Use the impulse momentum theorem and the following data table to answer the next three questions. Answer the following in your notes. 

Impulse Momentum Theory
FΔt = m (v_f - v_i)

1. A 5500 kg car stops in 45 seconds.  Its initial velocity is 15 m/s.  What force is required to make this happen?

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   F = m (v_f - v_i) / Δt

   F = (5500 kg) (0 - 15 m/s) / 45 s
   F = -1800N

   In this case, negative force means the car is stopping since the force acts against forward motion.  Momentum is a vector quantity.

   

2. Calculate the impulse of the stopping car.

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   Impulse:

   J = FΔt
   J = (1800 N) (45 s)
   J = 82,000 N·s

   Also,

   J = m (v_f - v_i)
   J = (5500 kg) (0 - 15 m/s)
   J = 82,000 kg·m/s

   In this case, negative force means the car is stopping since the force acts against forward motion.  Momentum is a vector quantity.

   

3. What happens to force if your time doubles? (Initial velocity stays the same)

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   It should become half the original value.

   F = (5500 kg) (0 - 15 m/s) / 90 s
   F = -900 N

   Just as predicted!

   In this case, negative force means the car is stopping since the force acts against forward motion.  Momentum is a vector quantity.

   

Let’s take a look at how engineers manipulate stopping time to control the amount of force required in various real-world situations:

1. How do firemen catch people who jump from high buildings?

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   Firemen use a net or airbag to increase the stopping time and reduce the force. Increasing the stopping time reduces the force required.

2. Engineers design car bumpers to “collapse” in a car crash to decrease the force acting.  How does this work?

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   If you increase stopping time, you decrease force.

3. Why do cars have airbags that deploy in a crash?

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   If you increase stopping time, you decrease force.

4. How do the braking system problems of cars that have been recalled for safety issues apply to the impulse momentum theorem?

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   If the brakes can't provide enough force, the stopping time will be longer.