Question

A spring is compressed 8 cm. It is then brought back to equilibrium and compressed 24 cm. How much more work is done in the second compression than in the first? (9x)

Answer 1

Answer:

Nine times

Explanation:

$x_{i}$ = Initial compression of the spring = 8 cm = 0.08 m

$x_{f}$ = Final compression of the spring = 24 cm = 0.24 m

$k$ = Spring constant of the spring

Initial spring energy is given as

$U_{i} = (0.5) k x_{i}^{2}\\U_{i} = (0.5) k (8)^{2}\\U_{i} = 32 k$

Initial spring energy is given as

$U_{f} = (0.5) k x_{f}^{2}\\U_{f} = (0.5) k (24)^{2}\\U_{f} = 288 k = (9) (32) k = 9 U_{i}$