Question

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3.A spherical ball with a radius R = 120 cm is thrown on a uniform horizontal lane with initial speed of 9.0 m/s. The ball is thrown in such a way that it skids for a distance before it starts pure rolling. Its motion is purely translational when it first hit the lane. The coefficient of kinetic friction between the ball and the lane is 0.22. (a)For how long the ball skids? (b)How many revolutions does it make before it starts to roll? Note: 1 =(2/5)MRP) (7-points)

Answer 1

Sol" Initially ball will be skielding them frictional fore acting f = ung on the ball, Vo f c m m So, I VE fR A 11 So, acceleration of ball, q= -f — ут -MG as, clockwise are angular acceleration supports the velocity of ball Torque - obra f&R stime it' Now, velocity of ball at a Volgt Vot at 4 ongular relocidy at time to Wot ate of bet at time A ball stops skidding, and starts fure soiling motion so for this conditions VE RW vo- M9+= (BRUJR vo (ugt fR? Mgt Mmgre I 2 2 Vo tug 2x9 > HE1.191 Sed 7 *.0.22*9.81 Ang ta 1:19) fee a time after which hall starts rolling. time for which ball skids. = لا Vo MRE 5 so,

1 Ah Hng 'R th 2 2 2 <boked angular displacement is 'o for ball during this period So, O= Wont + 12 xt² Oz ot Žlt (AR) 3 mpe OE 5 (48.).+?=540.2249.81.8(1:19112 OF 127.657 vac) 8 127.657 of novoj udion, evolution, N= 20.317 So, Son No. of revolution made boj boll, IN= 20 0.12. 6 Sol no 29 2 l Na Ang