AshPhys

Momentum and Newton’s laws of motion

AshPhys · Revision cheat sheet
AS Level9702 AS Ch.6Chapter 6: MomentumLesson 6.6Sections 6.6

Goal: Use force = rate of change of momentum, including for collisions and streams of fluid.

01The big picture

Newton’s second law in its general form: the resultant force on an object equals its rate of change of momentum. For a constant mass, Δp/Δt=m Δv/Δt=ma\Delta p/\Delta t = m\,\Delta v/\Delta t = ma.

Rearranged, FΔt=ΔpF\Delta t = \Delta p: the same change in momentum over a longer time needs a smaller force. That is why crumple zones, airbags and bending your knees on landing protect you.

Force (Newton’s second law) [paraphrase]
The resultant force on an object equals its rate of change of momentum.

02Key equations

Newton’s second law
F=ΔpΔtF = \frac{\Delta p}{\Delta t}
Constant mass
F=maF = ma
Rearranged
F Δt=ΔpF\,\Delta t = \Delta p
Symbols and units
  • FFresultant forceN\mathrm{N}
  • Δp\Delta pchange in momentumkg m s−1\mathrm{kg\,m\,s^{-1}}
  • Δt\Delta ttime takens\mathrm{s}

03Sample problems with solutions

Sample 1 · Hitting a ball
A 0.15 kg ball arrives at a bat at 20 m s⁻¹ and leaves in the opposite direction at 30 m s⁻¹. Contact lasts 0.010 s. Calculate the average force on the ball.

  1. Return direction positive, so u=−20u = -20 m s⁻¹:

    Δp=0.15 (30−(−20))=7.5 kg m s−1\Delta p = 0.15\,(30 - (-20)) = 7.5\ \mathrm{kg\,m\,s^{-1}}

  2. Rate of change of momentum:

    F=7.50.010=750 NF = \frac{7.5}{0.010} = 750\ \mathrm{N}
Answer: 750 N, in the direction the ball leaves
Unit check: kg m s−1s=kg m s−2=N ✓\frac{\mathrm{kg\,m\,s^{-1}}}{\mathrm{s}} = \mathrm{kg\,m\,s^{-2}} = \mathrm{N}\ \checkmark

04Practice problems

  1. P1
    A 1000 kg car goes from rest to 20 m s⁻¹ in 8.0 s. Find the average resultant force.
    Final answer2500 N
    Answer: 2500 N
  2. P2
    A hose sends 2.0 kg of water per second at 15 m s⁻¹ onto a wall, where it stops. Find the force on the wall.
    Final answer30 N
    Answer: 30 N
  3. P3
    A momentum change of 12 kg m s⁻¹ takes 0.040 s. Find the average force.
    Final answer300 N
    Answer: 300 N
  4. P4
    Why do you bend your knees when you land from a jump?
    Final answerLonger stopping time, so a smaller force for the same Δp
    Answer: Longer stopping time, so a smaller force for the same Δp

05Other useful information

Common mistakes

  • ✗ Wrong: Use F=maF = ma for a stream of fluid.

    ✓ Right: Use F=Δp/ΔtF = \Delta p/\Delta t: mass per second × change in velocity.

Exam tips

  • Check units: kg m s⁻¹ per second is kg m s⁻², which is N.

What the syllabus asks

  • 9702 topic 3: define and use force as rate of change of momentum. Coursebook 6.6.

Explore: Practice questions for this lesson