Question

What is the length a rubberband was stretched if it has a spring constant of 5700N/m and is currently holding 8600J OF POTENTIAL energy?

Answer 1

`\displaystyle \Delta x=1.74\ m`

Step-by-step explanation:

Elastic Potential Energy

Is the energy stored in an elastic material like a spring of constant k, in which case the energy is proportional to the square of the change of length Δx and the constant k.

`\displaystyle PE = (1)/(2)k(\Delta x)^2`

Given a rubber band of a spring constant of k=5700 N/m that is holding potential energy of PE=8600 J, it's required to find the change of length under these conditions.

Solving for Δx:

`\displaystyle \Delta x=\swrt{(2PE)/(k)}`

Substituting:

`\displaystyle \Delta x=\sqrt{(2*8600)/(5700)}`

Calculating:

`\displaystyle \Delta x=√(3.0175)`

`\boxed{\displaystyle \Delta x=1.74\ m}`