Forces, components and equilibrium
Resolve forces, balance moments and distinguish force from torque.
Work, energy and momentum questions
Calculate work and power, conserve signed momentum and compare collision energies.
Practise
Work at an angleA constant 32 N force pulls an object through a horizontal displacement of 7 m. The force is 30° above the displacement direction. Find the work done by this force. Give your answer to 3 significant figures.
Larger diagram
Treat the given values as exact unless an uncertainty is stated.
Hint
Only the force component parallel to displacement does work: W = Fs cos θ.
Worked solution
- W = 32 × 7 × cos(30°) J.
- Answer: 194 J (3 significant figures).
Question type: Work at an angle
Report a problem
Choose the system before conserving anything
Momentum is conserved when external impulse on the chosen system is negligible. Keep velocity signs in one-dimensional collisions. Objects that stick share a final velocity, but their total kinetic energy usually decreases. Total energy is still conserved; some becomes internal energy.
Work and power
A constant force does work Fs cos θ, using the angle between force and displacement. Useful lifting power is mgh/t. At steady speed against a resistive force F, the required mechanical power is Fv. Efficiency compares useful output with total input.
Impulse has a direction
Impulse = m(v − u). A rebound changes the velocity sign. Average resultant force is impulse divided by contact time; it is not necessarily the peak force. This resource covers selected constant-force energy calculations, one-dimensional sticking collisions and impulse, not a complete mechanics course.
A-level relevance
AQA 7408: 3.4.1.6–8 (selected); OCR A H556: 3.3.1–3; 3.5.1–2 (selected). Tasks cover the selected skills listed above.
AQA mechanics and materials specification · OCR A specification