Find the upward acceleration of the man

[avistein]

because we have not yet established that there is no acceleration

But here in the man+platform problem,how can we consider that the force applied by the man has no acceleration? then only we can write T-mg/2=0=>T=mg/2

 

[Doc Al]

But here in the man+platform problem,how can we consider that the force applied by the man has no acceleration? then only we can write T-mg/2=0=>T=mg/2

You do not assume no acceleration. You apply Newton's 2nd law and deduce it. (Here you are told that T = mg/2.)

 

[BvU]

Ah, now we are back to the original exercise somewhat. The idea is that you draw all the forces, including the gravitational forces (ahem, the weights). With the pulleys transferring the man's pulling force to the tensions in the ropes to the platform, you then have all that is needed to establish the acceleration of the platform. And then you will find ...

So: back to business and an answer to the question: what other forces play a role on the system in the dotted ellipse ? (post #21)

 

[BvU]

But here in the man+platform problem,how can we consider that the force applied by the man has no acceleration? then only we can write T-mg/2=0=>T=mg/2

Could it be that there is something in the concept of a tight rope -- with or without a pulley -- that hasn't completely settled in your mind? Just a hunch on my part, and believe me: it is so common and so basic that it is very, very often overseen.

So pardon me if I repeat the obvious (it will be of use many more times in PF, anyway):

In statics and in dynamics a tight, massless rope

• transfers force from one end to the other end.
  
  you pull the rope, the rope pulls whatever is attached at the other end​
• the forces on each end are equal and opposite
  
  Like action = - reaction at a distance
  the magnitudes of the forces must be exactly equal
  otherwise the rope itself would accelerate (with "infinite" acceleration, according to ΔF = ma)​
• the forces are aligned with the rope
  otherwise the rope would move sideways
  

  (Try it: push sideways against a dangling rope!)​

  If the rope is slung over a pulley, this is still true for all sections of the rope
  (a section is a straight piece of rope with a distinct direction
  -- it can be considered as a separate rope attached to something else
  -- the something else can also be a section of rope)
  ​

(open for clarifications, error correction, further questions)