Question

A block of mass m1 sits on a block of mass m2. Block m2 rests on a frictionless surface. The coefficient of static friction between block m1and m2 is µ. What is the maximum force F that can be applied to block m2 if block m1 is not to slip across the surface of m2? Express in terms of m1, m2, g, and µ.

Answer 1

There is no kinetic friction

F - F_sf = m1 a

But F_sf = m2 a ( for no slip condition )

F - m2 a = m1 a

F = (m1 + m2) a

F = (m1 + m2) F_sf / m2

maximum static friction is  µ m1 g

Hence

F_max = (m1+m2)  µ m1 g / m2

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Maximum force = µ ( m1/m2 ) ( m1 + m2 ) g