Energy Conservation

2026 Syllabus Objectives

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

  1. Understand the concept of work, and recall and use work done = force × displacement in the direction of the force
  2. Recall and apply the principle of conservation of energy
  3. Recall and understand that the efficiency of a system is the ratio of useful energy output from the system to the total energy input
  4. Use the concept of efficiency to solve problems
  5. Define power as work done per unit time
  6. Solve problems using P = W/t
  7. Derive P = Fv and use it to solve problems

1. Work and Energy

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What is Work?

In everyday language, "work" means any effort or activity. But in physics, work has a very specific meaning:

Work is done when a force causes an object to move (displace) in the direction of that force.

For example:

  • When you push a shopping cart and it moves forward, you are doing work
  • When you lift a book from the floor to a shelf, you are doing work against gravity
  • When you hold a heavy bag without moving, you are NOT doing work (even though you feel tired!) because there's no displacement

The Work Formula

The basic formula for work is:

W = F × s

Where:

  • W = work done (measured in joules, J)
  • F = force applied (measured in newtons, N)
  • s = displacement in the direction of the force (measured in metres, m)

Important: 1 joule (J) is the same as 1 newton metre (N m)

Key Points About Work

Work is a scalar quantity - this means it has size (magnitude) but no direction. You don't say "10 J to the left" - you just say "10 J".

Work done equals energy transferred. When work is done, energy moves from one place to another or changes from one form to another.

Work When Force is at an Angle

Sometimes the force isn't in the same direction as the movement. For example, if you pull a suitcase at an angle, only part of your pulling force actually moves the suitcase forward.

When the force is at an angle θ (theta) to the direction of movement, we use:

W = F × s × cos θ

Or you can think of it as:

W = (F cos θ) × s

Where F cos θ is the component (part) of the force that acts in the direction of movement.

Special case: If the force is perpendicular (at 90°) to the movement, then cos 90° = 0, so W = 0. No work is done! For example, when you carry a bag horizontally while walking, you're applying an upward force but moving horizontally - the force does no work in moving you forward.

Example Calculation

Question: A person pushes a box with a force of 50 N. The box moves 3 m in the direction of the push. How much work is done?

Solution:

  • F = 50 N
  • s = 3 m
  • W = F × s = 50 × 3 = 150 J

Question: A block of weight 100 N is moved 5 m up a slope. The vertical height gained is 3 m. How much work is done against gravity?

Solution:

  • Force (weight) = 100 N (acting vertically downward)
  • Displacement in direction of weight = 3 m (vertical height)
  • W = F × s = 100 × 3 = 300 J

Notice: We use the displacement in the direction of the force (vertical), not the total distance along the slope.

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