6.  In the figure masses m1 , m2 and M are 20 kg, 5kg and 50 kg respectively.  The coefficient of friction between M and ground is zero.  The coefficient of friction between m 1   a n d   M and that between m2 & ground is 0.3.  The pulleys & the string are massless.  The string is perfectly horizontal between P1 & m1 and also between P2 & m2 .  The string is perfectly vertical between P1 & P2 .  An external horizontal force F is applied to the mass M.  [ Take g = 10 m/s2 ]

a)  Draw a free-body diagram for mass M, clearly showing all the forces.
b)  Let the magnitude of the force of friction between m1 and M be fand that between m2 and ground be f2 . For a particular F it is found that f1 = 2f2 .  Find f1 and  f2  Write down equations of motion of all the masses.  Find F, tension in the string and accelerations of the masses.

Dear Student,


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