Problem X2.05 (35 points). A bungee jumping professional is an expert in the phy

Question

Problem X2.05 (35 points). A bungee jumping professional is an expert in the physics of energy conservation, springs and gravity. He has to in fact, as for them it is a matter of life or death. The most important parameter in choosing a jumping spot, besides the scenery, is the height from which you jump, given a bungee cord (see figure 4). Assume that you have a cord that when unstretched has a length L 20 m, and a spring constant k137.2 N/m. If your mass is m = 70 kg calculate the following: A What is the minimum height from which you need to jump so that you don't hit the ground? (Alternative way to say this: At which distance from the jumping spot wil you stop falling?). Note that when you jump you start with zero velocity. B What is your acceleration when you reach the minimum height? C After the jump is over, and you stop oscillating up and down, at what height will you hang? Figure 4: Diagram for problem 01.

Explanation / Answer

(A) Applying work - energy theorem,

work done by gravity + work done by elastic force = change in KE

m g H + k (H - L)^2 /2 = 0 - 0

70 x 9.8 x H + 137.2(H -20)^2 / 2 = 0

137.2 H^2 - 5488 H + 1373.4H + 54880 = 0

H = 40 m

(b) Fnet = k x - m g = m a
  
137.2 (20) - (70 x9.81) = 70 a

a =29.4 m/s^2

(C) Fnet = k x - m g = 0

137.2 x = 70(9.81)

x = 5 m

h = 40 -(20 + 5) = 15 m

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