The acceleration of the block B in the above figure assuming the surfaces and the pulley P1 and P2 are all smooth

Question

Calculate the acceleration of the block B in the figure, assuming the surfaces and the pulleys P₁ and P₂ are all smooth and pulleys and string are light(take F = 17N and m = 1kg)

Answer 1

The surfaces and the pulleys P₁ and P₂ are 3.

Comments

What does this answer mean?

Answer 2

Let T be the tension acting throughout the string. And also a and b be the accelerations of block A and B respectively.

So considering the forces on A we can write

F-2T= 2ma.............(1)

Again considering the forces on B we get

3T = 4mb.............(2)

Due to application of force for small interval of time t ,

the displacement of A will be =1/2at^2

and the displacement of B will be =1/2bt^2.

During this time work done by 2T and 3T will be same

Hence 2T×1/2at^2=3T×1/2bt^2

=> 2a= 3b..........(3)

From (1) and (2) we get  

F - (8/3)mb= 2ma......(4)

Combining (3) and (4) we get

F -(8/3)mb = 3mb

=>(17/3)mb =F

÷> b = (3F)/(17m)

Inserting F =17N and m =1kg we get

Acceleration of B , b= 3m/s^2

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