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Find minimum ratio of cofficient of frictions between block and block to block and surfacevso that both masses move together with application of force F.

Asked by anandpatel1081995 | 12 Oct, 2019, 07:54: PM
Figure shows two block of masses M1 = 5 kg and M2 = 10 kg . M1 is placed on M2 .

Friction coefficient between blocks is μ1 . Friction coeffienet between block M2 and  surface is μ2

Free body diagrams of both the mass blocks are given and forces acting on each block are shown

Normal force N1 acting on mass M1 is given by,  N1 = M1 g  = 5×10 N = 50 N

friction force f1 = μ1 N1 = ( 50 μ1 ) N

friction force f1 acting on mass M2 is due to reaction force of f1 acting on M1

Normal force N2 = (M1 + M2) g

friction force f2 acting on mass M2 is given by,  f2 = μ2 N2 = (10+5)×10×μ = ( 150 μ2 ) N

if applied force F ≥ f2  and  F ≤ f1 , system of two blocks move together

To get minimum ratio of friction coefficients let us consider the force are equal just balancing, i.e, F = f1 = f2

hence ,  50 μ1 = 150 μ2   or  μ1 / μ2 = 3
Answered by Thiyagarajan K | 12 Oct, 2019, 09:20: PM

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