Draw the F.B.D. (Free Body diagram) of two blocks

[Shivam]

Summary: In the situation given, all the surfaces are friction less, pulley is ideal and string is light, F=mg/2, Find the acceleration of block 2 ?

Here's the diagram--

My attempt- (i) I tried to solve the question by making FBD of the two blocks, but i am not able to draw all the forces, the forces that i drew are not able to explain the motion of the blocks.

[Moderator's note: Moved from a technical forum and thus no template.]

 

[scottdave]

What forces act on the pulley?

 

[Shivam]

What forces act on the pulley?

Net √2F will be acting on pulley due to tension making an angle of -45° with +x-axis, and this Force has to be balanced by the opposite Force but I don't know how to associate this opposite Force and to whom should I associate .

 

[nasu]

You don't need to analyse the bodies separately to answer the question. Just consider the system and the horizontal external forces. The body 2 had no vertical acceleration.

 

[hutchphd]

Net √2F will be acting on pulley due to tension making an angle of -45° with +x-axis, and this Force has to be balanced by the opposite Force but I don't know how to associate this opposite Force and to whom should I associate .

The pulley is rigidly attached to the box (not with a rope). @nasu is also correct but there is nothing wrong with your method. You do need to include the pulley applying F to the right on the box through the attachment. It will also push down on the box with force F .

 

[Shivam]

You don't need to analyse the bodies separately to answer the question. Just consider the system and the horizontal external forces. The body 2 had no vertical acceleration.

I saw one method where these boxes are considered under a system. I understood that method , but I wanted to know FBD of the boxes separately and actually which force is opposing the contact force .. if can draw the FBD then please do post here.

 

[nasu]

Your FBD is almost correct. Just that F is horizontal and not vertical. The force acting vertically on the the small body is the tension in the string. As the pulley is rigidly connected to body 2, F acts horizontally on body 2. This is where is supposed to be in the FBD, if you split the system into two objects. If you consider the force in the pulley connection then you should have a 3 body diagram: body 1, body 2 and pulley. But you don't need this for the problem. Even 2-body is not necessary.