The height in the potential gravitational energy

Click For Summary
SUMMARY

The discussion centers on the calculation of gravitational potential energy (GPE) for objects, specifically spheres, in relation to their height. It is established that the height "h" in the formula for GPE, given by GPE = mgh, should be measured from the bottom of the object to the reference point, typically the Earth's surface. The center of gravity is relevant when considering symmetrical objects like spheres, but the critical factor is the change in potential energy rather than the absolute height. The GPE is zero when the object reaches the Earth's surface, regardless of the height measured from the center of gravity or the bottom of the object.

PREREQUISITES
  • Understanding of gravitational potential energy (GPE)
  • Familiarity with the concepts of mass (m) and height (h)
  • Knowledge of center of mass and its significance in physics
  • Basic principles of physics concerning energy conservation
NEXT STEPS
  • Study the derivation of the gravitational potential energy formula GPE = mgh
  • Explore the concept of center of mass in various geometrical shapes
  • Learn about energy conservation principles in physics
  • Investigate the effects of height on potential energy in different gravitational fields
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding gravitational potential energy and its calculations.

terryds
Messages
392
Reaction score
13
Is the height in the formula the vertical distance from the bottom to the center of gravity of object, or is it just the vertical distance from the bottom to the very top of the object.

I mean..
If there is a sphere with mass m and radius r and placed at height h, what is its potential gravitational energy ?
Is it just mgh or mg(h-r) ?
 
Physics news on Phys.org
terryds said:
If there is a sphere with mass m and radius r and placed at height h
Height "h" measured from what point? Also, is that the height of the center of the sphere or the bottom?

Realize that the reference point for measuring the gravitational PE is arbitrary. What really matters is the change in PE.
 
  • Like
Likes   Reactions: terryds
Doc Al said:
Height "h" measured from what point? Also, is that the height of the center of the sphere or the bottom?

Realize that the reference point for measuring the gravitational PE is arbitrary. What really matters is the change in PE.

So, it is the vertical distance from Earth surface to the very bottom of an object, right ?
I think when I refer the height to the center of gravity or anything that is above the very bottom of an object, when it reaches the Earth surface, it'll still have the height (measured to the center of gravity or radius in a sphere). But, the fact is that it has no potential gravitational energy since it has reached the Earth surface.
Am i right?
 
Last edited:
terryds said:
So, it is the vertical distance from Earth surface to the very bottom of an object, right ?
As I said before, the GPE = 0 point is arbitrary.

terryds said:
I think when I refer the height to the center of gravity or anything that is above the very bottom of an object, when it reaches the Earth surface, it'll still have the height (measured to the center of gravity or radius in a sphere). But, the fact is that it has no potential gravitational energy since it has reached the Earth surface.
Am i right?
If you want to measure the GPE from some reference level (using the Earth's surface is fine) one usually measures the height of the center of mass with respect to that reference. But for a sphere, it doesn't matter, since it is symmetric.

Again, what matters is the change in GPE when the object moves from one point to another.
 
  • Like
Likes   Reactions: terryds

Similar threads

High School Can energy be decomposed?
  • · Replies 2 ·
Replies
2
Views
1K
High School Potential energy and lifting an object vertically
  • · Replies 29 ·
Replies
29
Views
4K
Undergrad What is the zero point for Potential Energy and how to find it from integral limits?
  • · Replies 6 ·
Replies
6
Views
2K
High School Conceptually understanding change in potential energy with 0 net work
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Gravitational potential energy
  • · Replies 46 ·
2
Replies
46
Views
5K
Undergrad Question about potential energy: gravity and a vertical spring
  • · Replies 12 ·
Replies
12
Views
4K
High School How does an object gain potential energy?
  • · Replies 54 ·
2
Replies
54
Views
6K
High School Why Do Objects Bounce? Exploring Momentum and Energy Conservation
  • · Replies 6 ·
Replies
6
Views
2K
High School Conservation of KE in a moving frame
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Gravitational potential energy -- Why is it always negative?
  • · Replies 10 ·
Replies
10
Views
3K