The Elementary Part of a Treatise On the Dynamics of a System of Rigid Bodies : Being Part I of a Treatise On the Whole Subject

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By oonsidering the particle m', we find the tension to be also m' {g sin a' -/cos a'). Equating these two we have j_ m' sin g' - m sin g "" m' cos a' + m cos a Hence F is found.
209. Ex. 2. A cylindrical cavity whose section is any oval cnrvc and wlwse generating lines are horizontal is made in a cubical mass which can slide freely on a smooth horizontal plane. The surface of the cavity is perfectly rough and a sphere is placed in it at rest so that the vertical plane through tlie centres of gr
...avity of the mass and the sphere is perpendicular to the generating lines of the cylinder.
A tnomentum B is communicated to the cube by a blow in this vertical plane. Find the motion of tlie sphere relativehj to the cube and the least value of the blow that the sphere may not leave tlie surface of the cavity.
Simultaneously with the blow B there will be an impulsive friction between the cube and the sphere. Let M, m be the masses of the cube and sphere, a the radius of the sphere, fc its radius of gyration about a diameter.


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