Respuesta :
Answer:
k = 1755 N/m
Explanation:
Given:
- The length of the cord L = 23.4 m
- Weight of the student W = 818 N
- The elevation of balloon H = 31.3 m
Find:
Calculate the required force constant of the cord if the student is to stop safely 2.74 m above the river.
Solution:
- We know the potential energy of the student changes by
ΔP.E = m*g*( H - 2.74 )
mg*(31.3 - 2.74) = 818*28.56 = 23362.08 J
- When he stops at 2.74 m above ground his KE = 0 so ALL his lost potential energy must be stored in the extended or stretched bungee cord.
- He falls 23.4 m before the bungee cord starts to stretch. That means it doesn't start stretching until he is 31.3 - 23.4 = 7.9 m above the ground.
- It has to stop stretching at 2.74 m above the ground so the
total stretch = 7.9 - 2.74 = 5.16 m
- Therefore his PE from 31.3 m to 2.74 m is stored in a 5.16 m stretch of the bungee cord.
½kx² = ΔP.E
k = 2*ΔP.E / x^2
k = 2*23362.08 / 5.16^2
k = 1755 N/m
