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

Answer:

Part a)

U = 31.25 J

Part b)

U = 312.5 J

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

$U = \frac{1}{2}kx^2$

$U = \frac{1}{2}(250)(0.5)^2$

$U = 31.25 J$

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

$U = \frac{1}{2}kx^2$

$50 = \frac{1}{2}k(0.2)^2$

$k = 2500 N/m$

now by the formula of energy stored in spring

$U = \frac{1}{2}kx^2$

$U = \frac{1}{2}(2500)(0.5)^2$

$U = 312.5 J$