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. Model it as a stiff rod of negligible mass 3.00 m long and joining particles of mass 65.0 kg and 0.160 kg at its ends. It can turn on a frictionless horizontal axle perpendicular to the rod and 14.0 cm from the particle of larger mass. The rod is released from rest in a horizontal orientation. Find the maximum (a) angular speed.
(b) linear speed that the object of smaller mass attains

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. Model it as a stiff rod of negligible mass 3.00 m long and joining particles of mass 65.0 kg and 0.160 kg at its ends. It can turn on a frictionless horizontal axle perpendicular to the rod and 14.0 cm from the particle of larger mass. The rod is released from rest in a horizontal orientation. Find the maximum (a) angular speed. (b) linear speed that the object of smaller mass attains

Explanation / Answer

Torque about the pivot
= (65*9.8*0.14 - 0.160*9.8*3)*cos(?)

So the work done is integral (65*9.8*0.14 - 0.160*9.8*3)*cos(?)d? (evaluated from 0 to ?/2) =
(65*9.8*0.14 - 0.160*9.8*3)*(sin(?/2) - sin(0)) = 84.476J

Work = ?K = 1/2*I*?^2 where I = 65*0.14^2 + 0.160*3^2 = 1.754kg-m^2

1) ? = sqrt(2*W/I) = sqrt(2*84.476/1.754) = 9.814rad/s

2) v = r*? = 23*9.814 = 29.44m/s

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