Andrew]

Your answer is correct; however, it is important you understand why the approach is valid. Do you?