Chapter 6. Work done to stretch a spring (6-13)

Question

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{"title":"Work that must be done on a spring to strech it from x = x sub 1 to x = x sub 2","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"4,13,38,53\"}]"} {"title":"Spring constant of the spring (a measure of its stiffness)","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"114,21,132,53\"},{\"shape\":\"rect\",\"coords\":\"243,19,264,55\"}]"} {"title":"x sub 1 = initial stretch of the spring, x sub 2 = final stretch of the spring","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"132,26,151,52\"},{\"shape\":\"rect\",\"coords\":\"263,31,287,53\"}]"}

Question

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{"title":"Work that must be done on a spring to strech it from x = x sub 1 to x = x sub 2","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"4,13,38,53\"}]"} {"title":"Spring constant of the spring (a measure of its stiffness)","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"114,21,132,53\"},{\"shape\":\"rect\",\"coords\":\"243,19,264,55\"}]"} {"title":"x sub 1 = initial stretch of the spring, x sub 2 = final stretch of the spring","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"132,26,151,52\"},{\"shape\":\"rect\",\"coords\":\"263,31,287,53\"}]"}

Question

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{"title":"Work that must be done on a spring to strech it from x = x sub 1 to x = x sub 2","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"4,13,38,53\"}]"} {"title":"Spring constant of the spring (a measure of its stiffness)","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"114,21,132,53\"},{\"shape\":\"rect\",\"coords\":\"243,19,264,55\"}]"} {"title":"x sub 1 = initial stretch of the spring, x sub 2 = final stretch of the spring","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"132,26,151,52\"},{\"shape\":\"rect\",\"coords\":\"263,31,287,53\"}]"}

Review

Figure 6-18 graphs the force that you exert as a function of the distance x that the spring has been stretched. If the spring is initially stretched a distance \(x_1\) and you stretch it further to \(x_2\), the work W that you do is equal to the area of the colored trapezoid in Figure 6-18. From geometry, this area is equal to the average height of the graph multiplied by the width \(x_2 - x_1\). Equation 6-12 can be simplified to: