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

Question

Awar-wolfortrebuchetis 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=3.20m long, joining particles of massm1=0.100kg andm2=59.0kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and15.0cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation.

Explanation / Answer

Torque about the pivot = (59*9.8*0.15 - 0.100*9.8*2.80)*cos(?) So the work done is integral (59.9*9.8*0.15 - 0.100*9.8*2.80)*cos(?)d? (evaluated from 0 to ?/2) = (59.9*9.8*0.15 - 0.110*9.8*2.80)*(sin(?/2) - sin(0)) = 85 Work = ?K = 1/2*I*?^2 where I = 59.9*0.15^2 + 0.110*2.80^2 = 4.10kg-m^2 So ? = sqrt(2*W/I) = sqrt(2*85/4.10) = 41.46rad/s So v = r*? = 2.80*41.46 = 116.09m/s

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