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

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 = 3.25 m long, joining particles of mass m1 = 0.110 kg and m2 = 71.5 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 (b) While the small-mass object is gaining speed, does it move with constant acceleration? Yes No (c) Does it move with constant tangential acceleration? Yes No (d) Does the trebuchet move with constant angular acceleration? Yes No (e) Does it have constant momentum? Yes No (f) Does the trebuchet—Earth system have constant mechanical energy? Yes No

Explanation / Answer

r1 and r2 the distance from the rotation axis to mass m1 and m2 respectively.

r1 = d - r2

r1 = 3.25 - 0.15 = 3.1 m

energy conservation

0 = m1g*r1 - m2gr2 + 1/2*I*w^2

0 = m1gr1 - m2g*r2 + 1/2(m1r1^2 + m2*r2^2) * (v/r1)^2

v = r1 * sqrt([2g(m2r2 - m1r1) / (m1r1^2 + m2r2^2) ]

given = m1 = 0.110 kg

m2 = 71.5 kg

r1 = 3.1 m

r2 = 0.15 m

v = 27.086 m/s

part b )

No , acceleration vector will change

part c ) and part d )

No . because torque will be change , distance will go from r1 to 0

part e )

No initialially L = 0 but after L = Iw

part f )

yes .

because here we assume sum of all forces = 0

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