Understanding Spring Compression: How Doubling It Affects Stored Energy

[NewJersey]

If compression of a spring is doubled, the stored energy increased by a factor of?

I think that the stored energy is increased by a factor of 2.

Right?

 

[Mindscrape]

What is the equation for a spring's potential energy?

 

[NewJersey]

Fs1=1/2 kx^2 so if k = 25 v=4
= 200

Fs2= k=50 v=4
=400

so by factor of 2

 

[Mindscrape]

Ah, you are doubling the wrong thing. k is the spring constant. The question is asking about changing x by a factor of 2.

$$F_{s1} = .5kx^2$$

$$F_{s2} = .5k(2x)^2$$

$$\frac{F_{s2}}{F_{s1}} = ?$$