Energy, Work and Power

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand the concept of work done by a force, and calculate the work done by a constant force when its point of application moves a distance not necessarily parallel to the force (using W = Fd cos θ)

  2. Understand the concepts of gravitational potential energy and kinetic energy, and use the appropriate formulas

  3. Understand and use the relationship between the change in energy of a system and the work done by external forces, and use the principle of conservation of energy (including cases with curved paths)

  4. Use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity (P = Fv)

  5. Solve problems involving the instantaneous acceleration of vehicles moving on hills against resistance

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1. Work Done by a Force

What is work?

In everyday language, "work" means effort or activity. But in physics, work has a very specific meaning: work is done when a force moves an object in the direction of that force.

This is important: if you push against a wall as hard as you can but the wall doesn't move, you haven't done any work in the physics sense (even though you're tired!). For work to be done, there must be both a force AND movement.

Calculating work when force and movement are in the same direction

When a force acts in the same direction as the movement, the formula is simple:

W = F × d

Where:

  • W = work done (measured in Joules, J)
  • F = force applied (measured in Newtons, N)
  • d = distance moved in the direction of the force (measured in metres, m)

Example: If you push a box with a force of 20 N and it moves 5 m in the direction you're pushing, the work done is: W = 20 × 5 = 100 J

Calculating work when force acts at an angle

Often, a force doesn't act exactly in the direction of movement. For example, when you pull a suitcase, you pull at an angle upward and forward, but the suitcase only moves forward along the ground.

In this case, only the component of the force in the direction of movement does work. We use:

W = Fd cos θ

Where:

  • θ (theta) = the angle between the force and the direction of movement
  • cos θ = the cosine of that angle (a number you can find using your calculator)

The term "F cos θ" gives us the component of the force that acts in the direction of movement.

Example: You pull a suitcase with a force of 30 N at an angle of 30° above the horizontal. The suitcase moves 10 m horizontally. The work done is: W = 30 × 10 × cos 30° = 30 × 10 × 0.866 = 259.8 J

Important points about work:

  • If there's no movement (d = 0), then no work is done, even if you're applying a force
  • If the starting point and ending point are the same (like going in a circle and coming back), the net displacement is zero, so the net work done is zero
  • Force and displacement must be measured in the same direction or you must use the angle formula
  • The unit of work is the Joule (J), which is the same as Newton-metres (N·m)

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