Question

You and a friend decide to go bungee jumping off a nearby bridge. Tests of the bungee demonstrate that it behaves like an ideal spring. When your friend (mass=75kg) jumps you are on a rock 40.0m below the bridge and observe him to pass you at 25m/s. The bungee hangs 20.0m below the bridge when nothing is attached and 25.0m when a 75kg mass is attached but at rest (equilibrium).

a) Use conservation of energy to write down a relation between the amplitude, A, position, x, and velocity, v for the system when oscillations begin.

b) Write down the equation describing your friend’s motion from when he stretches the bungee beyond the equilibrium position. Your equation should have numeric values for the variables.

c) Calculate how much time elapses for your friend to travel from your position to when the bungee is fully stretched.

EDIT: no figure given

Answer 1

mg = KX (a) - Ken K xo xo is equilibrium position. 75x9 = kx(255) K=15g K= 15x9.8 = 147 N/m. for amplitude, velocity and a I mu?= 1 KA² - I kx2 & is displacement from mean position 2- x2) A is amplitude) x = o t A sin wt W=27= x= 5+ A Din it v=25m/ at x = 15m. 25=147 (A2 - 152) U 75 A = 23.32 m

. x = 5+23.32 sin (147 t. J 75 en 5 +23 Din (1.4) 12=5+23.32 Din (1.4)t x = 18 20 2 -5 = 23.32 Din (1.4) t (1.4) t = 29.048 1.03 rad t = 0.74 sec Please Rate Positive