a fearless 58 kg physics student decides she wants to go bungee jumping from a 7

Question

a fearless 58 kg physics student decides she wants to go bungee jumping from a 75 m high bridge above a crocodile infested river. unfortunately, she must calculate the minimum spring constant for the bungee cord which will allow her to complete the jump successfully.

assuming the minimum spring constant is the one which allows her to descend the full 75 m (but no more) and the bungee cord does not begin to stretch until she has fallen 15 m, find the minimum value of the spring constant of the bungee cord.

(hint: it will be best to put h=0 at the height where the bungee cord begins to stretch.)

plz show all the work thank you.

Explanation / Answer

at h = 15 m

initial kinetic energy k1 = m*g*(h) = 58*9.8*15 = 8526 J

initial potentialenergy u1 = m*g*(h-h1) = 58*9.8*(75-15)

when she decends 75 m

potential energystored in spring = U2 = 0.5*k*(h1-h2)^2 = 0.5*k*(75-15)^2

U1 + k1 = u2

8526 + (58*9.8*(75-15)) = 0.5*k*(75-15)^2

k = 23.7 N/m

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