Potential energy in a uniform gravitational field

Repair the common break

Common misconception: The path length replaces vertical height in ΔEp = mgΔh.

Correct model: Use the signed vertical height change in ΔEp = mgΔh and keep the field approximately uniform.

Worked transfer

Raising a 3.0 kg object by 2.0 m changes its near-Earth gravitational potential energy by mgΔh ≈ +59 J, independent of whether the path was vertical or sloped.

Guided practice

Explain why “The path length replaces vertical height in ΔEp = mgΔh.” fails. Then construct one example that correctly applies potential energy in a uniform gravitational field.

Independent practice

A 0.40 kg ball moves from a platform 1.2 m high to a point 0.30 m below the launch level. Find ΔEp for the ball–Earth system.

Return to the recorded repair plan when the explanation and application are secure enough to re-test.