Calculating Work via Integration Video Lessons

Concept

Problem: In an experiment, one of the forces exerted on a proton is F = αx2 i, where α = 12 N/m2.How much work does F do when the proton moves along the straight-line path from the point (0.30m, 0) to the point (0.10m, 0)?

FREE Expert Solution

Work:

$\overline{){\mathbf{W}}{\mathbf{=}}{{\mathbf{\int }}}_{{\mathbf{i}}}^{{\mathbf{f}}}\stackrel{\mathbf{⇀}}{\mathbf{F}}{\mathbf{·}}\stackrel{\mathbf{⇀}}{\mathbf{d}\mathbf{l}}}$

dl = (dx i + dy j)

F = -12x2 i

x1 = 0.30m, x2 = 0.10 m

y1 = 0 m, y2 = 0 m

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Problem Details

In an experiment, one of the forces exerted on a proton is F = αx2 i, where α = 12 N/m2.

How much work does F do when the proton moves along the straight-line path from the point (0.30m, 0) to the point (0.10m, 0)?