Derive the displacements movable pulleys.

[Legendon]

Homework Statement

Obtain the accelerations of mass a and mass b.

Homework Equations

Once i derive the displacement relation constraint, then i just have to diff twice w.r.t time. This part is ok.

The Attempt at a Solution

I am trying to reason this way: suppose 2M moves up by x. Following the right string of 2M to pulley2 then to pulley 1 = This means pulley1 move down by x. Following the left string of 2M to pulley1 = this causes M to move down by x. So M moves by 2x. the acc of m must be 2a and acc of 2m is a. but the answer is m acc at 3a and 2m acc at a.

 

[ehild]

The right piece of the left string gets shorter by 2x when the block B rises by x, as the left pulley descends by x. So the left block moves down by 2x with respect to the left pulley.

ehild

 

[Legendon]

Ok, I'm getting it. The right piece of left string gets shorter by 2x meaning that the left piece of the right string must increase by 2x thus left block moves 2x w.r.t left pulley. Since left pulley is moving at dist x w.r.t right pulley. left block is moving 3x wrt right pulley. this explains the 3:1 acc ratio. Am I right.
Thanks

 

[ehild]

It is right now.

ehild