Gravitational Potential Energy
Calculating and applying the potential energy of an object due to its position in a gravitational field, typically near the Earth's surface.
What is Gravitational Potential Energy?
The energy possessed by an object due to its position in a gravitational field.
Key formula / rule: Gravitational Potential Energy (near Earth's surface)
Key points
- Define Gravitational Potential Energy.
- Derive the formula for GPE near the Earth's surface.
- Calculate GPE for objects at different heights.
- Understand the concept of GPE in the context of celestial mechanics.
Common exam trap
Incorrectly choosing the reference level for potential energy.
Definitions
- Term
Gravitational Potential Energy
- Meaning
The energy possessed by an object due to its position in a gravitational field.
- Term
Reference Level
- Meaning
An arbitrary point or surface chosen as the zero point for potential energy calculations.
- Term
Gravitational Field
- Meaning
A region of space around a massive object where another massive object experiences a gravitational force.
Learning objectives
Define Gravitational Potential Energy.
Derive the formula for GPE near the Earth's surface.
Calculate GPE for objects at different heights.
Understand the concept of GPE in the context of celestial mechanics.
Relate changes in GPE to work done.
Formulae
- Name
Gravitational Potential Energy (near Earth's surface)
- Note
m = mass of object, g = acceleration due to gravity, h = height above reference level. Assumes 'g' is constant.
- Expression
U = mgh
- Name
Gravitational Potential Energy (universal)
- Note
G = Gravitational constant, M = mass of the central body, m = mass of the object, r = distance between the centers of the two bodies. Reference potential is zero at infinite separation.
- Expression
U = -GMm/r
- Name
Change in Gravitational Potential Energy
- Note
Uf is the final potential energy and Ui is the initial potential energy.
- Expression
ΔU = Uf - Ui
- Name
Work done by Gravitational Force
- Note
The work done by the gravitational force is equal to the negative of the change in potential energy.
- Expression
Wg = -ΔU
- Name
Work done against Gravitational Force
- Note
The work done against the gravitational force is equal to the change in potential energy.
- Expression
Wag = ΔU
Prerequisites
Work and Energy
Gravitation
Newton's Law of Universal Gravitation
Uniform and Non-uniform Fields
Common mistakes
Incorrectly choosing the reference level for potential energy.
Confusing potential energy with kinetic energy.
Forgetting the negative sign when calculating GPE at large distances from a central mass.
Assuming 'g' is constant at very large heights.
Keywords
Gravitational Potential Energy
GPE
Potential Energy
Work
Gravity
mgh
-GMm/r
Reference Level
Practice preview
The work done against gravity to lift an object from the Earth's surface to a height 'h' is equal to:…
easy
Consider a system of two particles of masses m and M, separated by a distance r. If the particles are brought closer to each other, the gravitational potential energy of the system:…
medium
A particle of mass m is projected vertically upwards with velocity v. The maximum height it reaches is H. If the gravitational potential energy is taken as zero at the surface of the Earth, what is the ratio of kinetic e…
hard