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A ball slides without friction down an inclined groove from a height h and then follows a closed loop of radius R (Fig.). What is the force exerted by the ball on the groove at a point B, if the radius from the centre of the loop to point B makes an angle a with the vertical? The mass of the ball is m, the height h equals 5/2R. The dimensions of the ball can be taken to be negligibly small.

 

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Answer: F = 3mg(1 - cosα).

Explanation:

Newton's second law and the of conservation of energy lead to the equations

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