Question

The axis of a smooth fixed ciular cylinder of radius R is horizontal. A particle of mass m is attached to a model string and is initially at rest level with the cre of the cylinder with the string draped over the top, whee t slids without frictian as if on a model pulley, s shown in the diagram below. A constant force P of magnitude P pulls the model string downwards. Let 0 denote the angle subtended at the axis of the cylinder between the initial position of the particle and its current position. Let e, and ee be the radial and tangential unit vectors, as shown i the diagram. Tn page 2 of 6 (a) Draw a orce diagra shwing l the fo acting on the particle. (b) Express each force in terms of the unit vectors shown in the diagram. 3 (e Derive the equation of motion of the particle. Resolve radially and tangentially to show that the tangential component is given by Pmg cos 6 where g is the magnitude of the acceleration due to gravity respect to t, determine θ2 as a function of 9, and hence show that the mR (a By multiplying the equation in part (c) by and integrating with magnitude of the normal reaction of the cylinder on the particle is 3mg sin 0 2P

Answer 1

(Cy 此レ庇 7)