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5.9.4Forces

Force and Momentum

5 min read 5 parts Lesson 66 of 67 Unit quiz

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Section 1 of 5Momentum and Force

Momentum is mass multiplied by velocity, and a resultant force changes an object's momentum at a rate that depends on the size of the force.

Momentum
  • Momentum Momentum equals mass multiplied by velocity, and it is a vector quantity measured in kilogram metres per second.
Newton's second law
  • Newton's second law The resultant force on an object equals its rate of change of momentum: F = Δp ÷ Δt.
    What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Change in momentum
  • Change in momentum Δp is the final momentum minus the initial momentum, and it takes the direction of motion into account.
Force and time
  • Force and time Force multiplied by the time it acts equals the change in momentum, so F × t = Δp.

Section 2 of 5Crash Safety and Stopping Time

In a collision the change in momentum is fixed, so safety devices work by changing the time.

1
In a collision a passenger's momentum changes from a value to zero, so the change in momentum is the same whatever safety device is used.
2
Crumple zones increase the time over which the car slows down, which reduces the force for the same change in momentum.
3
Airbags spread the stopping force over a longer time, which reduces the force on the head and chest.
4
Seatbelts stretch slightly and hold passengers back, lengthening the stopping time compared with hitting a hard dashboard.
Time of collisionChange in momentumForce on the person
Short, such as hitting a hard surfaceSameLarge
Long, such as an airbag or crumple zoneSameSmaller

Section 3 of 5Using the Relationship

Using the Relationship
Calculation
  • Calculation Rearranging F = Δp ÷ Δt gives the force directly once the change in momentum and the time are known.
Direction
  • Direction A stopping force acts opposite to the direction of motion, so it is given a negative sign in calculations.
Safety design
  • Safety design Designers aim to increase the stopping time, because the momentum change cannot be removed.

Section 4 of 5Worked Example

Question

  • A 1000 kg car slows from 20 m/s to 0 m/s in 4 s.
  • Calculate the change in momentum and the average force acting on the car.

  1. Initial momentum = 1000 × 20 = 20 000 kg m/s
  2. Final momentum = 1000 × 0 = 0 kg m/s
  3. Change in momentum = 0 − 20 000 = −20 000 kg m/s
  4. Force = change in momentum ÷ time = −20 000 ÷ 4 = −5000 N

Answer The average force is 5000 N, acting opposite to the direction of motion.

Section 5 of 5Exam Checklist & Tips

5.9.4 – Key Points for the Exam

  • Momentum The product of an object's mass and velocity, which is a vector quantity.
  • Resultant force The overall force on an object after all the forces acting on it are combined.
  • Rate of change of momentum The change in momentum divided by the time taken for that change.
  • Crumple zone A part of a car designed to deform in a collision, which increases the stopping time.
  • Vector A quantity that has both a magnitude and a direction, such as velocity.

Common Mistakes

  • Forgetting to subtract the initial momentum, or using speed rather than velocity, so the direction is lost.
  • Saying that an airbag reduces the change in momentum;
    • it reduces the force by lengthening the time of the collision.
  • Using grams instead of kilograms for mass, which gives a momentum that is 1000 times too small.
  • Forgetting that a stopping force acts opposite to the motion, so its sign must be negative in calculations.
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