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
Objects sticking togetherOn a horizontal track, a 9 kg trolley at +10 m s⁻¹ collides with a 3 kg trolley at -3 m s⁻¹. They stick together. External horizontal impulse is negligible. Find their signed common velocity. Give your answer to 3 significant figures.
Larger diagram
Treat the given values as exact unless an uncertainty is stated.
Hint
Conserve signed momentum to find the common velocity. Kinetic energy is not conserved when the trolleys stick.
Worked solution
- (9+3)v = 9 × 10 + 3 × (-3).
- v = (81)/(12) m s⁻¹.
- Answer: 6.75 m s⁻¹ (3 significant figures).
Question type: Objects sticking together
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