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I have 2 doubts,questions are in the attached image. How can I find the acceleration of the individual blocks and the pulley(s) if the pulley itself is moved upwards? In the second question, I used constraint relations to find the relations between accelerations. I got 2a 1 +a 2 +a 3 = 0.After this , I also got the freebody equations. BUt while substituting for a 1 for eg, do I substitute as (- a 2 - a 3 ) /2 or ( a 2 +a 3 ) / 2, or this approach totally wrong. Please clarify.Thanks in advance.

I have 2 doubts,questions are in the attached image.
  1. How can I find the acceleration of the individual blocks and the pulley(s) if the pulley itself is moved upwards?
  2. In the second question, I used constraint relations to find the relations between accelerations. I got 2a1 +a2+a= 0.After this , I also got the freebody equations. BUt while substituting for afor eg, do I substitute as   (-a2 - a3) /2 or (a2+a3) / 2, or this approach totally wrong. Please clarify.Thanks in advance.

Question Image
Grade:11

1 Answers

Sandeep Pathak
askIITians Faculty 25 Points
6 years ago
Problem 1:
Approach: You calculate Tension forces on blocks by dividing applied force as F->F/2->F/4. Now calculate acceleration of a block is F/4m – g. If it is less than zero, a = 0. Acceleration of a pulley is equal to (a1+a2)/2 where a1, a2 are accelerations (rate of change of change of length) of two sides of string.
 
Problem 2: Your approach is totally correct. You got the correct constraint equation. 
If m1 is moving to right and both m2, m3 moving downwards, you apply a1=(a2+a3)/2.
Also keep in mind that these acceleration are in the reference frame of earth.

Please let us know if that clarifies your query or you need further explanation.
Thanks,
Sandeep

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