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A.2 · 2 · A.2 Forces and momentum · Newton’s laws, momentum

Newton's second law

The law of acceleration: force is the rate of change of momentum.

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Hook

A footballer’s kick and a gentle tap can send the ball in the same direction. What is different about the push?

Newton’s second law
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Name, words, maths

Newton's second law
1What it is called
Law of acceleration
links force, momentum and acceleration
2In words

“The rate of change of momentum is directly proportional to the net external force.”

3In maths
  1. Fnet,ext ∝ Δp / t
  2. Fnet,ext = Δp / t = (pf − pi) / t
  3. = (mfvf − mivi) / t
  4. = m(vf − vi) / t (mass constant)
  5. Fnet,ext = ma
in SI units the constant of proportionality is 1
Check 1 of 3

The unit N s is equivalent to…

Check 2 of 3

The gradient of a momentum–time graph gives…

Check 3 of 3

A 2.0 kg trolley’s velocity changes from 1.0 m s⁻¹ to 5.0 m s⁻¹ in 4.0 s. The net force is…

Apply

A friend says "F = ma is the whole second law". Explain what the law says in terms of momentum, and when F = ma can be used.

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Remember earlier lessons
From lesson A.2 · 1

If F_net = 0, then…

From lesson 0.6

36 km/h in m s⁻¹ is…

Summary card

Key points

  • • F_net,ext = Δp / t: net force is the rate of change of momentum.
  • • p = mv is a vector, unit kg m s⁻¹ = N s.
  • • For constant mass, F = ma.
  • • The gradient of a p–t graph is the net force.

Formulas

  • p = mv
  • Fnet,ext = Δp / t
  • F = ma (constant mass)

Key terms

Momentum
:
mass × velocity, a vector
Newton second law
:
net external force = rate of change of momentum

Common errors

  • • Using F = ma when the mass changes.
  • • Forgetting that momentum has a direction.
Checks solved: 0 of 3