I've been given the following problem: enter image description here

I honestly have no clue on how to approach it. I don't know how to approach those forces. Can someone give me some guidance?


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  • $\begingroup$ The text says "which of these forces...". $F_1$ and $F_2$ are forces. What is your question about these? $\endgroup$ – Steeven May 2 '17 at 7:58
  • $\begingroup$ @Steeven Let me rephrase it. I don't know how to approach those forces. I don't know how to get the meaning of deltaxy(i+j) and apply it to calculate it times the distance to get W. $\endgroup$ – carloscc May 2 '17 at 8:03
  • $\begingroup$ $\hat i$ and $\hat j$ are the coordinate axes (base vectors). They just define the direction of the forces. Do you know the formula to calculate work? $\endgroup$ – Steeven May 2 '17 at 8:04
  • $\begingroup$ @Steeven It is Force times Distance. So I just plug the x and y values and then time it with the distance? $\endgroup$ – carloscc May 2 '17 at 8:07
  • 1
    $\begingroup$ That is unfortunately not correct. The formula $W=Fd$ is a shortcut. It requires a constant and parallel force. Your two forces are neither. (The first one seems to be parallel to the first path all the way though, but it isn't constant.) you will have to use the more general expression for work. $\endgroup$ – Steeven May 2 '17 at 8:18

Work done by a force is the dot product of the force and the displacement of the force.
If the force and displacement are in the same direction then the work done is the product of the magnitude of the force and the magnitude of the displacement.
However since the forces depend on position you will have to integrate along the chosen path so you will be using work done = $\int \vec F \cdot d \vec s$.

If a force is conservative then the work done by the force when displaced between two points is independent of the path taken by the force between the two points.


Work done =force ×displacement. Actually it's the dot product of two vectors, force and displacement. At first we should make sure that the force we are using, if it is conservative or non conservative. If it is conservative then we need to calculate the potential of corresponding points. And then the difference of two potentials is the work done by the force. If the force is non conservative then one can use simple line integral. One must know the function of path yet. This line integral is appropriate of 1D,2D,3D too. To calculate the potential of the corresponding force we will use, F =-del V. ....v=potential. ☺


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