Force spreading out - over time

Two separate collisions: one over a longer duration than the other

Wrong Track: The force is spread out over a longer time, and over a greater distance.

Right Lines: There's a lot of momentum to remove from the moving body as the body is brought to a halt. The time over which the force acts is longer, so the force exerted is smaller. There's a lot of energy to shift from the kinetic store as the body is brought to a halt. The distance over which the force acts is greater, so the force exerted is less.

A focus on compensation

Thinking about the learning

It's a common pattern of reasoning amongst students, when faced with two physical quantities that affect a third, to foreground one of the pair and reason about changes to the third based on this chosen quantity alone. This is the difficulty common to focusing on changing either kind of measure of motion (energy in the kinetic store or the momentum of the moving object.)

There's another, quite separate, difficulty, that arises from the use of the phrase the force. Underlying this is often a tacit assumption that it's the same force in both the shorter duration collision and the longer duration collision. The interactions in the two collisions are rather different in magnitude so the forces that represent these two interactions will also be different.

It might seem a small point, but anything that leads to careful consideration of the two situations from first principles, and then compares them, is more likely to support meaningful learning than a rather careless phrase that could be used as a prop for an inappropriate short-cut. In particular, forces are not the kind of things that can be spread out. This kind of talking and analysis, where the force is worked on as one moves from one situation to the other, tends to lead off down the wrong tracks.

Thinking about the teaching

There are several representations in the Physics Narrative that support paying equal attention to both force and time or force and distance. We'd suggest using them, as well as the algebraic and verbal modes of reasoning.

Force and time are compensated quantities ( Δ momentum = force × time).

Force and distance are compensated quantities ( Δ energy = force × distance).

To counter the second difficulty, we'd suggest that you analyse the two collisions as two separate processes, and only then compare the magnitudes of the forces at the end.

Teacher Tip: Avoid referring to the force without qualification when comparing two collisions of different durations.