Problem 10.70 It\'s your birthday, and to celebrate you\'re going to make your f
ID: 1393645 • Letter: P
Question
Problem 10.70 It's your birthday, and to celebrate you're going to make your first bungee jump. You stand on a bridge 110m above a raging river and attach a 32-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 43N/m Assume that your mass is 76kg . After a long hesitation, you dive off the bridge. Part A How far are you above the water when the cord reaches its maximum elongation? Express your answer with the appropriate units.Explanation / Answer
Solution:
When the person is at the height of 110 m, there is maximum potential energy . Kinetic energy at that height =0 .
Gravitational potential energy at h=110m = U1= mgh= (76)(9.8)(110)= 81928 j.
When the spring elongates to a maximum stretch, the spring potential energy = 1/2 k h1^2
h1= new height = 110 - 32 - x = 78 - x
x= height of the person above the water.
gravitational potential energy at the height x = mg x = 76 * 9.8 * x = 744.8 x
total energy = mgx + 1/2k (78-x)^2 = 744.8 x + (0.5 * 43 * ( 78-x)^2)
from the energy conservation, mgh = 744.8 x + (0.5 * 43 * ( 78-x)^2)
=> 744.8 x + 21.5 ( 6084 - 156 x + x^2) = 81928
=> 744.8 x +130806 - 3354 x - 81928 +21.5 x^2 =0
=> -2565.2 x + 48878 +21.5 x^2 =0
=>21.5 x^2 + 588.8 x +48878 = 0 is a quadratic equation in x
solving for x , we get x = 23.8 m and 95.5 m
therefore the height above the water when the bungee reaches its maximum length = 23.8 m
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