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In the arrangement shown, the apppreciable friction exisits only b/w the bodym and the wedge.The frictional coeff being equals to @. The masses of pulley and the thread are negligible. Show that the acc of body m w.r.t the horizontal surface on which the wedge slides is given by

mg / [2m+@m+M]

7 years ago


Answers : (1)



fbd of m

fbd of M

let the acceleration of m in horizontal direction be  a, then from fbd.

        N = ma..............................(1)

the acce. of the M will also be a,

so,     T - N = Ma

     T- ma = Ma .....................................(2)

from the constraint of the length of the cord,

    the vertical accel. of  m  will be the same as horizontal one,

balancing the vertical forces on m ,

    mg -T - @ma = ma

   mg -T -ma (@+1)  =0 ......................................(3)

putting T = Ma +ma   from eq. (2)   to (3)    we get,

    mg - (M+m)a - ma (@+1) = 0

     (2m+ M + @m) a = mg

     a = mg /(2m+ M + @m)


7 years ago

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