"Proving Central Force is a Conservative Force

Click For Summary

Homework Help Overview

The problem involves proving that a central force is a conservative force. The context is centered around the definitions and properties of forces in physics, particularly focusing on central forces and their characteristics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of a conservative force and its implications regarding energy conservation. There are attempts to express work done by a central force, with some participants questioning the relationship between force, displacement, and work.

Discussion Status

The discussion is ongoing, with participants exploring definitions and attempting to clarify the relationship between force and work. Some guidance has been offered regarding the use of vector notation and the dependence of force on displacement, but confusion remains about how to approach the proof.

Contextual Notes

Participants are grappling with the mathematical representation of work done by a force and the implications of varying force with displacement. There is a noted lack of consensus on how to proceed with the proof, and assumptions about the nature of the force are being examined.

m2287
Messages
11
Reaction score
0

Homework Statement



If a force on an object is always directed along a line from the object to a given point, and the magnitude of the force depends only on the distance of the object from the point, the force is said to be a central force. Show that any central force is a conservative force.

Homework Equations





The Attempt at a Solution



i really don't have a clue...

im guessing work done = force * distance

and F = ma might be used but i don't know how!
 
Physics news on Phys.org
What is the definition of a conservative force?
 
that if you move an object around and place it back in its original position no energy is lost?
 
m2287 said:
that if you move an object around and place it back in its original position no energy is lost?
Correct. Can you therefore write an expression for the work done by a central force?
 
wd= ma * d ?
 
m2287 said:
wd= ma * d ?
Close but don't forget that the magnitude of the force is dependent on the displacement. Use vector notation for the displacement and write ma as F.
 
does than not just give you wd = f* d

im very confused about how to prove this!
 
m2287 said:
does than not just give you wd = f* d
No. Note that the magnitude of the force is a function of displacement and note that we are looking at displacement which is a vector quantity. Now, because the force is not constant (because is varies with displacement), we cannot use the simple relationship you outlined above. Do you know a general definition of the work done by a force (involving calculus)?
 

Similar threads

Conservation of angular momentum under central forces
  • · Replies 4 ·
Replies
4
Views
2K
Is potential energy defined only for internal conservative forces?
  • · Replies 15 ·
Replies
15
Views
2K
Angular momentum conservation on a merry-go-round
  • · Replies 5 ·
Replies
5
Views
2K
Why is source force + electrostatic force = 0 inside battery?
  • · Replies 10 ·
Replies
10
Views
2K
Spring Problem Involving Variables and Constants Only
  • · Replies 3 ·
Replies
3
Views
2K
Understanding the generic nature of linearity in Physics
  • · Replies 2 ·
Replies
2
Views
1K
Why is a 1d conservative force approximately linearly related to position?
  • · Replies 3 ·
Replies
3
Views
859
How to prove that a force is conservative?
  • · Replies 40 ·
2
Replies
40
Views
5K
What is considered the "System" here? (conservation of energy problem)
  • · Replies 20 ·
Replies
20
Views
3K
Two particles moving in a central potential
  • · Replies 1 ·
Replies
1
Views
1K