Gravitational Energy and Mechanical Conservation
Near Earth, U_g=mgy relative to a chosen datum; when only conservative forces do work, the sum of kinetic and potential energies remains constant between states.
Why this shows up in the exam
Falling and rising bodies · Pendulums and smooth tracks · Projectile energy comparisons
Learn the idea
Gravity trades kinetic energy with gravitational potential energy. As an object rises, kinetic energy can become gravitational potential energy; on descent the exchange reverses if no dissipative work intervenes.
🧠 Memory hook: Choose two heights; energy handles the speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U_g = mgy — near-Earth gravitational potential energy
- K_i+U_i = K_f+U_f — mechanical-energy conservation
- v_f² = v_i²+2g(y_i-y_f) — gravity-only speed relation
How to approach it
- 1Choose a potential-energy datum
- 2Mark initial and final heights and speeds
- 3Check nonconservative work before conserving K+U
Common slip-ups that cost marks
- •Treating the zero of U as physical
- •Conserving mechanical energy through friction or collision
- •Using path length instead of vertical height
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg body speeds up from 3 m/s to 7 m/s. What net work is done on it?
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.