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

Question

14-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 = 2.70 m long, joining particles of mass m1 = 0.110 kg and m2 = 63.0 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 15.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation.

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

Explanation / Answer

the centripetal force on both the masses balance therefore

m1 x v1^2/r1 = m2 x v2^2/r2

or v1^2 = r1/m1 x m2/r2 x v2^2

or v1 = (m2 x r1/m1 x r2)^1/2 x v2

where m2 = 63.0 kg,m1 = 0.110 kg,r1 = (2.70 - 0.15) m and r2 = 0.15 m and v2 is the speed of mass m2

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