impulse question?

Question

I have a question about impulse. So, impulse equals change in momentum or average force * change in time. So I have a couple of questions actually. Does impulse only apply for extremely small changes in time? Like if a car crashed and was in contact with something for a second before it stopped, is that still considered 'impulse'? Also, via the formula, the impulse becomes greater when the change in time becomes greater. But I thought there was a larger impulse when time was smaller? If anyone could help clear these up for me that would be great. Thanks :)

Answer 1

If you calculate impulse by multiplying force x ∆t, then ∆t must be small so that the force can be considered constant during the interval. If this is not the case, the true formula is

I=∫F(t)*dt

and it does equal the momentum change ∆(mv)

In your second question, I think you are confusing force magnitude with impulse. In a car crash, ∆(mv) is fixed (the mass of the car times its velocity before crash, assuming it comes to a complete stop). Then the smaller ∆t means bigger force magnitude, not bigger impulse.

Answer 2

Bob R - I believe you are remembering the basic formula incorrectly: Impulse is the change in momentum PER unit time. It's division, not multiplication.
The change in momentum of 5000 k-m/s in 2 seconds is 2500k-m/s/s. The same change in momentum in .5 sec is 10,000k-m/s/s.

Answer 3

Impulse = Average Force x time = change in momentum.

If the force is constant, longer the time, greater is the impulse and shorter the time smaller is the impulse.

If time is constant, greater the force, greater is the impulse and smaller the force smaller is the impulse.

If impulse is constant, greater the force, shorter is the time and smaller the force longer is the time.

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You have stated that
you thought there was a larger impulse when time was smaller.

via the formula, the impulse becomes greater when the change in time becomes greater.
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Since impulse is equal to change in momentum, the impulse remains the same if the change in momentum remains the same.
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A car of mass m moving with a speed v collides with a wall and brought to rest in time t1.

The impulse is mu [ cahnge in momentum]

The same car moving with the same speed collides with a rubber wall and brought to rest in time t2 > t1.

The impulse is the same as mu [ cahnge in momentum].

In the former case force was large and in the latter case force is small.
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Therfore, for the same impulse force is greater if time is less.