# Block attached to spring - calculate how far it will move

## 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?

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.

lewando
Homework Helper
Gold Member
You need to look at this problem from an energy conservation standpoint.

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.

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
Homework Helper
Gold Member
Looks like a good way to get the answer!

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