What's the "d" in that formula? (work formula)

  • Context: High School 
  • Thread starter Thread starter Austin Gibson
  • Start date Start date
  • Tags Tags
    Formula
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
4 replies · 1K views
Austin Gibson
Messages
47
Reaction score
1
What's the definition of the "d" in that formula?

6610e8b9afb0081cafb278ee28bb1ce0.png
 

Attachments

  • 6610e8b9afb0081cafb278ee28bb1ce0.png
    6610e8b9afb0081cafb278ee28bb1ce0.png
    1.3 KB · Views: 595
Physics news on Phys.org
Austin Gibson said:
This equation assumes a constant force?

No it doesn't. This is because to find W, you have to integrate F over the appropriate range of dr.

Zz.
 
  • Like
Likes   Reactions: Austin Gibson
[itex]dW=\vec F \cdot d\vec r[/itex] is an infinitesimal amount work done over the infinitesimal displacement [itex]d\vec r[/itex],
where [itex]\vec F[/itex] is approximately constant during that displacement.

When this is evaluated over a path, then [itex]\vec F[/itex] and [itex]d\vec r[/itex] will vary as you progress along the path.

It's probably not a good idea to think of these [itex]d[/itex]'s as differentials (as in [itex]dW[/itex] is a differential of [itex]W[/itex]
since there is generally no such [itex]W[/itex] because the work done generally depends on the path. In thermodynamics books, this is sometimes written as [itex]đW[/itex].)
 
Last edited:
  • Like
Likes   Reactions: Austin Gibson