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 = 3.15 m long, joining particles of mass m1 = 0.115 kg and m2 = 55.0 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 the small object mass obtains when it leaves the trebuchet.

b) While the small-mass object is gaining speed, does it move with constant acceleration?

c) Does it move with constant tangential acceleration?

d)  Does the trebuchet move with constant angular acceleration?

e) Does it have constant momentum?

f) Does the trebuchet—Earth system have constant mechanical energy?

Please, could you draw a diagram and give me the "for dummies" version of your work and explain the intermediate steps? Thanks so much!!!

Explanation / Answer

Given,

d = 3.15 m ; m1 = 0.115 kg ; m2 = 55 kg ; r = 15 cm

a)The moment of inertia of m1:

Im = m1 (d - r)^2

that of me

I' = m2 r'^2

Itot = m2 r'^2 + m1 (d - r)^2

from conservation of energy

Ei = Ef

0 = m1 g r - m2 g r' + 1/2 I w^2

0 = m1 g (l - r) - m2 g r' + 1/2 [m2 r'^2 + m1 (d - r)^2] w^

w = sqrt [2 g [m2r' - m1(d - r)/(m2r'^2 + m1(d 0 r))^2]

Linear velocity is v r w

v = (d - r)sqrt [2 g [m2r' - m1(d - r)/(m2r'^2 + m1(d - r))^2]

r = 3.15 - 0.15 = 3

v = 3 sqrt [2 x 9.81 (55 x 0.15 - 0.1 x 3)/(55 x 0.15^2 + 0.1 x 3^2)] = 25.63 m/s

Hence, v = 25.63 m/s

b)No

it changes with direction

c)No

d)No

e)Yes

f)Yes

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