C10B.4 Suppose an external force acts on a system that has a constant magnitude

Question

C10B.4 Suppose an external force acts on a system that has a constant magnitude of 100 N but changes direction at a constant rate from being directly horizontal to directly vertical as the point where the force is applied moves a horizontal distance of 10 cm at a constant speed. (a) Estimate the work that the interaction exerting this force does on the system by dividing the process into ten equal displacements, calculating dW, F dr, for each step, and adding the results. (Note: Calculate the angle between F and dr, at the midpoint of each step.) (b) Compare to the (more) exact result (20/T) N, which one can find using calculus. Are you close?

Explanation / Answer

a) work done = f.dr

W = intgeral( 100. dr from r = 0 to 10)

= 100*(10-0) /100 = 10 J

b) W = F*r

= 20/pi * 0.1

= 2/pi = 0.64 J

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