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?

My Way

The formula for rest weight is:


RW = 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 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 m ³ ∕ s ² × 1 kg ÷ 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


Rest weight goes up ten joules, so gravitational potential energy goes down ten joules.



Their Way

This is their formula for gravitational potential energy:


GPE = − GMm / r


They get this formula by integrating the formula for the force of gravity.

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


GPE = − 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:


GPE = − 399 trillion m ³ ∕ s ² × 1 kg ÷ 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


Gravitational potential energy goes down ten joules.

We both get the same answer. The difference is, they have negative energy and I don't. Negative energy is stupid.