what happens when you shorten the duration of an impact?

Answer 1

All else equal, here's what you get: p = mv; where p is momentum, m is mass of the impacting thing, and v is its velocity at impact. Now, when something runs into something, like a chicken runs into a speeding 737 doing 250 kts, we have a real sudden change in that chicken's momentum. That happens because it's lolly gagging around 2 kts flying, when all of a sudden its going 250 kts (and backwards at that).

Change in momentum over time is written as dp/dt = d(mv)/dt = m dv/dt = m a = force. That is, that impact creates a change in momentum, which is called force...good old f = ma. So, keeping m the same and the change in velocity the same (e.g., from 2 kts forward to 250 kts backwards), the only thing changing is the time of impact (dt).

Thus, from f = m dv/dt, we can see as we make dt --> 0 force has to increase. In fact, if that change in velocity were instantaneous (where dt = 0 because it takes no time at all), the force (impact) on the jet liner's windshield would be infinite. Good news for us is that inertia makes instantaneous velocity changes impossible.

So there you are. Shorten the duration of the impact, that dt in f = m dv/dt, and you increase the force of the impact...when both mass and dv are held constant. What happens in real life, however, is that the dv usually also changes when shortening the dt. How much it changes is based on some complex physics; so let's not go there here.

Good question.

Answer 2

1

Answer 3

The opposite of what I answered to your other question.

8^)

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