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Energy Concepts

Kinetic energy and the work-energy relationship

  • 3 things to know
  • Component 1

Overview

Recall questions on the kinetic energy equation, the fourfold change when speed doubles, the relationship Fx = ½mv² − ½mu² and its derivation, what a negative value indicates, and worked problems on accelerating and braking.

What you need to know

Answer each one before you reveal it.

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Key term

State the equation for kinetic energy, defining every symbol and its unit.

Key term

State the work-energy relationship for a constant force acting along the line of motion, defining each symbol.

Key term

Define kinetic energy.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define kinetic energy.

    Model answer

    Kinetic energy is the energy a body possesses because of its motion.

  2. 2

    State the equation for kinetic energy, defining every symbol and its unit.

    Model answer

    The equation is Eₖ = ½mv², where Eₖ is the kinetic energy in J, m is the mass in kg and v is the speed in m s⁻¹.

  3. 3

    State the work-energy relationship for a constant force acting along the line of motion, defining each symbol.

    Model answer

    The relationship is Fx = ½mv² − ½mu², where F is the resultant force in N, x is the distance moved in m, m is the mass in kg, u is the initial speed and v the final speed in m s⁻¹.

  4. 4

    Derive the work-energy relationship from an equation of motion and Newton's second law.

    Model answer

    The equation v² = u² + 2ax rearranges to ax = ½(v² − u²), and multiplying through by m and using F = ma gives Fx = ½mv² − ½mu².

  5. 5

    A car of mass 1200 kg travels at 25.0 m s⁻¹. Calculate its kinetic energy.

    Model answer

    The kinetic energy is ½ × 1200 × 25.0² = 3.75 × 10⁵ J. Rearranging gives v = √(2 × 375000/1200) = 25.0 m s⁻¹.

  6. 6

    By what factor does the kinetic energy of a car change when its speed is doubled?

    Model answer

    Kinetic energy is proportional to the square of the speed, so doubling the speed multiplies the kinetic energy by four.

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