Question

A spring with a spring constant of 3050 N/m is initially stretched until the elastic potential energy is 1.72 J. (U = 0. for no stretch.) What is the change in the elastic potential energy if the initial stretch is changed to a stretch of 2.0 cm? What is the change in the elastic potential energy if the initial stretch is changed to a compression of 2.0 cm? What is the change in the elastic potential energy if the initial stretch is changed to a compression of 4.0 cm?

Answer 1

Given spring constant k = 3050 N/m

let initial stretching is   'x1'

The initial potential energy is 1.72 J

a)

we have U1 = 1/2 * k * (x1)^2

1.72 = 1/2 * 3050 * (x1)^2

x1 = 0.0336 m

When it is stretched to x2 = 2 cm = 0.02 m the potential energy is

U2 = 1/2 * k * (x2)^2

U2 = 1/2 * 3050 * (0.02)^2

U2 = 0.61 J

Change in potential energy is delta U = U2 - u1 = 0.61 - 1.72

delta U = - 1.11 J

b)

When it is compressed to 2 cm the change in potential energy is same

That is   delta U = - 1.11 J

c)

When it is compressed to x2 = 4 cm = 0.04 m

The potential energy is U2 = 1/2 * k * (x2)^2

U2 = 1/2 * 3050 * (0.04)^2

U2 = 2.44 J

the change in potential energy is

delta U = U2 - U1 = 2.44 - 1.72

delta U = 0.72 J