A CD case slides along a floor in the positive direction of an x axis while an a

Question

A CD case slides along a floor in the positive direction of an x axis while an applied force Fa acts on it. The force is directed along the x axis and has the x component Fax = 15x - 3x2, with x in meters and Fax in newtons. The case starts at rest at the position x = 0, and it moves until it is again at rest. Plot the work done on the case by Fa rightarrow versus position x. (Do this on paper. Your instructor may ask you to turn in this work. ) at what position is the work maximum? m What is the maximum value of the work? J at what position has the work decreased to zero? m at what position is the case again at rest? m

Explanation / Answer

(A) the case again comes to rest when 3*x^2-15*x=0....x=5 m....therefore the required plot is the curve y=15*x-3*x^2 from x=0 to x=5..........(b)work=(15*x-3*x^2)*x....for max its differential is made 0.....30*x-9*x^2=0....x=3.33m.............(c)at x=3.33 work=15*3.33^2-3*3.33^3=55.9 J.....(d)the work is 0 at 15x^2-3x^3=0.....that is x=5m.....(e)case is again at rest at 15x-3x^2=0....x=5m

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