Energy conservation in two dimensions

AI Thread Summary
The discussion revolves around calculating the work done by a force F = −αx^2i on a proton as it moves along specified paths in a two-dimensional space. The participants seek to determine the work done for three different paths, emphasizing the need for a clear understanding of the work formula as a line integral of force. There is also a query about whether the force is conservative and the potential-energy function associated with it, with U defined as zero when x = 0. The lack of examples in textbooks and classroom instruction is noted as a barrier to understanding the problem. The conversation highlights the importance of grasping the concepts of work and potential energy in physics.
SPiazzo
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In an experiment, one of the forces exerted on a proton is F = −αx^2i , where α = 14.4 N/m2.
(a) How much work does F do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.5 m)?
(b) Along the straight-line path from the point (0.09 m, 0) to the point (0.32 m, 0)?
(c) Along the straight-line path from the point (0.32 m, 0) to the point (0.09 m, 0)?
If F is conservative, what is the potential-energy function for it? Let U = 0 when x = 0. (Use the following as necessary: x and α. If F is not conservative, enter NC.)

I have no idea how to do this one, there where no relevant examples in my textbook and my teacher did not teach this in our class if we have reached the topic at all.
 
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Hey SPiazzo! Can you write the Formulae for the Work done on an object By a force?
 
Work is a line integral of a force along a path. Can you calculate it?
 
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