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

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 large vegetables and pianos as a sport. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass, d = 2.85 m long, joining particles of mass m1 = 0.125 kg and m2 = 55.0 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 12.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation.

Explanation / Answer

Torque about the pivot
= (73.5*9.8*0.15 - 0.130*9.8*2.80)*cos(?)

So the work done is integral (73.5*9.8*0.15 - 0.130*9.8*2.80)*cos(?)d? (evaluated from 0 to ?/2) =
(73.5*9.8*0.15 - 0.130*9.8*2.80)*(sin(?/2) - sin(0)) = 104.5J

Work = ?K = 1/2*I*?^2 where I = 73.5*0.15^2 + 0.130*2.80^2 = 2.67kg-m^2

So ? = sqrt(2*W/I) = sqrt(2*104.5/2.67) = 8.847rad/s

So v = r*? = 2.80*8.847 = 24.8m/s

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