Question

EXAMPLE 6.3 Bungee Jumper A bungee jumper locates a suitable bridge that is 75.0 m above the river below, as shown in Figure 6.14. The jumper has a mass of m-80.0 kg and a height of Ljumper 1.85 m, we can think of a bungee cord as a spring. The spring constant of the bungee cord is k-50.0 N/m. Assume that the mass of the bungee cord is negligible compared with the jumper's mass Lo PROBLENM The jumper wants to know the maximum length of bungee cord he can safely use for this jump. Lmax-Lo SOLUTION We are looking for the unstretched length of the bungee cord, Lo, as the jumper would measure it standing on the bridge. The distance from the bridge to the water is Lmax = 75.0 m. Energy conservation tells us that the gravitational potential en- ergy that the jumper has, as he dives off the bridge, will be converted to potential energy stored in the bungee cord. The jumper's gravitational potential energy on y FIGURE 6.14 A bungee jumper needs to ca

Answer 1

Stretched length of cord x = 75 - l_0 - 1.85 x = 73.15 - L_0 Force balance in vertical: - mg = kx [spring force] 80 times 9.7 = 50 times [73.15 - L_0] 15.68 = 73.15 - L_0 L_= 57.47 meter