Gravity and Changes in Energy

Distinguish near-surface energy changes from the full inverse-distance model.

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For small height changes where g is nearly constant, change in gravitational potential energy is m g delta-h. In an isolated spherical-source model with zero potential at infinity, U = -GMm/r. Potential energy belongs to the interacting system.

Worked example

Near Earth, lifting 2 kg through 3 m at g = 10 N/kg increases potential energy by 60 J. The same fall can supply 60 J of kinetic energy if other transfers are negligible.

With potential energy zero at infinity, U equals minus GMm divided by r. At center distances r0, 2r0 and 4r0, relative energies are minus one, minus one half and minus one quarter.

Would you believe it?

Gravity does more than pull a dropped ball down. It also helps hold the air around Earth.

NASA Space Place: gravity

Question 1 Lift 4 kg through 2 m at g = 10 N/kg. What is the potential-energy increase? 80 J 20 J 8 J

Question 2 Starting from rest, an object falls 5 m at g = 10 m/s^2 without drag. Its speed is what? 50 m/s 5 m/s 10 m/s

Question 3 In U = -GMm/r, what happens to U as r increases? It must remain constant It becomes less negative It becomes more negative

Question 4 Changing the chosen zero of potential energy changes what? Its numerical reference, not energy differences The gravitational force itself The measured mass

Question 5 Why not use mgh with a fixed surface g for an enormous altitude change? Mass must become zero Energy conservation stops working g changes appreciably with center distance

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