The force component F cos reaches a maximum at s = 0.306 m. Find the percentage

Question

The force component F cos reaches a maximum at s = 0.306 m. Find the percentage of the total work that is done when the bowstring is moved in the following ways.
(about 242 squares total from 0 - .500 m)

http://www.webassign.net/CJ/6-22fig.gif

(a) from s = 0 to 0.306 m

(b) from s = 0.306 to 0.500 m The force component F cos reaches a maximum at s = 0.306 m. Find the percentage of the total work that is done when the bowstring is moved in the following ways.
(about 242 squares total from 0 - .500 m)

http://www.webassign.net/CJ/6-22fig.gif

(a) from s = 0 to 0.306 m

(b) from s = 0.306 to 0.500 m

Explanation / Answer

Work for a variable force is ?F•ds, or ?Fcos?ds. If you don't know calculus, it's basically the area under the curve. Since there isn't an actual function given for Fcos?, just estimate it by counting the number of squares under the curve (including all the fractions of squares that are split by the curve). Then each square is 9 N by 2.78 x 10^-2 m. So the work (W = Fd) for each square is 9 x 2.78 x 10^-2 = 0.2502 Joules. So the number of squares times the work per square is the total work.

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