10. -1 points SerCP9 5.AE.016. My Notes Ask Y EXAMPLE 5.16 Estimating Work by Co

Question

10. -1 points SerCP9 5.AE.016. My Notes Ask Y EXAMPLE 5.16 Estimating Work by Counting Boxes GOAL Use the graphical method and counting boxes to estimate the work done by a force F. N pp (N) 100 PROBLEM Suppose the force applied to stretch a thick piece of elastic changes with position as indicated in figure a. Estimate the work done by the applied force 8.0 6.0 4.0 20 0.0 0.2 04 06 08 10 80 60 40 20 x (m) x (m) 0 0. 03 0.5 0.7 STRATEGY To find the work, simply count the number of boxes underneath the curve and multiply that number by the area of each box. The curve will pass through the middle of some boxes, in which case only an estimated fractional part should be counted. SOLUTION There are 62 complete or nearly complete boxes under the curve, 6 boxes that are about half under the curve, and a triangular area fromx0 m to x 0.10 m that is equivalent to 1 box, for a total of about 66 boxes. Because the area of each box is 0.10 J, the total work done is approximately 66 × 0.10 J = 6.6 J. LEARN MORE REMARKS Mathematically, there are a number of other methods for creating such estimates, all involving adding up regions approximating the area. To get a better estimate, make smaller boxes

Explanation / Answer

From the figure there are total 22full boxes are there in the limit x=0 to x=0.4

For each box work done is 10N x0.1 =1J

Now for 22 boxes total work done is

W = 22 x1J = 22J

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