Question

Calculating work for different springs Calculate the work required to stretch the following springs 0.5 m from their equilibrium positions. Assume Hooke’s law is obeyed. a. A spring that requires a force of 50 N to be stretched 0.2 m from its equilibrium position. b. A spring that requires 50 J of work to be stretched 0.2 m from its equilibrium position.

Answer 1

Part a)

U = 31.25 J

Part b)

U = 312.5 J

Step-by-step explanation:

Part A)

A spring that requires a force of 50 N to be stretched 0.2 m from its equilibrium position.

So here we have

`F = kx`

`50 = k(0.2)`

k = 250 N/m

now the energy stored in the spring is given by

`U = (1)/(2)kx^2`

`U = (1)/(2)(250)(0.5)^2`

`U = 31.25 J`

Part B)

A spring that requires 50 J of work to be stretched 0.2 m from its equilibrium position.

So here we know the formula of spring energy as

`U = (1)/(2)kx^2`

`50 = (1)/(2)k(0.2)^2`

`k = 2500 N/m`

now by the formula of energy stored in spring

`U = (1)/(2)kx^2`

`U = (1)/(2)(2500)(0.5)^2`

`U = 312.5 J`