Advanced Physics mousetrap car elastic energy measurement

W = Σ F Δx

Elastic energy is the work you put into stretching the string. The lever rotates, the string gets longer, and the force climbs. You already have force at known angles out to 180°. That is enough. Add the work from each slice. Do not multiply peak force by the whole swing, and do not treat the Vernier F vs t area as joules.

What you measured

The mousetrap arm is a lever. As it rotates, it pulls the string farther out, so the force on the Vernier hook goes up. You held the hook at a set of angles and read F at each one, ending at 180°, maximum extension.

Work still needs a distance. The angles are how you get that distance. Measure r once, pivot to where the string or Vernier hook actually sits.

How to add the slices

For each neighboring pair of points, from the start angle out to 180°:

Δθ has to be radians. Degrees in the table stay degrees until that first line. The average of the two forces is the trapezoid. Add every W_step. That sum is the energy stored at max extension.

If you marked string length

If you also wrote down string length, or how far the hook actually moved, at each angle, use those x values instead of r Δθ. Same formula. Better if the string does not follow a clean arc.

One slice, so the units are obvious

Repeat that to 180° and add. The 0.288 J is only 30° to 60°. The lab number is the whole sum.

What the Vernier graph is not

Vernier's default plot is F vs t. The area under that curve is impulse, N·s, not joules. Ignore time if you already have F at known angles.

If you pulled at a roughly constant slow speed instead of discrete holds, the same idea still needs a distance. W = v × (area under F vs t) only works because Δx = v Δt. You still measured a speed. You still did not call the raw integral the energy.

Do not do F_max × the full swing. Force changes with angle. That is why you took the steps.