Question

A spring has a relaxed length of 7 cm and a stiffness of 200 N/m. How much work must you do to change its length from 12 cm to 16 cm?

Answer 1

Force constant of the spring = k = 200 N/m

Relaxed length of the spring = L = 7 cm = 0.07 m

Initial length of the spring = L₁ = 12 cm = 0.12 m

Initial extension of the spring = X₁

X₁ = L₁ - L

X₁ = 0.12 - 0.07

X₁ = 0.05 m

Final length of the spring = L₂ = 16 cm = 0.16 m

Final extension of the spring = X₂

X₂ = L₂ - L

X₂ = 0.16 - 0.07

X₂ = 0.09 m

Initial potential energy of the spring = E₁ = kX₁²/2

Final potential energy of the spring = E₂ = kX₂²/2

Work done to change the length of the spring from 12 cm to 16 cm = W

The work done is equal to the change in the potential energy of the spring.

W = E₂ - E₁

W = kX₂²/2 - kX₁²/2

W = (200)(0.09)²/2 - (200)(0.05)²/2

W = 0.56 J

Work done to change the length of the spring from 12 cm to 16 cm = 0.56 J