WOrk done by a variable force (in two dimension)

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Homework Help Overview

The discussion revolves around calculating the work done by a variable force in two dimensions, specifically given the force function F = ax^2 i + b y^3 j, and considering the movement from point (x1, y1) to (x2, y2).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to find the total work by separating the calculations into x and y components, questioning if this method is correct. Some participants raise concerns about the importance of the path taken between the two points, suggesting that different paths yield different results.

Discussion Status

Participants are actively questioning the validity of the original poster's approach, particularly regarding the consideration of the path taken. Some guidance has been offered regarding the definition of infinitesimal work and the need for a vector expression for the straight line path.

Contextual Notes

There is an emphasis on the assumption that the path taken is a straight line, but the implications of this assumption are being debated. The original poster is encouraged to provide further details of their work for additional feedback.

daivinhtran
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Homework Statement



How to find the work done by a variable force in (two dimension)

When
F = ax^2 i + b y^3 j

If a subject move from (x1,y1) to (x2, y2)

Homework Equations



F = dW/dr

The Attempt at a Solution



I tried to solve them separately by x-direction and y-direction, and then I added them up
like Wx + Wy = W
Am I right?
 
Last edited:
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In this problem the path taken from (x1,y1) to (x2, y2) is important, different paths taken give different results. In this problem I assume the path is a straight line. If you solve the problem as you suggested I'm not sure you took into account the path taken? Can you scan your work and post it?

Hopefully others will help.
 
Spinnor said:
In this problem the path taken from (x1,y1) to (x2, y2) is important, different paths taken give different results. In this problem I assume the path is a straight line. If you solve the problem as you suggested I'm not sure you took into account the path taken? Can you scan your work and post it?

Hopefully others will help.


https://www.physicsforums.com/attachment.php?attachmentid=51764&stc=1&d=1349922834

I hope I solve it right
 

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I don't think what you did is right. You did not take the path into account only the end points. Start from the diffinition of infitesimal work, dW = vector F dot vector dr and plug and chug. You must come up with a vector expression for dr for the straight line path. You can do this as you know the endpoints.
 
Spinnor said:
I don't think what you did is right. You did not take the path into account only the end points. Start from the diffinition of infitesimal work, dW = vector F dot vector dr and plug and chug. You must come up with a vector expression for dr for the straight line path. You can do this as you know the endpoints.

as I stated before, the particle goes from (x1,y1) to (x2, y2)
so the end point is (x2, y2)

So, am I doing this right?

P/s: however, the path between the two points is straight line
 
I don't think so. Hopefully others will confirm.
 

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