A bungee cord is 30.0 in long and when stretched a distance x, it exerts a resto

Question

A bungee cord is 30.0 in long and when stretched a distance x, it exerts a restoring force of magnitude kx. Your father-in-law (mass 93.0 kg) stands on a platform 45.0 in above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 in before the cord stops him. You had several bungee cords to select from and you tested them by stretchy them out, tying one end to a tree and pulling on the other end with a force of 420 N When you do this, what distance will the bungee cord that you should select haw stretched?

Explanation / Answer

Using energy conservation at both points

Ea = Eb

KEa + PEa = KEb + PEb

since va and vb is zero.

KEa = 0

KEb = 0

PEa = m*g*ya + 0.5*k*xa^2 = 0 + 0 = 0

PEb = m*g*yb + 0.5*k*xb^2

PEb = -m*g*hmax + 0.5*k*xb^2

k = 2*m*g*hmax/xb^2

k = 2*93*9.81*41/(11^2) = 618.27 N/m

Now we know that

F = kx

x = F/k

x = 420/618.27 = 0.68 m

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