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 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 = 69.5 kg at its ends. It can turn on a frictionless horizontal axle perpendicular to the rod and 13.5 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.

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 p/2) = (73.5*9.8*0.15 - 0.130*9.8*2.80)*(sin(p/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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