Potential energy in stretched spring

[RoboNerd]

Homework Statement

Five identical masses of mass M are suspended by a spring stretched a distance of L. If three of the masses are removed, what is the potential energy stored in the spring?

1) (4 / 25) * M * g * L
2) (2 / 5) M * g * L^2
3) (5 / 2) * M g * L
4) (4 / 25 ) * M * g L^2
5) 5 * M * g * L

Homework Equations

Fspring = -k * x

The Attempt at a Solution

Hi everyone. I get 2 to be the answer while my solutions manual says that 4 is correct. I suspect the solutions manual is wrong, but I wanted to get someone's opinion on this first.

So firstly, I got the value of the "K" for the spring:
Fspring = Fg of the masses

k * x = 5 * M * g

k = (5 * M * g) / LThen, I got the amount of stretch of the spring with only two masses.

Fspring = Fg of the masses

k * d = 2 * M * g

[ (5 * M * g) / L ] * d = 2 * M * g

solved for d = (2 /5 ) * L.

Then, I took equation Uspring = (1 / 2) * k * x^2.

I plugged the expressions for K and D for the stretch and I got the expression for answer 2.

Have I done something wrong?

Thanks in advance for the help!

 

[PhanthomJay]

You did the Physics correctly, But if you did your math correctly, you would have got 2MgL/5. None of the choices match that correct answer.

 

[RoboNerd]

ohh yes, I got a single L, now that I remember, instead of L squared. Right. thanks