I\'m confused with the limits of integration for part b webassign.net A Bungee C

Question

I'm confused with the limits of integration for part b

webassign.net A Bungee Cord Is Essentially A Very Long Rubber Ba... Chegg.com PHYS 211 HW 5 Fall 17 Work- OpenStax University Physics-All Volumes- OpenStax CNX A bungee cord is essentially a very long rubber band that can stretch up to four times its unstretched length. However, its spring constant varies over its stretch.t Take the length of the cord to be along the x-direction and define the stretch x as the length of the cord minus its unstretched length loi that is, x-lo Suppose a particular bungee cord has a spring constant, for 0sx s 2.88 m, of k1-206 N/m and, for x > 2.88 m, of k2 as a function of its stretch below. (Recall that the spring constant is the slope of the force Fx) versus its stretch x.) 103 N/m. The function of the force F(x) is displayed k,X x s 2.88 2.88k1 k2(x - 2.88) x> 2.88 (a) What is the tension (in N) in the cord when the stretch is 17.7 m (the maximum desired for a given jump)? 2120 N (b) How much work (in ) must be done against the elastic force of the bungee cord to stretch it 17.7 m? 21385

Explanation / Answer

B] work = integral F dx = 0.5 kx1^2 + 2.88k1x + 0.5k2x^2 - 2.88k2*x. with appropriate limits

= 0.5 k1 *2.88^2 + 2.88k1*(17.7-2.88) + 0.5k2*(17.7^2 - 2.88^2) - 2.88k2*(17.7-2.88)

= 0.5 *206 *2.88^2 + 2.88*206*(17.7-2.88) + 0.5*103*(17.7^2 - 2.88^2) - 2.88*103*(17.7-2.88)

= 20958 J answer

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