Question regarding setting up Newton's second law equations

[MrJoseBravo]

Homework Statement

So the question revolves around two blocks, one of mass A and one of mass B. The Mass A block is on a smooth horizontal surface, connected by a thin chord that passes over a pulley to the second block, of Mass B. The question asks to draw a free body diagram of both objects, and then apply Newtons second law to find the formulas for the acceleration of the system, and for the tension of the chord.

Homework Equations

block a: ƩF=Ft=ma

block b: ƩF=Ft-mg=ma

The Attempt at a Solution

I am able to draw the free body diagram, but when i try to find the formulas i get confused. I looked up the answer to the acceleration formula on the back of the book, and it is
g(m(b))/m(a)+m(b). I worked backwards to find this, but i had to re-arrange my block b equation to ƩF=mg-Ft=ma, in order to get the acceleration. What i did was i substituted the block B (Ft) with the block A (ma), and then solved for acceleration. My first question regards the block B equation, i could not solve for the answer with my original equation (Ft-mg) , i had to flip them. How do i know which force comes first in the equation? Secondly, was my substitution between the two formulas correct? Thank you for your help!

 

[PhanthomJay]

Two simultaneous equations can be solved by substitution or adding the equations together to elimimate one of the variables. Your substitution method is correct.

Note that acceleration is always in the direction of the net force. If the block on the table accelerates to the right, the hanging block must accelerate down. Therfore the net force on the hanging block must also act down. So which is greater..Mg or Ft?

 

[MrJoseBravo]

the Mg would be greater since it is accelerating downwards, right? I think i grasp it now, the acceleration depends on the net force, so the placement of the variables in the formula is determined by the motion of the object.

So the motion force comes first in the equations? is this a full-proof or are there instances where it could be different, say when there is a component force you have to take into consideration.

thanks for your help!

 

[PhanthomJay]

Acceleration is always in the direction of the net force which acts on an object. It is not always in the direction of the motion of the object. Suppose you throw a ball straight up in the air. It's motion is up, but the net force acting on it, it's weight, mg, acts down. So it's acceleration must be in the down direction, in the direction of the net force, not the motion. Or if you push a block up a plane with friction , then let go, both friction and the component of the gravity force act down the plane, so they add to give a net force down the plane, and the acceleration is down the plane. This latter example makes use of component forces ...it is often best to break up forces into their perpendicular component vectors, and look at accelerations in each of the directions independently.