A 60 kg bungee jumper jumps from a bridge. She is tied to a bungee cord that is 15 m long

when unstretched and falls a total distance of 31 m. Calculate

(i) the spring constant of the bungee cord.

(ii) the maximum acceleration experienced by the jumper

(i) 140 N/m

(ii) 28 m/s²

Explanation:

(i)

At the top of the jump, the bungee jumper has gravitational potential energy.

At the bottom of the jump, the bungee jumper has elastic potential energy.

mgh = ½ kx²

(60 kg) (9.8 m/s²) (31 m) = ½ k (31 m - 15 m) ²

k = 140 N/m

(ii)

At the bottom of the jump:

∑F = ma

kx - mg = ma

(140 N/m) (31 m - 15 m) - (60 kg) (9.8 m/s²) = (60 kg) a

a = 28 m/s²