Step 4: Analysis Using Basic Physics
I wanted to examine the behavior of a trap using a model based on physics, to provide a comparison against the observed timing.
I put together an analysis of the system using a simplified model based on the physics of ideal springs and simple harmonic motion. In this simplified analysis, many things have been idealized. Frictional forces, air resistance, and gravitational forces have been neglected. The energy used to push the hook up and out of the way has not been considered. The spring is assumed to be ideal, where the torsion constant of the spring does not change with the angle.
The attached PDF document contains the equations which describe the simplified physical model of the rat trap. It shows how the equations of motion are determined, and it includes a spreadsheet of the system parameters and the performance for the rat trap. All the equations and concepts contained in the analysis apply for both the mouse trap and the rat trap.
I’ll just list a couple of the more important results for the rat trap here, and leave it to you to look at the PDF for more details.
The main thing I wanted to get from the analysis was a calculated value for the time to close, for comparison with the measured value.
Measured and Calculated Results for the Rat Trap:
T_close_measured = 23ms
These results agree reasonably well with the observation. It makes sense that the calculated value would predict a faster closing time, as it does not include any frictional forces that would reduce the speed.
The potential energy stored in the rat trap when set was calculated to be 3.16 Joules. That doesn’t seem like very much energy, but it is apparently enough to break a rat’s neck. I didn’t perform the calculations for the mouse trap, but the torsion constant of the spring would be much lower than that of the rat trap, so the energy needed to kill a mouse would be even less.