Calculating Potential Energy in a Rotary Mousetrap Spring System

In summary, the potential energy created by the spring in the mousetrap can be calculated using the equation PE = ∫Fdx = ∫ kxdx = ∫k rΘ rdΘ. This can be simplified to ½k(rΘ)^2 if the spring is linear. To determine if the spring is linear and to find the spring constant, measurements such as torque and angle can be taken. It is also worth noting that mousetraps typically use torsion springs.
  • #1
JLT
52
4

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?
 
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  • #2
Is this an experiment? What measurements could you take to help determine if it is linear and to determine k?
 
  • #3
JLT said:
the spring in the mousetrap
Is there a diagram with this?
It sounds like a so-called torsion spring. Mousetraps generally use those.
 
  • #4
OK, although for a rotary system the spring constant is usually given as τ = kθ, τ = torque, then
p.e. = 1/2 kθ2.
 

1. What is potential energy in a mousetrap?

Potential energy in a mousetrap is the stored energy that is waiting to be released when the trap is triggered. It is the result of the mechanical force applied to the spring when it is set.

2. How does the potential energy in a mousetrap work?

The potential energy in a mousetrap works by utilizing the energy stored in the spring. When the trap is triggered, the potential energy is transformed into kinetic energy, causing the bar to snap down and trap the mouse.

3. What factors affect the potential energy in a mousetrap?

The potential energy in a mousetrap is affected by several factors, including the stiffness of the spring, the distance the spring is pulled back, and the weight of the object on the trap. The more the spring is pulled back and the heavier the object, the greater the potential energy.

4. Can potential energy in a mousetrap be increased?

Yes, the potential energy in a mousetrap can be increased by pulling the spring back further, using a stiffer spring, or adding weight to the trap. However, it is important to be careful when increasing potential energy as it can also make the trap more dangerous.

5. How is potential energy in a mousetrap related to real-world applications?

Potential energy in a mousetrap is related to real-world applications such as energy storage and release mechanisms. It is also used in engineering and design to create mechanisms that store and release energy for various purposes, such as in toys and machines.

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