## Impulse and Momentum Ranking Task

Six automobiles are initially traveling at the indicated velocities. The automobiles have different masses and velocities. The drivers step on the brakes and all automobiles are brought to rest.

A) Rank these automobiles based on their momentum before the brakes are applied, from largest to smallest.

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B) Rank these automobiles based on the magnitude of the impulse needed to stop them, from largest to smallest.

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“You know the impulse needed to stop the cars. However, this impulse could be a very large force exerted over a fraction of a second, a very small force exerted over several minutes, or any situation in between, so long as the force multiplied by the time gives the proper impulse. You must know the time intervals over which the stopping forces are exerted to determine the magnitudes of the stopping forces from the impulses.”

## Answer ( 1 )

Automobile 2: 2000kg, 5m/s → p = 10 000 kg·m/s

Automobile 3: 500kg, 20m/s → p = 10 000 kg·m/s

Automobile 4: 1000kg, 20m/s → p = 20 000 kg·m/s

Automobile 5: 1000kg, 10m/s → p = 10 000 kg·m/s

Automobile 6: 4000kg, 5m/s → p = 20 000 kg·m/s

A: 6,4 (tied); 5,3,2 (tied); 1

B: Same. Impulse = change in momentum.

C: We can’t say anything about the forces required until we know about the timeframes required for each one to stop. If they all stopped in the same time interval, then the rankings are the same.