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Question

Consider the situation shown in the figure. The horizontal surface below the bigger block is smooth. The coefficient of friction between the blocks is μ. Find the minimum and the maximum force F that can be applied in order to keep the smaller blocks at rest with respect to the bigger block.
768363_265df7c249b0402abc6f8911fcad368f.png

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Solution

ref. image I
ma+μmg=T ___(1)
force on block 2 are :-
(i) gravitatia force = mg
Ref. image II
μma+T=mg ___(2)
Given: the horizontal surface below the bigger block is smooth. The coefficient of friction between the blocks is μ
To find the minimum and the maximum force F that can be applied in order to keep the smaller blocks at rest with respect to the bigger block
Solution:
Force acting on block 1 are:
(i) gravitational force = mg downward
(ii) Normal force exerted by the surface of block 3 = N1 (upward)
(iii) The force of the tension exerted by the string = T (towards right)
(iv) Friction force = μN1
(v) Pseudo force = ma
So adding the equation (1) and (2) shown in above figure, we get
ma+μmg+μma+T=T+mga+μg+μa=ga(μ+1)=g(1μ)a=g(1μ1+μ)
Hence the force is,
ma=mg(1μ1+μ)F=mg(1μ1+μ)

1003759_768363_ans_8826c7ec7cec4609baecc139c81abbec.png

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