Question

I uetermi ine how high to start to just touch the water below? Experiment Overview This experiment will model a bungee jumper who jumps from a The bridge into a canyon. bungee jumpe bouncing back up towards the bridge. The ex spring represents the connected r fa Ils and just barely touches the water in the river below before perimental apparatus is shown in Fig. 1. The e bungee cord. The egg represents the surface of the water. A mass to a spring represents the bungee jumper. Before the mass falls, it will be tied y a string to the stand. The length of the string (yi) will be equal to the unstretched length of the spring. You will cut the string, allowing the mass to fall. Your task is to calculate the height y2 that is needed for the mass to barely touch the egg before it bounces back up. 'i Unstretched position of spring y2 Figure 1: Experimental apparatus

Answer 1

(e) consider the mass or bungee jumper + spring of the system (f) Forces acting are: - Gravitational force due to attraction from earth - extended force Force due to the spring - Internal force Force due to resistance from air during motion - external force Yes, these force does work on the system (g) The system has gravitational potential energy at the initial instant The system possess the potential energy due to gravitational attraction as well as due to extension of the spring \r\n (i) Drawn in previous figure (j) KE_i + PE_i + W_external = KE_f + PE_f + delta E_thermal KE_i = 0 (system state with zero velocity) PE_i = mgy_2 I W_external n0 (Assuming n theta air resistance) KE_f = 0 (mass stops moving) PE_f = 1/2 ky^2_2: k rightarrow Spring constant Delta E_thermal = 0 (k) mgy_2 = 1/2 ky_2^2 y_2 = 2mg/k (l) For a stiffer spring (K rightarrow large), y_2 will be small If mass is larger