A catapult with a radial arm 4.12 m long accelerates a ball of mass 19.3 kg thro

Question

A catapult with a radial arm 4.12 m long accelerates a ball of mass 19.3 kg through a quarter circle. The ball leaves the apparatus at 40.9 m/s. The mass of the arm is 29.4 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.

____________ rad/s2

(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

Explanation / Answer

Let angular velocity be w, angular acceleration be a

wf^2 = wi^2 + 2*a*theta

We know that v = w*r and vf = 40.9 so wf = 40.9/4.12 = 9.93
Assume wi = 0 and theta = pi/2
a = 9.93^2/pi = 31.37 rad/s2

The energy imparted to the ball is the energy in the catapult
1/2 *I*w^2 = 1/2 *m*v^2 = 0.5*19.3*40.9^2 = 16142.6J
I = 327.42  kg · m2

Torque = I*a = 10271.2 Nm

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