Mechanics> friction...

Find the acceleration of mass M in the situation of figure. The coefficient of friction between the two blocks isµ1and that between thebiggerblock and the ground isµ2.

Jayesh Arun Kadam , 14 Years ago

Grade 12

5 Answers

Badiuddin askIITians.ismu Expert

Last Activity: 14 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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Faraz Nassar

Last Activity: 8 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

Last Activity: 7 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

Last Activity: 7 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

Last Activity: 7 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.