Static equilibrium and tension problem

[Vanessa23]

Homework Statement

Four blocks with masses 2kg, 4kg, 6kg, 3kg are held together with ropes with tensions Tx, Ty, Tz. There is a force of 20N pointing to the right and 50N to the left. Find Tz.

Homework Equations

The Attempt at a Solution

This is like the static equilibrium problems, yet everything is moving. How do I find Tz?

 

[Dale]

F=ma on each block. Since the ropes are not stretching a is the same for all blocks.

 

[Vanessa23]

So, since a is the same for all the blocks would I say:

50N-20N=15kg*a
a=2m/s

then F on box D would be Tz-48N=3kg*2m/s
Tz=54N

I feel hesitant not including the other masses and tensions...

 

[Dale]

I feel hesitant not including the other masses and tensions...

If you want to work out all of the other tensions for each mass you certainly can, but all it will do is make you feel more confident :)

EDIT:

Tz-48N=3kg*2m/s
Tz=54N

Where did the 48N come from, shouldn't that be either 20N or 50N depending on how the blocks are arranged?

 

[Vanessa23]

Sorry, I meant
Tz-20N=3kg*2m/s
Tz=26N

but why does it not matter what all of the other tensions, masses, and forces are? Why doesn't the calculation for Tz include the fact that there is a 50N force in the other direction as well as other blocks and other ropes?

 

[rl.bhat]

While calculating the acceleration of the whole system you have taken into account all the forces and masses. They have named the tensions as Tx,Ty and Tz to make sure that which tension you have to calculate, proveded you arrange the blocks in same order as given in the problem.

 

[Vanessa23]

So, then what would happen if the question asked for the middle tension?

 

[rl.bhat]

Wright the expression for Ty - Tz