AshPhys

Understanding motion

AshPhys · Revision cheat sheet
AS Level9702 AS Ch.6Chapter 6: MomentumLesson 6.7Sections 6.7

Goal: Link Newton’s three laws to momentum, and explain conservation of momentum with the third law.

force

01The big picture

First law: an object stays at rest or at constant velocity unless a resultant force acts. Second law: the resultant force equals the rate of change of momentum. Third law: when A pushes on B, B pushes on A with an equal and opposite force of the same type.

In a collision the two forces of a third-law pair act for the same time, so the two changes in momentum are equal and opposite. That is why the total momentum is conserved.

Third-law pair [paraphrase]
Equal, opposite forces of the same type, acting on two different objects.
Fig. 1 · A third-law pair
A third-law pairTwo skaters, A of 60 kg on the left and B of 80 kg on the right, are in contact. A force of 120 N on A points left and an equal force of 120 N on B points right.A60 kgB80 kgFBAFABcontact
Each skater pushes the other: 120 N on each, in opposite directions, for the same time.

02Key equations

Second law
F=ΔpΔtF = \frac{\Delta p}{\Delta t}
Third law
FAB=−FBAF_\mathrm{AB} = -F_\mathrm{BA}
So momentum is conserved
ΔpA=−ΔpB\Delta p_\mathrm{A} = -\Delta p_\mathrm{B}
Symbols and units
  • FABF_\mathrm{AB}force on A by BN\mathrm{N}
  • Δp\Delta pchange in momentumkg m s−1\mathrm{kg\,m\,s^{-1}}

03Sample problems with solutions

Sample 1 · Skaters push apart
Skaters A (60 kg) and B (80 kg) stand at rest and push apart with a force of 120 N for 0.50 s (Fig. 1). Find each skater’s velocity and their total momentum.

  1. Equal and opposite forces for the same time:

    Δp=F Δt=120×0.50=60 kg m s−1 each\Delta p = F\,\Delta t = 120 \times 0.50 = 60\ \mathrm{kg\,m\,s^{-1}} \text{ each}

  2. Velocities (A to the left, negative):

    vA=−6060=−1.0 m s−1,vB=6080=0.75 m s−1v_\mathrm{A} = -\frac{60}{60} = -1.0\ \mathrm{m\,s^{-1}}, \quad v_\mathrm{B} = \frac{60}{80} = 0.75\ \mathrm{m\,s^{-1}}
Answer: A: 1.0 m s⁻¹ left; B: 0.75 m s⁻¹ right; total momentum still zero

04Practice problems

  1. P1
    State Newton’s first law.
    Final answerAt rest or constant velocity unless a resultant force acts
    Answer: At rest or constant velocity unless a resultant force acts
  2. P2
    The Earth pulls a book down. What is the third-law partner of this force?
    Final answerThe book’s gravitational pull on the Earth, upwards
    Answer: The book’s gravitational pull on the Earth, upwards
  3. P3
    A rocket ejects 50 kg of gas per second at 2000 m s⁻¹. Find the thrust.
    Final answer1.0 × 10⁵ N
    Answer: 1.0 × 10⁵ N
  4. P4
    Why are a book’s weight and the table’s push on it not a third-law pair?
    Final answerThey act on the same object and are different types
    Answer: They act on the same object and are different types

05Other useful information

Common mistakes

  • ✗ Wrong: Third-law forces cancel out.

    ✓ Right: They act on different objects, so they never cancel.

Exam tips

  • For a third-law pair, swap the names: “force of A on B” ↔ “force of B on A”.

What the syllabus asks

  • 9702 topic 3: Newton’s laws of motion; force and momentum. Coursebook 6.7.

Explore: Practice questions for this lesson