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Space, Time and Motion

Work, energy and its conservation

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on work done ΔE = FΔs and FΔs cos θ, forces at right angles to motion, the joule, conservation of energy, kinetic energy Eₖ = ½mv² and gravitational potential energy mgh with calculations, the landing speed v = √(2gh), why doubling speed quadruples kinetic energy, braking, and energy lost to friction.

What you need to know

Answer each one before you reveal it.

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Key term

Why does a car's kinetic energy quadruple when its speed doubles, where does the energy go during braking, and why does friction waste energy?

Key term

Define the work done by a force.

Key term

State the equation for work done when the force is parallel to the displacement.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define the work done by a force.

    Model answer

    Work done is the product of the force and the distance moved in the direction of that force.

  2. 2

    State the equation for work done when the force is parallel to the displacement.

    Model answer

    The work done is ΔE = FΔs.

  3. 3

    State the equation for work done when the displacement is at an angle θ to the force.

    Model answer

    The work done is ΔE = FΔs cos θ.

  4. 4

    Why is no work done by a force that acts at right angles to the motion?

    Model answer

    cos 90° is zero, so there is no displacement in the direction of that force and it transfers no energy.

  5. 5

    A crate is dragged 12 m across a floor by a rope pulling with a force of 80 N at 30° to the horizontal. What is the work done by the rope?

    Model answer

    ΔE = FΔs cos θ = 80 × 12 × cos 30° = 8.3 × 10² J.

  6. 6

    Define the joule.

    Model answer

    One joule is the energy transferred when a force of one newton moves its point of application one metre in the direction of the force.

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