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CALC In an experiment, one of the forces exerted on a
Chapter 9, Problem 30E(choose chapter or problem)
CALC In an experiment, one of the forces exerted on a proton is where ? = 12 N/m2. (a) How much work does do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.40 m)? (b) Along the straight-line path from the point (0.10 m, 0) to the point (0.30 m, 0)? (c) Along the straight-line path from the point (0.30 m, 0) to the point (0.10 m, 0)? (d) Is the force conservative? Explain. If is conservative, what is the potential-energy function for it? Let U = 0 when x = 0.
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QUESTION:
CALC In an experiment, one of the forces exerted on a proton is where ? = 12 N/m2. (a) How much work does do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.40 m)? (b) Along the straight-line path from the point (0.10 m, 0) to the point (0.30 m, 0)? (c) Along the straight-line path from the point (0.30 m, 0) to the point (0.10 m, 0)? (d) Is the force conservative? Explain. If is conservative, what is the potential-energy function for it? Let U = 0 when x = 0.
ANSWER:Solution 30E x 2 Work done by a variable force, say F(x) is given by, W =F(x)dx…..(1), where x i1 x1 the initial displacement and x is the final displacement of the body. 2 2 Given that, F = x i Given, = 12 N/m 2 2 So, F = 12x i (a) When the body moves from the point (0.10 m,0) to (0.10 m, 0.40 m), there is displacement only along the y-axis, No displacement happens along the x-axis. The force F = 12x i acts along the x-axis. Hence force and displacement are perpendicular to each other. This signifies that work done by the