Gravitational Potential Energy

If a one kilogram body falls one meter near the surface of the Earth, the kinetic energy of the body goes up ten joules. What is the change in gravitational potential energy of the body?

Their Way

The formula for gravitational potential energy is:


GPE = –GMm ⁄  r


The value of GM for the Earth is 399 trillion meters cubed per seconds squared. The mean radius of the Earth is 6,371,000 meters.

The gravitational potential energy of a one kilogram body on the surface of the Earth is:


RW = –399 trillion m ³ ∕ s ² × 1 kg ÷ 6,371,000 m = –62,627,531 J


The gravitational potential energy of a one kilogram body at a height of one meter is:


RW = –399 trillion m³ ∕ s ² × 1kg ÷ 6,371,001 m = –62,627,521 J


If a one kilogram body falls one meter near the surface of the Earth, the change in gravitational potential energy is:


ΔGPE = –62,627,531 J – – 62,627,521 J = –10 J



My Way

The formula for rest weight is:

RW = GMm ⁄  r


The rest weight of a one kilogram body on the surface of the Earth is:

RW = 399 trillion m ³ ∕ s ² × 1 kg ÷ 6,371,000 m = 62,627,531 J


The rest weight of a one kilogram body at a height of one meter is:

RW = 399 trillion m³ ∕ s ² × 1kg ÷ 6,371,001 m = 62,627,521 J


If a one kilogram body falls one meter near the surface of the Earth, the change in rest weight is:


ΔRW = 62,627,531 J – 62,627,521 J = 10 J


If rest weight goes up ten joules, gravitational potential energy goes down ten joules.