When the 1 kg ball starts to rotate around the horizontal circular path A with a

Question

When the 1 kg ball starts to rotate around the horizontal circular path A with a Constant speed of 1 m/s the rope connecting the ball passes through a pulley (in point C, not shown in the figure), which is fixed to the ceiling. A force F is applied as shown in the figure. If the force F on the cord increases, the ball rises and eventually reaches a new position and rotates around the horizontal circular path B. The distances between the pulley and the point-mass in the two conditions are shown in the figure. a. Determine the analytical relationship relating the applied force F and the angle theta_1. b. Determine the speed of the ball and the angle between the cord and vertical when the ball is rotating around the path B (a different force F is applied in this condition)

Explanation / Answer

a )

using equation

F = [ ( m g )2 + ( m v2 / L sin )2 ]1/2   

F = [ 1 X 9.82 + ( 1 X 1 / 0.62sin )2 ]1/2   

F = ( 9604 + 2.78 / sin21 )1/2  

b )

cos1 / sin1 = ( L2 sin2 ) g / V12

V1 X L1 X sin1 = V2 X L2 X sin2   

V2 = 2 sin1 / sin2   

V2 cos2 / 2 sin1 = 0.3 X 2 X sin1 X g / V23

V24 = 0.3 X 4 X g X sin21 / cos2

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