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Dynamics

Force as the rate of change of momentum

  • 3 things to know
  • Component 1

Overview

Newton's second law in terms of momentum and terms of momentum why an air bag protects a driver.

What you need to know

Answer each one before you reveal it.

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Key term

Write the equation linking force, time and change of momentum, defining each symbol with its unit.

Key term

Show that F = ma follows from the statement that force is the rate of change of momentum, when the mass is constant.

Key term

Explain why a car's crumple zone reduces the force on the occupants in a crash.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State Newton's second law in terms of momentum.

    Model answer

    The resultant force on a body is equal to the rate of change of its momentum, and the change occurs in the direction of that force.

  2. 2

    Write the equation linking force, time and change of momentum, defining each symbol with its unit.

    Model answer

    The equation is Ft = Δp, where F is the constant resultant force in N, t is the time for which it acts in s and Δp is the change of momentum in kg m s⁻¹.

  3. 3

    Show that F = ma follows from the statement that force is the rate of change of momentum, when the mass is constant.

    Model answer

    The rate of change of mv with mass constant is m multiplied by the rate of change of v, and the rate of change of velocity is the acceleration, so F = ma.

  4. 4

    Define impulse.

    Model answer

    Impulse is the product of a force and the time for which it acts, and it equals the change of momentum produced.

  5. 5

    State the unit of impulse and show it is equivalent to that of momentum.

    Model answer

    Impulse is measured in N s, and since 1 N = 1 kg m s⁻², N s is the same as kg m s⁻¹.

  6. 6

    How is the impulse of a varying force obtained from a force-time graph?

    Model answer

    The impulse is the area between the force-time graph and the time axis.

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