## A catapult with a radial arm 3.81 m long accelerates a ball of mass 18.2 kg through a quarter circle. The ball leaves the apparatus at 49.8

Question

A catapult with a radial arm 3.81 m long accelerates a ball of mass 18.2 kg through a quarter circle. The ball leaves the apparatus at 49.8 m/s. The mass of the arm is 22.6 kg and the acceleration is constant. Hint: Use the time-independent rotational kinematics equation to find the angular acceleration, rather than the angular velocity equation.

(a) Find the angular acceleration.

(b) Find the moment of inertia of the arm and ball.

kg · m2

(c) Find the net torque exerted on the ball and arm.

N · m

in progress 0
6 months 2021-07-24T02:50:14+00:00 1 Answers 10 views 0

(a)

(b)   I =428

(c)

Explanation:

GIVEN

mass = 18.2 kg

radial arm length = 3.81 m

velocity = 49.8 m/s

mass of arm = 22.6 kg

we know using relation between linear velocity and angular velocity

for  angular acceleration, use the following equation.

since

here  for one circle is 2 π radians.   therefore for one quarter of a circle is π/2 radians

so   for one quarter

on solving

(b)

For the catapult,

moment of inertia

For the ball,

so total moment of inertia =  428

(c)