Q6.
Does the potential energy of an object near the surface of the Earth change if it moves with constant velocity in the horizontal direction? What if the object is gradually raised in the vertical direction?
Answer
Horizontal motion: no change. Vertical raising: the potential energy increases by mgΔh.
U = mgh
(a) Horizontal motion: the height h above the ground does not change
ΔU = mg × 0 = 0 J — no change
(b) Raised gradually through Δh:
ΔU = mg × Δh — the potential energy increases
e.g. a 2 kg book lifted 1.5 m: ΔU = 2 kg × 10 m s–2 × 1.5 m = 30 J
(a) Horizontal motion: the height h above the ground does not change
ΔU = mg × 0 = 0 J — no change
(b) Raised gradually through Δh:
ΔU = mg × Δh — the potential energy increases
e.g. a 2 kg book lifted 1.5 m: ΔU = 2 kg × 10 m s–2 × 1.5 m = 30 J
Why it happens: gravity pulls straight down. Moving sideways is perpendicular to that pull, so gravity does no work and nothing is stored. Moving up is directly against the pull, so you must do work mgΔh against gravity — and that work is stored in the Earth–object system as potential energy, ready to be returned if the object is released.
Tip: "gradually" matters. If you raise the object slowly the applied force is just mg and there is no leftover kinetic energy — every joule you supply goes into potential energy.