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A very small cube of mass III is placed on the inside of a funnel (see Fig.) rotating about a vertical axis at a constant rate of w revolutions per second. The wall of the funnel makes an angle θ with the horizontal. The coefficient of static friction between cube and funnel is μ s and the center of the cube is at a distance r from the axis of rotation. Find the (a) largest and (b) smallest values of ω for which the cube will not move with respect to the funnel.

A very small cube of mass III is placed on the inside of a funnel (see Fig.) rotating about a vertical axis at a constant rate of w revolutions per second. The wall of the funnel makes an angle θ with the horizontal. The coefficient of static friction between cube and funnel is μs and the center of the cube is at a distance r from the axis of rotation. Find the (a) largest and (b) smallest values of ω for which the cube will not move with respect to the funnel.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
(a)
Use Newton’s second law of motion for the forces along the length of incline surface, and assume smaller angular velocity.
236-415_1.PNG
Also, the frictional force is given as:
236-352_1.PNG
236-658_1.PNG
(b) The figure below shows the forces on the block when the angular velocity of the funnel is extremely large:



236-198_1.PNG


236-1647_1.PNG
Also, the frictional force is given as:
236-970_1.PNG
236-1041_1.PNG

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