Question

Done by Vang Forces foes that we have considered so far typically do not vary as the object Thus, the work can be found simply by finding the scalar product of this constant mot change of position. Some forces vary as the object moves, meaning that there single fixed value of force over the full extent of the motion. Therefore, W F . be used to find the work done by these forces because there is no single value of cannot be the displacements. The work done by any variable force can be approximated breaking the total change of position up into a number of smaller displacement aments, finding the average force over each of these small segments, finding the work in each segment, and summing them, such that W S F Here, is simply the scament number counter and N is the total number of segments. This approach is strated graphically on page 189 in figure 7.7 of the text. This approximation approaches the actual work done by a variable force if the number of segments N is allowed to approach infinity, with each segment being infinitely small. This is the definition of an integral. So, the work done by a variable force is written as W="F.ds. Work Done by the Elastic Force Substitute the elastic force F, -ks into the integral equation above and find the work done by this force. W. = 1 .ds Is the work done by the elastic force positive or negative when the spring is stretched? Is the work done by the elastic force positive or negative when the spring contracts?

Answer 1

Soin: Fs -KS os joks ds = [12] when spring is stretch, Spy Si =) Wsco & work done is negative. when spring contracts, she Sia) Ws>o 10 & work done is positive.