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Find the acceleration of mass M in the situation of figure. The coefficient of friction between the two blocks is µ1 and that between the bigger block and the ground is µ2.

147 Points
11 years ago

dear jayesh

let normal reaction between two block is N1 ,and the normal reaction between biggger block and ground in N2

for smaller block

so mg - T -μ1N1 =m2a.....1

N1=ma .............2

for bigger block

N2 =Mg +μ1N1 +T

or  N2=Mg + mg-2ma (from equation 1).......3

and  T +T -N1 -μ2N2=Ma

2T -ma -μ2(Mg +mg-2ma) =Ma ........4

put value of T from equation 1

2(mg -μ1ma-2ma) -ma -μ2(Mg +mg-2ma) =Ma

solve for a

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Regards,

Faraz Nassar
11 Points
4 years ago
Why is N2= mg +u1N1 + T as u1N1 and T are in opposite direction to Mg? And why did we take 2T in the equation of M?
Vineeth Chennabhoina
14 Points
4 years ago
N2 is the normal reaction force on the bigger block, it’s equal to the sum of it’s own weight, and u1N1 because the smaller as the smaller body goes down, it rubs against the bigger body, and the friction between them is u1 and the Normal reaction between them is due to the weight of the smaller body. And T because, do you see the upper pulley attached to the bigger body, that’s causing a tension T on the body.

And we’ve taken 2T in the equation because there’s two sets of ropes that have tention T in them, the top and the bottom, the vertical rope doesn’t have tension in it. That’s why we’ve taken 2T.

I hope that clarifies your doubts Faraz.
shubham choubey
26 Points
4 years ago
How do we know that smaller block have 2a accl. And bigger block have a accl.??? Since it is not given in question...
Soumyajit Bagchi
14 Points
3 years ago
we can assume that the bigger block is moving with acceleration a then the smaller block will fall with 2a acceleration as when the bigger block moves a distance d the lower ripe length reduces by d and the small block falls d and also the upper pulley is connected with the bigger block thus the upper rope also reduces by d and the block again has a fall of d thus, a displacement of d in the bigger block has a displacement of 2d in the smaller block....and thus calculating you can see why while the upper block has acceleration of a and the smaller block an acceleration of 2a.