The 4 kg ball and the attached light rod rotate in the vertical plane about the

Question

The 4 kg ball and the attached light rod rotate in the vertical plane about the fixed axis at O. If the assembly is released from rest at? = 0 and moves under the action of the 60 N force, which is maintained normal to the

rod,determine the velocity of the ball as theta approached 90 degrees.

Treat the ball as a particle.

The 4 kg ball and the attached light rod rotate in the vertical plane about the fixed axis at O. If the assembly is released from rest at? = 0 and moves under the action of the 60 N force, which is maintained normal to the rod,determine the velocity of the ball as theta approached 90 degrees.

Explanation / Answer

considering ball as particle

at the centre we have

4*9.8=39.2N force due to 4 kg ball

torque = 60*0.2-39.2*0.3 = 0.24 N-m

I=mr^2 = 4*(.3)^2 = 0.36 kg-m2

torque = I*a

a= 0.24/0.36 = 1/3

we have final velocity v^2=v1^2+2*a*thita

initial vel=0 so v1=0

v=sqrt(2*1/3*pi/2) = 1.02 s^-1

linear velocity=v*r = 1.02*0.3 =0.307 m/s   

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