A catapult with a radial arm 4.00 m long accelerates a ball of mass20 kg through

Question

A catapult with a radial arm 4.00 m long accelerates a ball of mass20 kg through a quarter circle. The ball leaves the apparatus at 45m/s. If the mass of the arm is 25 kg and the acceleration isconstant. find
a. anglular acceleration.
b. the moment of inertia of the arm and ball
c. the net torque exerted on the ball and arm
hint: use time-independent rotaional kinematics equation tofind the angular acceleration rather than angular velocityequation. find
a. anglular acceleration.
b. the moment of inertia of the arm and ball
c. the net torque exerted on the ball and arm
hint: use time-independent rotaional kinematics equation tofind the angular acceleration rather than angular velocityequation.

Explanation / Answer

length of arm l = 4.00 m mass of ball m = 20 kg the ball accelerates for a quarter circle that is =(/4) radians The ball leaves the apparatus at v = 45 m/s mass of arm M = 25 kg a.the time for which the ball accelerates is v = u + gt u = 0 or t = (v/g) the angular displacement is = wot + (1/2)t2 wo= 0 or = (1/2)t2 or = (2/t2) is anglular acceleration. b.the moment of inertia of the arm is I = m * (l2/3) the moment of inertia of the ball is (1/2)m * v2 = (1/2)I * w2 I is moment of inertia of ball I is moment of inertia of ball or m * v2 = I * (v/r)2 = I *(v2/r2) or I = m * r2 ---------(1) the angular speed is w = wo + t wo= 0 or w = t We know that v = r * w or r = (v/w) -----------(2) from (1) and (2) I = m *  (v/w)2 c.the net torque exerted on the ball is = F * r = m * g * r the net torque exerted on the arm is = F * l = M * g * l substitute the values c.the net torque exerted on the ball is = F * r = m * g * r the net torque exerted on the arm is = F * l = M * g * l substitute the values

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