Known mobster and gambler Larry the Loser is found dead, hanging at about the 7

Question

Known mobster and gambler Larry the Loser is found dead, hanging at about the 7 story level from a bungee cord tied to the top of the 15 story (45m) Prudential Building in downtown Chicago.  Larry has a mass of 90 kg and when the bungee cord is cut down, it is found to have a relaxed length of 5 stories.  Detective Lestrade from the Chicago Police Department thinks that Larry must have been bungee jumping from the top of the building and just unluckily hit the ground, but you know that Larry was murdered.  What is your evidence?

Note: a bungee cord will not exert any force on the jumper until the jumper has fallen a distance equal to the bungee cord's relaxed length.  Also, the force a bungee cord exerts actually exceeds Ks[x] in magnitude when it is stretched a lot.

Explanation / Answer

height of 1 story = 45/15 = 3m

natural length L = 5 x 3 = 15 m

mg = kx

mg = k (21-15)

6k = mg

now using energy conservation to find maximum alongation,

kx^2 /2 = mg x

(mg/6) x^2 /2 = mg x

x = 12 m

totall length = 15+12 = 27 m

but height of buliding is 45 m

so larry was murdered.

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