7th Sep '25

Impulse and Your Safety

When a force acts on a body that is moving, or able to move, a change in momentum occurs, this change in momentum is known as an impulse. From Newton's second law we can derive that:

Impulse = change in momentum = Force × Time taken for the change
(kilogram metre per second)   (kilogram metre per second)   (Newtons)   (seconds)
(kg(m/s))   (kg(m/s))   (N)   (s)

The higher the rate of change of momentum, the the force required and therefore the chance of injury.

Safety features such as:

are all designed to reduce the force applied to the person, by reducing the rate of change of momentum. There are two ways to do this:

  • Reduce the change in momentum
  • increase the time taken to change the momentum.

In practice the change of momentum is normally fixed, but travelling more will reduce your momentum, as will reducing your . Instead safety features aim to the time taken to slow them down normally by increasing the time they are in contact with you and deforming around you.

Example:

Two men are traveling at 20 m/s (approx 45 mph) in a car with only a drivers air bag. They hit a tree and the car comes to an abrupt halt. Both their heads have a mass of 5 kg. The passengers head hits the hard dashboard and is brought to a stand still in 0.01 seconds, while the drivers head impacts the relatively soft air bag and is slowed to stationary over 0.1 seconds.

Answer to 0 d.p.

  1. What is the momentum of each man's head before the crash?
    kg m/s
  2. What is the momentum of each man's head after the collosion?
    kg m/s
  3. What is change in momentum of each man's head?
    kg m/s
  4. What is the force applied to the passenger's head?
    N
  5. What is the force applied to the driver's head?
    N

Note: In addition to reducing the force, soft objects also increase the suface area over which the force is applied, reducing the pressure. The human forehead can withstand approximately 5000 N of blunt force.

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Use of Air Bags in Cars