Question

1. Suppose an object is subjected to a force F that varies with position: where β 20N/m is a constant. a) The object begins at the origin (x,y) = (0,0) and travels to point P located at (z,y)-(1m,3m): 3m 4m Calculate the work done by F along each of the three possible paths shown in the figure above by the dashed lines. Note that there could be other forces acting on the object in order to ensure the object travels along the paths drawn in the figure, but we will just consider the work done by F b) Do you think the force F is conservative? If not, explain why. If yes, find a suitable potential energy function and use this potential energy function to calculate the work done along the three paths from part a). c) Now suppose the force F is given by where α = 10N/m2 is a constant. Do you think the force F is conservative in this case? If yes, find an appropriate potential energy function. If not, show or explain why it's not possible for such a force to be the gradient of a scalar function. If you're not sure, try computing the work done by F along the paths from part a)

Answer 1

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