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Newton's Laws of Motion

Newton's second law and F = ma

  • 3 things to know
  • Unit AS 1

Overview

Recall questions on the statement of the second law and the equation with its units, the definition of the newton, why it is the resultant force that matters, how W = mg follows, why mass is fixed but weight is not, and worked problems on a car, a struck ball, a parachutist and uniform braking.

What you need to know

Answer each one before you reveal it.

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Key term

State the equation F = ma, defining each symbol with its unit and stating the condition under which it applies.

Key term

Explain how the equation W = mg follows from Newton's second law.

Numbers

A car of mass 800 kg has a driving force of 2400 N and experiences 900 N of resistance. Calculate its acceleration.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State Newton's second law of motion for a body of constant mass.

    Model answer

    The acceleration of a body of constant mass is directly proportional to the resultant force acting on it and takes place in the direction of that force.

  2. 2

    State the equation F = ma, defining each symbol with its unit and stating the condition under which it applies.

    Model answer

    The equation is F = ma, where F is the resultant force in newtons (N), m is the mass in kilograms (kg) and a is the acceleration in metres per second squared (m s⁻²); it applies when the mass of the body is constant.

  3. 3

    Define the newton.

    Model answer

    One newton is the resultant force that gives a mass of one kilogram an acceleration of one metre per second squared.

  4. 4

    State the relationship between the direction of the resultant force and the direction of the acceleration.

    Model answer

    The acceleration is always in the same direction as the resultant force, whatever direction the body happens to be moving in at the time.

  5. 5

    Explain how the equation W = mg follows from Newton's second law.

    Model answer

    A body falling freely has only its weight acting on it and accelerates at g, so putting F = W and a = g into F = ma gives W = mg, where W is the weight in newtons, m the mass in kilograms and g the acceleration of free fall in m s⁻².

  6. 6

    Explain why the mass of an object is the same everywhere but its weight is not.

    Model answer

    Mass is the quantity of matter in the object and does not depend on location, whereas weight is mg and so changes wherever the gravitational field strength g differs, such as on the Moon.

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