Question

In: Physics

Suppose a mass m is on a spring that has been compressed a distance h. How...

Suppose a mass m is on a spring that has been compressed a distance h. How much further must the spring be compressed to triple the elastic potential energy?

1.7 h

0.73 h

1.0 h

3.0 h

2.0 h

Expert Solution

Mass on the spring = m

Force constant of the spring = k

Initial compression of the spring = h

Initial potential energy of the spring = E₁

E₁ = kh²/2

New compression of the spring = X

New potential energy of the spring = E₂

E₂ = kX²/2

The potential energy of the spring is tripled in this compression.

E₂ = 3E₁

kX²/2 = 3kh²/2

X² = 3h²

X = 1.73h

Additional compression of the spring from the initial compression = X

X = X - h

X = 1.73h - h

X = 0.73h

Additional compression of the spring to triple the elastic potential energy = 0.73h

genius_generous answered 2 years ago

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