Question

Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle. He falls for 15 m before the bungee cord begins to stretch. Chris’s mass is 75kg and we assume the cord obeys Hooke’s law, , with 50 N/m. If we neglect air resistance, estimate how far below the bridge Chris’s foot will be before coming to a stop. Ignore the mass of the cord (not realistic, however) and treat Chris as a particle.

Answer 1

Chris's foot will be approximately 18.75 m below the bridge before coming to a stop.

Step-by-step explanation:

To find the distance below the bridge before Chris's foot comes to a stop, we can use the principles of Hooke's law and conservation of energy. Firstly, we can determine the force constant of the bungee cord using the given information of 500 J of work done to compress a spring by 10 cm. The force constant is equal to the change in potential energy divided by the change in length, which gives us a value of 50 N/m. Using this force constant, we can calculate the maximum deflection of the bungee cord when Chris jumps off the bridge.

Assuming Chris is treated as a particle, the maximum deflection of the bungee cord is the sum of the initial fall distance (15 m) and the maximum stretch of the cord. Since the cord stretches up to four times its unstretched length, the maximum stretch is 4 times the unstretched length of the cord. Using the calculated force constant and equations of motion, we can find the maximum stretch of the cord, which is 3.75 m. Therefore, the distance below the bridge before Chris's foot comes to a stop is 15 m + 3.75 m = 18.75 m.