Hanging mass on a massless pulley

[kasnay]

Homework Statement

A 3.5kg block is on a tabletop and is attached by a string to hanging block of mass 2.8 kg. The blocks are released from rest and allowed to move freely. If the table has a coefficient of friction of 0.4

A) Find the Acceleration

Relevant Equations

fnet x and fnet y

I have a conceptual question about this problem.
I can write the 3.5 kg block equation as Fnet(block 1)=(Force of tension)-(Force of friction)=m1a
I can write the 2.8 kg block as Fnet(block 2)=(Force of tension)-(Force of gravity2)=m2a

My question is this
If I set the forces of friction equal I get the wrong answer. However If I assume the fnet of block 2 is negative (because its going to fall) I get the correct answer.
Why do I need to assume the second block fnet is negative? Shouldnt the math already account for what needs to happen?

 

[TSny]

You used the same symbol $a$ for the acceleration of both blocks. That means you are assuming the two blocks have the same acceleration - including the sign of their acceleration. If you take the positive direction for block 1 to be in the direction of the tension force acting on block 1, then what must be the positive direction for block 2 (downward or upward)?

 

[Lnewqban]

I can write the 2.8 kg block as Fnet(block 2)=(Force of tension)-(Force of gravity2)=m2a

My question is this
If I set the forces of friction equal I get the wrong answer.

How can tension and weight of mass 2 have different values?
How those two compare if you screw mass 1 to the table?

You mention forces of friction, but there is only one, if mass 2 is freely hanging from the pulley.