Calculating Potential Energy in a Rotary Mousetrap Spring System

[JLT]

Homework Statement

Calculate the potential energy created by the spring in the mousetrap as a function of the angle the spring is pulled back.

Homework Equations

PE = ∫Fdx = ∫ kxdx = ∫k rΘ rdΘ ??

The Attempt at a Solution

Is this a linear spring? we can use x = rΘ, and dx = rdΘ, so PE = ½k(rΘ)^2

↑↑ does that look good to everyone, or is there a better soln to this?

 

[scottdave]

Is this an experiment? What measurements could you take to help determine if it is linear and to determine k?

 

[haruspex]

the spring in the mousetrap

Is there a diagram with this?
It sounds like a so-called torsion spring. Mousetraps generally use those.

 

[rude man]

OK, although for a rotary system the spring constant is usually given as τ = kθ, τ = torque, then
p.e. = 1/2 kθ².