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Question

The friction coefficient between the two blocks shown in figure (6-E9) is μ but the floor is smooth.
(a) What maximum horizontal force F can be applied without disturbing the equilibrium of the system?
(b) Suppose the horizontal force applied is double of that found in Part (a). Find the accelerations of the two masses.


Solution

Both upper block and lower block will have acceleration 2 m/s^2.

R1=mg,  f=μR1T=0TμR1=0
and Fμmg=TT=μmg
Putting T=μmg,F=μmg+μmg=2μmg
(b) 2F=Tμmgma=0Tmaμmg=0T=ma+μmg
Putting value of T in (i), we have
 2FMaμmgμmgma=0
Putting F=2μmg
2(2μmg)2μmg=a(M+m)
4μmg2μmg=a(M+m)
a=2μmgM+m
Both blocks move with this acceleration 'a' in opposite directions.
 

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