Mechanics
Work, Energy and Power
5th Year · 6th Year (Leaving Cert)
- ✓By the end of this lesson students will be able to define work done and calculate it using W = Fs cos θ.
- ✓By the end of this lesson students will be able to define and calculate kinetic energy (KE = ½mv²) and gravitational potential energy (GPE = mgh).
- ✓By the end of this lesson students will be able to state and apply the Principle of Conservation of Mechanical Energy.
- ✓By the end of this lesson students will be able to define power and calculate it using P = W/t or P = Fv.
- ✓By the end of this lesson students will be able to solve problems involving work, energy, and power in various physical contexts.
Key concepts
Work is done when a force causes a displacement of an object in the direction of the force. It is a scalar quantity, meaning it has magnitude but no direction. The unit of work is the Joule (J).
Kinetic energy is the energy an object possesses due to its motion. It is a scalar quantity. The unit of kinetic energy is the Joule (J).
Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is relative to a chosen reference level (e.g., the ground). It is a scalar quantity. The unit of gravitational potential energy is the Joule (J).
In an ideal system where only conservative forces (such as gravity) do work, the total mechanical energy (the sum of kinetic energy and gravitational potential energy) remains constant. This principle assumes that non-conservative forces like friction or air resistance are negligible.
Power is the rate at which work is done or energy is transferred. It is a scalar quantity. The unit of power is the Watt (W).
Key facts to remember
- 1Work, kinetic energy, and potential energy are all scalar quantities measured in Joules (J).
- 2Power is the rate at which work is done or energy is transferred, measured in Watts (W).
- 31 Watt is equivalent to 1 Joule per second (1 W = 1 J s⁻¹).
- 4The angle θ in the work formula W = Fs cos θ is the angle between the force vector and the displacement vector.
- 5Gravitational potential energy is always measured relative to a chosen reference level.
- 6The Principle of Conservation of Mechanical Energy is valid only when non-conservative forces (like friction or air resistance) are negligible or not doing work.
- 7Kinetic energy depends on the square of the speed, meaning doubling the speed quadruples the kinetic energy.
- 8The formula P = Fv is applicable when the force is constant and in the direction of constant velocity.
Worked examples
Example 1
A student pushes a box with a force of 50 N at an angle of 30° below the horizontal. If the box moves 4 m horizontally, calculate the work done by the student.
Answer
173.2 J
Only the component of the force in the direction of displacement does work.
Example 2
A 2 kg ball is dropped from a height of 10 m. Calculate its speed just before it hits the ground, assuming no air resistance. (Take g = 9.8 m s⁻²).
Answer
14 m/s
Notice that the mass of the ball cancels out, meaning the final speed is independent of the mass.
Example 3
A car engine develops 40 kW of power while moving at a constant speed of 20 m/s. Calculate the force exerted by the engine.
Answer
2,000 N
Ensure all units are in their base SI forms (Watts, metres per second) before calculation.
Common mistakes
- ✗Using the wrong angle (e.g., angle with the vertical instead of the horizontal) or forgetting the 'cos θ' term in the work formula.
- ✗Not converting units correctly, especially kilowatts to Watts or grams to kilograms.
- ✗Confusing the conditions for the Principle of Conservation of Mechanical Energy, applying it when significant non-conservative forces are present.
- ✗Incorrectly identifying the initial and final states or the reference level for potential energy in conservation problems.
- ✗Forgetting that energy and work are scalar quantities, so direction is not considered in their values, only in the force component for work.
Exam tips
- ★Always draw a clear diagram to visualise the forces, displacements, and heights involved in a problem.
- ★Clearly state the formula or principle you are using at the beginning of each calculation step.
- ★Pay meticulous attention to units and ensure all quantities are in their standard SI units (kg, m, s, N, J, W) before performing calculations.
- ★For conservation of energy problems, explicitly define your initial and final points and your zero potential energy reference level.
- ★Show all steps in your calculations, even if they seem simple, to ensure you receive full marks for method.
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