Your help will be greatly appreciated!! 7. Bungee Jumping:6 A bungee cord is ess
ID: 1786039 • Letter: Y
Question
Your help will be greatly appreciated!!
7. Bungee Jumping:6 A bungee cord is essen- tially a very long rubber band that can stretch up to four times its unstretched length. How ever, its spring constant varies over its stretch see Menz, P.G. "The Physics of Bungee Jumping" The Physics Teacher (November 1993) 31: 483-487]. Take the length of the cord to be along the x-direction and define the stretch x as the length of the cord l mi nus its un-stretched length that is, x = 1-10 (see figure). Suppose a particular bungee cord has a spring constant, for 0 4.88 m, of k1 = 204 Nm-1 and for 4.88 m-a, of K2 = 111 Nm-1. (Recall that the spring con- stant is the slope of the force F(x) versus its stretch x.) (a) Compute the tension in the cord when the stretch is 16.7m (the maximum de- sired for a given jump) (b) Calculate how much work must be done against the elastic force of the bungee cord to stretch it 16.7 mExplanation / Answer
tension in the cord = spring constant * stretch
since the stretch is more than 4.88 m so,
spring constant = 111 Nm^-1
tension = 111 * 16.7
tension in the cord = 1853.7 N
work done against elastic force = 0.5 * kx^2
work done against elastic force = 0.5 * 111 * 16.7^2
work done = 15478.395 J
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