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

Nine times

Step-by-step 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)`