Momentum-Impulse Theorem

Momentum-Impulse Theorem

Mr. Hawboldt

Momentum-Impulse Theorem

• states that the impulse done on a system is equal to the change in momentum of that system

• in equation form this looks like $J=\Delta p$   

•  $\Delta p=p_f-p_{i_{ }}$  

• combine the two equations to get $J=p_f-p_i$  

• knowing that  $J=F\times t$  , you can go one step further and say  $F\times t=p_f-p_i$  

Side Note about Impulse

• There are now TWO ways to find impulse

• 1. Force x time

• 2. change in momentum (final minus initial)

• This also means that you can set these two equations equal to each other to say that

• Force x time = final momentum - initial momentum

Momentum Impulse Theorem

• This is exactly like the Work-Energy Theorem from last unit

• Doing Work added Energy to a system

• Replace the word "Work" with 'Impulse"

• Replace the word "Energy" with "Momentum"

• Doing Impulse adds Momentum to a system

Multiple Choice

A 20 Newton force is exerted for 2 seconds on an object that initially has 50 kg * m/s of momentum. How much momentum does the object have after the force is exerted?

• 20 kg * m/s

• 40 kg * m/s

• 50 kg * m/s

• 90 kg * m/s

Applications

• Safety devices in cars use the Momentum-Impulse Theorem to keep you safe in the event of a crash.

• Example: You (100 kg) go from 30 m/s to 0

• Your change in momentum is (0 x 100 - 30 x 100) = -3000 kg * m/s

• This will be true regardless of safety features on your car. Your impulse is fixed.

• What CAN change are the components of impulse (force and time)

• They still must multiply to equal -3000

Multiple Choice

The change in momentum is -3000 kg * m/s during the car crash. This means the impulse done to you is 3000 N*s. Let's say the crash takes 0.5 seconds. How much force is exerted in this case?

• -3000 N

• -1500 N

• -6000 N

• -4500 N

Multiple Choice

The change in momentum (and impulse) are still 3000 N*s. Safety devices (like airbags, seatbelts and crumple zones) cause crashes to take more time to occur. Now the crash takes 1.5 seconds. How much force is exerted on you in this case?

• 3000 N

• 15000 N

• 2000 N

• 6000 N

Summary

• by increasing the time of impact, you decrease the force

• force is the thing that hurts you so decreasing it lowers your chances of being hurt during an impact

• EGG DEMO