There is a small sphere inside the tube. The tube rotates in a vertical plane, s

Question

There is a small sphere inside the tube. The tube rotates in a vertical plane, so that the sphere remains at the end of the tube and describes a vertical circle of radius 0.6m. The mass of the sphere is 0.05 kg and tube is made to rotate at constant angular speed of 10 radians per second. a.) Calculate the magnitude of the acceleration of sphere. b.) What are the period and frequency of rotation of the tube? c.) Find the magnitude of the horizontal reaction force exerted by the end of the tube on the sphere when the tube is horizontal. d.) Find the magnitude of the vertical reaction force exerted by the end of the tube on the sphere when the sphere is at its lowest point.

Explanation / Answer

acceleration = W^2 R = 60 m/s^2 W= 10 rad/s f= 2 pi /W= 0.628 Hz. T= 1/f= 1.59 s. reaction= mg + mW^2 R = 3.49N

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