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Energy Concepts

The work–energy relationship

  • 3 things to know
  • AS Unit 1

Overview

Recall questions on The work–energy relationship.

What you need to know

Answer each one before you reveal it.

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Key term

Define each symbol in the relationship Fx = ½mv² − ½mu², giving its unit.

Key term

Write down the relationship between the work done by the resultant force on a body and the change in the body's kinetic energy.

Key term

What does it mean for the work done on a body to be negative?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Write down the relationship between the work done by the resultant force on a body and the change in the body's kinetic energy.

    Model answer

    Fx = ½mv² − ½mu², so the work done by the resultant force is equal to the gain in kinetic energy.

  2. 2

    Define each symbol in the relationship Fx = ½mv² − ½mu², giving its unit.

    Model answer

    F is the resultant force in newtons, x the distance moved in metres, m the mass in kilograms, u the initial speed and v the final speed, both in m s⁻¹.

  3. 3

    Show that the work–energy relationship follows from F = ma together with v² = u² + 2ax.

    Model answer

    Rearranging the equation of motion gives a = (v² − u²)/2x, and substituting that into F = ma gives F = m(v² − u²)/2x, so Fx = ½mv² − ½mu².

  4. 4

    What does it mean for the work done on a body to be negative?

    Model answer

    The force has a component opposing the motion, so energy is taken from the body and its kinetic energy falls.

  5. 5

    A 1200 kg car moving at 20 m s⁻¹ comes to a halt over a braking distance of 40 m. Use energy to find the mean braking force.

    Model answer

    The kinetic energy to be removed is ½ × 1200 × 20² = 2.4 × 10⁵ J, and dividing that by 40 m gives a mean braking force of 6.0 × 10³ N.

  6. 6

    Why does doubling the speed of a car quadruple its braking distance for the same braking force?

    Model answer

    The kinetic energy to be removed is proportional to the square of the speed, and the distance is that energy divided by a fixed braking force.

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