How do you integrate a force with a scalar function to find the total work done?

AI Thread Summary
To find the total work done by a force represented by the scalar function (x² + 2xy) from point O (0,0) to point P (1,1), one must recognize that the force is not conservative, meaning the work depends on the chosen path. The work can be calculated using a line integral of the force along the specified path. However, the discussion highlights a misunderstanding, as the force should be a vector function rather than a scalar function for proper integration. Consequently, the integration cannot be performed as initially thought. Understanding the nature of the force is crucial for accurately determining the work done.
Alia Al-Hajri
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Homework Statement



Assalam Alikum
Hi everybody… a work done by a force=( x2+2xy) in a distance from..pt O =(0,0) to pt P=(1,1)




Homework Equations



Evaluate the total work?

The Attempt at a Solution



I know the solution is by integrate the force from (0,0) to (1,1)
But how that will be?
 
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since your force is not conservative, the work will depend on the path you take from (0,0) to (1,0). the work will be the line integral of F over that path.

W = /int _C F ds

where C is the path.
 
Last edited:


Thanks...but I'm afraid that I did't get your idea!
I mean how do you know that the force is not conservative?
 


well, really, i did not look carefully enough. the force needs to be a vector function, you have given a scalar function.
 


So...you said that I can not integrate with a force has scalar function..!
Thanks allot
 

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