5.2 Gravitational potential energy and kinetic energy

For a near-Earth height change ∆h, work done against gravity is ∆E_P=mg∆h. Raising an object transfers energy to its gravitational potential store.

Use the vertical height change, not the length of a sloping path, when g is uniform. A downward move reverses the sign of the store change.

Lifting 2.0 kg through 3.0 m at g=9.8 m s⁻² increases gravitational potential energy by 58.8 J.

The energy change depends on height difference, not route length; friction would add a separate thermal transfer.

In a uniform field, the change in gravitational potential energy is ∆E_P=mg∆h, with g treated as constant over the height interval.

Define the reference level and keep the sign of ∆h consistent. Only differences in potential energy affect energy conservation calculations.

A 0.50 kg mass lowered 4.0 m has ∆E_P=−19.6 J relative to its starting level; that energy can become kinetic or thermal.

Zero potential at the floor is a choice, not a physical claim that the object has no energy anywhere else.

The constant-acceleration equations give links between u, v, a, s and t; kinetic energy is E_K=½mv² and changes when the net work changes speed.

Check that acceleration is constant before selecting an SUVAT equation, then use the signed velocity and the correct mass in the energy calculation.

An object accelerating from rest at 2.0 m s⁻² for 3.0 s reaches 6.0 m s⁻¹, so its kinetic energy is 18m joules for mass m.

SUVAT is not valid for arbitrary changing acceleration, and kinetic energy depends on speed squared, not velocity sign.

The kinetic-energy store of a mass m moving at speed v is E_K=½mv². It is a scalar and is never negative.

Use speed magnitude and consistent units; doubling speed quadruples kinetic energy, while doubling mass doubles it.

A 4.0 kg trolley moving at 3.0 m s⁻¹ has kinetic energy 18 J.

Kinetic energy does not carry the direction sign of momentum, and stopping does not destroy it—it transfers it to other stores.