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 = 3.20 m long, joining particles of mass m1 = 0.130 kg and m2 = 57.0 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 13.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation.

Find the maximum speed that the small-mass object attains when it leaves the trebuchet horizontally.
m/s

Explanation / Answer

conserving energy

m2*g*H = m1g*h + 0.5*m2v2^2 + 0.5*m1*v1^2

here H = height of m2 below pivot = 13cms = 0.13 m

Final energy of m1 = 0.5*m1*v^2 +m1gh

here v2 is horizontal velocity of m2 nad v1 is horizontal velocity of m1 finally and h, is hight when m1 is leving horizontally

so h = d - 13cms = 320-13 = 307 cms = 3.07 m

substituting values

57*9.8*0.13 = 0.13*9.8*3.07 + 0.5*57*v2^2 + 0.5*0.13*v1^2

let w be the final angular velocity,

so v1=w*h, v2=w*H

substitute v1 and v2 in above equation
we get 72.618 = 3.911 + 28.5(w*0.13)^2 + 0.065(w*3.07)^2
so w^2 = 68.707/(28.5*0.13^2 + 0.065*3.07^2)

so w^2 = 15.913

so w = 3.99

and v1 = h*w = 3.07*3.99 = 12.25 m/s

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