- #1
SuspendedFour
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Homework Statement
A 8.00 kg stone lies at rest on a spring. The spring is compressed 10.0 cm (.1 m) by the stone. What is the spring constant?
Homework Equations
F = -kx
E = (1/2)kx^2
U = mgh
The Attempt at a Solution
The solution provided uses a net force equation balancing Hooke's Law with mg:
-kx = mg
k = mg/x = 784 N/m
When I first tried this problem, I approached it using conservation of energy:
U0 + E0 = Uf + Ef
Ef = U0 + E0 - Uf = U0 + 0 - 0 = U0 = 7.84 J
Where t=0 is the rock at the top of the uncompressed spring and t=f is the rock in equillibrium on the compressed spring.
k = 2Ef/x^2 = 1568 N/m
Using my approach, I am off by a factor of 2. Where is my misunderstanding here? I understand the solution involving net force, but shouldn't the conservation of energy work out too?