Free Body Diagram: Explaining 3 Cord Tensions for Block C

[princejan7]

Homework Statement

http://postimg.org/image/5h0hvdi4l/
Can someone explain why the FBD of Block C would involve three cord tensions?

Homework Equations

The Attempt at a Solution

 

[Doc Al]

Can someone explain why the FBD of Block C would involve three cord tensions?

Whoever is claiming that is probably considering the bottom pulley, which is connected to block C, as part of the block C system. Perfectly OK.

But you certainly do not have to! If you consider block C separately, you'll also need a diagram for that bottom pulley.

 

[SteamKing]

Can someone explain why the FBD of Block C would involve three cord tensions?

It can't. There are only two cords directly connected to block C.

Now, if you were to make a horizontal cut between the two smaller sheaves, you would have the tension in three cords to consider.

 

[princejan7]

Whoever is claiming that is probably considering the bottom pulley, which is connected to block C, as part of the block C system. Perfectly OK.

But you certainly do not have to! If you consider block C separately, you'll also need a diagram for that bottom pulley.

http://postimg.org/image/oxb74l6t1/

so here they've considered the block + the bottom pulley as the system?
is there any reason for why they did that instead of just considering Block C as the system?

 

[Doc Al]

http://postimg.org/image/oxb74l6t1/

so here they've considered the block + the bottom pulley as the system?

Yes, for the purpose of that FBD they consider 'block + bottom pulley' as a single unit.

is there any reason for why they did that instead of just considering Block C as the system?

Just saves a bit of time. If you just considered Block C alone, you'd have to do another FBD for the bottom pulley to figure out the tension in the cable connecting it to the block. No big deal; either way is fine.