Work and power (A-level only) — AQA A-Level Physics

This topic covers the definitions of work and power and their application to mechanical systems. You will learn that work is the energy transferred when a force moves an object through a distance, and that power is the rate of doing work or transferring energy. These concepts are fundamental to understanding energy conservation, efficiency, and the motion of vehicles and machines.

In AQA A-Level Physics, you must be able to calculate work done by a force at an angle, use the work-energy principle to relate net work to changes in kinetic energy, and apply P = Fv to problems involving constant power. This topic links closely to Newton's laws, energy conservation, and momentum, and is essential for analysing real-world systems such as lifts, pumps, and accelerating vehicles.

• →Work done by a constant force is defined as W = Fs cos(theta), where F is the magnitude of the force, s is the displacement, and theta is the angle between the force and the displacement. Only the component of force in the direction of displacement does work.
• →Power is the rate of doing work or transferring energy: P = W/t. The instantaneous power delivered by a force moving an object at velocity v is P = Fv, where F is the component of force in the direction of motion.
• →The work-energy principle states that the net work done on an object equals its change in kinetic energy: W_net = delta E_k = 0.5mv^2 - 0.5mu^2. This is a powerful tool for solving problems involving forces, distances, and speeds.
• →Efficiency is the ratio of useful output energy or power to total input energy or power, often expressed as a percentage: efficiency = (useful power output / total power input) x 100%.
• →For a vehicle moving at constant speed, the driving force equals the total resistive force, and the power required is P = Fv. At maximum speed, the resultant force is zero, so the driving force equals the resistive force.

• Recalls and applies W = Tθ for work done by a constant torque through an angular displacement.
• Recalls and applies P = Tω for mechanical power in rotational motion.
• Converts angular displacement between degrees and radians correctly when using W = Tθ.
• Explains that frictional torque opposes rotation and must be subtracted from the applied torque to find the net torque.
• Calculates useful work or power by using the net torque after accounting for friction.
• Relates energy lost to friction to heating of components and reduced efficiency of the machine.

• 💡Write down the equation W = Tθ or P = Tω before substituting values, and check that θ is in radians.
• 💡When friction is present, calculate the net torque first, then use it in the work or power equation.
• 💡State clearly whether you are calculating total input work or useful output work, and show how friction affects the result.
• 💡Always show your working clearly, including the formula, substitution, and final answer with correct units. In calculation questions, method marks are awarded for correct use of equations even if the final answer is wrong due to arithmetic errors.
• 💡When a force acts at an angle, draw a diagram and resolve the force into components. State explicitly that you are using the component of force in the direction of motion. This demonstrates understanding and secures full marks.
• 💡For questions involving power and speed, remember that P = Fv applies when the force and velocity are in the same direction. If the force is at an angle, use P = Fv cos(theta). At maximum speed, set resultant force to zero and equate driving force to resistive force.

• Using degrees directly in W = Tθ without converting to radians; the correction is to convert θ to radians before substitution.
• Ignoring frictional torque and using the applied torque as the net torque; the correction is to subtract the frictional torque to find the net torque.
• Confusing torque with force or angular velocity with linear velocity; the correction is to use the rotational definitions T, θ and ω consistently.
• Students often think that if an object is moving, work is being done on it. In fact, work is only done when a force causes a displacement. An object moving at constant velocity on a frictionless surface has no net work done on it.
• Many students confuse power and energy, believing that a more powerful machine does more work. Power is the rate of doing work; a more powerful machine can do the same work in less time, or more work in the same time, but the total energy transferred depends on both power and time.
• Students frequently forget that work is a scalar quantity and can be negative. When the force opposes the displacement (e.g., friction), the work done by that force is negative, representing energy transferred away from the object.

1. 1Start by revising the definitions of work and power, and learn the equations W = Fs cos(theta) and P = W/t = Fv. Make flashcards with the equations and their conditions of use.
2. 2Practice resolving forces at angles and calculating work done by each force. Use past paper questions to become familiar with the style of AQA questions, focusing on showing clear method.
3. 3Work through problems involving the work-energy principle, including those with friction and changes in height. Always draw a diagram and label all forces and displacements.
4. 4Study vehicle motion problems where power is constant, and understand how driving force varies with speed. Practice calculating maximum speed and acceleration at a given speed.
5. 5Complete a timed past paper section on work and power, then review your answers against the mark scheme. Identify any recurring mistakes and revisit those concepts.

• 📋Calculation of work done by a force at an angle: Resolve the force into components, use W = Fs cos(theta), and ensure the correct component is used. Watch for forces that do no work (perpendicular to motion).
• 📋Application of the work-energy principle: Calculate net work done and equate to change in kinetic energy. Often involves friction and multiple forces; draw a free-body diagram and consider the sign of each work term.
• 📋Power and efficiency calculations: Use P = W/t or P = Fv, and efficiency = useful output / total input. Be prepared to convert between power, energy, and time, and to calculate mass flow rates in pump problems.
• 📋Graphical analysis: Interpret force-displacement graphs (area under graph = work done) and power-time graphs (area under graph = energy transferred). Calculate gradients where appropriate.