Calculate the work done in Rectangle?

AI Thread Summary
The discussion focuses on calculating the work done by a force F acting on a particle moving in the XY plane from the origin to the coordinates (5,5) along various paths. The force is defined as F = 2y i + x^2 j, and participants explore the work done along paths OAC, OBC, and OC using integration. Key insights include the application of the work integral and the clarification that when integrating with respect to y, x can be treated as a constant. The conversation also touches on whether the force F is conservative. Participants share helpful tips and resources for solving the problem.
abrowaqas
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Homework Statement



A force acting on a particle moving in XY plane is given by F= 2y i + x^2 j . particle moves from origin to a final position having coordinates (x,y)=(5,5). calculate the work done by force F along

B_____________C
| |
| |
O |____________| A

a) Path OAC
b) Path OBC
c) Path OC
d) is force F is conservative ?

Homework Equations


work. ∫ f. dx


The Attempt at a Solution



a)
Path OAC
W= ∫(O to A) + ∫(O to B)
= ∫ (O to A) F. dx + ∫ (O to B) F. dy
= ∫( 0 to 5 ) 2y dx + ∫(0 to 5 ) x^2 dy

how it goes in the intergration ..
kindly help i am not getting it cleary..
 
Physics news on Phys.org
hi abrowaqas! :wink:

yes that's fine :smile: …

in ∫ f(x) dy, x is a constant, so you can take it outside the ∫ …

f(x) ∫ dy :wink:​
 

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