A war-wolf , or trebuchet , is a device used during the Middle Ages to throw roc

Question

A war-wolf, or trebuchet, is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling pumpkins and pianos. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass 3.00 m long and joining particles of mass

m1 = 0.120 kg

and

m2 = 53.5 kg

at its ends. It can turn on a frictionless horizontal axle perpendicular to the rod and 13.0 cm from the particle of larger mass. The rod is released from rest in a horizontal orientation. Find the maximum speed that the object of smaller mass attains when it leaves the trebuchet horizontally.
m/s

Explanation / Answer

The 63.5 kg mass has a potential energy of 53.5*9.81*0.13 = 68.22 J
The 0.120 kg mass requires an extra potential energy of 0.120*9.81*(3m-0.13m)=3.37 and kinetic energy of 1/2*0.120v^2 = 3.37 + 1/2*0.120v^2 .
Energy is conserved so:
68.22 - 3.37 - .06v^2 = 1/2*53.3(v*0.13/2.87)^2
65.85 - .06v^2 = .0546v^2
65.85= .114 v^2
v^2 = 577.63
v = 24 m/s

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