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Unformatted text preview: 1 Work When a body moves a distance d along a straight line as a result of being acted on by a force of constant magnitude F in the direction of motion, then the work W done by the force is W = Fd . We will generalize the definition of work to the case of variable force. Given a force function F ( x ) defined and continuous at each point x of the straight line segment [ a, b ] , we will define the work W done by this variable force in moving a particle along the x-axis from the point x = a to the point x = b . Partition the interval [ a, b ] into n subintervals with the same length x . Choose an arbitrary point c k in the k th interval [ x k- 1 , x k ] . Approximate the work W k done by the force from the point x = x k- 1 to the point x = x k by W k F ( c k ) x. We approximate the total work by summing from 1 to n , so W n X k =1 F ( c k ) x. This is a Riemann sum for F ( x ) . When x , the sum approaches the definite integral of F ( x ) from a to...
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This homework help was uploaded on 02/15/2008 for the course MATH 1910 taught by Professor Berman during the Fall '07 term at Cornell University (Engineering School).
- Fall '07