A particle P of mass m is projected horizontally with speed 7/2ga from the lowest point of
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A particle P of mass m is projected horizontally with speed √7/2ga from the lowest point of the inside of a fixed hollow smooth sphere of internal radius a and centre O. The angle between OP and the downward vertical at O is denoted by θ. Show that, as long as P remains in contact with the inner surface of the sphere, the magnitude of the reaction between the sphere and the particle is 3/2 mg(1 + 2cos θ).
Find the speed of P
i. When it loses contact with the sphere,
ii. When, in the subsequent motion, it passes through the horizontal plane containing O. You may assume that this happens before P comes into contact with the sphere again.
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Related Book For
Cambridge International AS & A Level Further Mathematics Coursebook
ISBN: 9781108403375
1st Edition
Authors: Lee Mckelvey, Martin Crozier
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