# Compression of a spring. Hooke’s Law vs. Conservation of Energy

**1. The problem statement, all variables and given/known data**

Lets say I have a spring with a stiffness of k = 250 N/m originally unstretched. I then gently place a 5 kg block on top of the spring. How much does the spring compress?

**2. Relevant equations**

W = mg

F = -ks

mgΔh = 0.5k(Δh)^{2}

**3. The attempt at a solution**

Using Hooke’s Law I get the following result

W = 5*9.81 = 49.05 N

W = F = -kx

49.05 = 250x meaning x = 0.1962 m

Using conservation of energy I get this though:

mgx = 0.5kx^{2}

0 = 125x^{2} – 49.05x

x = 0.3924 m

So which one is the correct answer? Why is one double the other?

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

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