Basic forces question with a pulley problem

[Eitan Levy]

Homework Statement

A boy holds the rope so it can't move. What is the tension in point A?

Homework Equations

ma=F

The Attempt at a Solution

The answer in the book is 4N. I understand how to get it, but, I believe that the tension of S1 would be 9N (due to m1), and then the forces on m2 would be gravity, T_A and T_S1. Together, we don't get zero, but 3N. Is there a problem or am I wrong?

 

[haruspex]

A boy holds the rope so it can't move. What is the tension in point A?

No way of knowing without being told where the boy is holding the rope.
If somewhere on S1 then the tension at A will indeed be 4N (and your other method doesn't work because you are not taking into account the force the boy exerts).
If somewhere on S2 then it will depend exactly where on S2.

 

[Eitan Levy]

No way of knowing without being told where the boy is holding the rope.
If somewhere on S1 then the tension at A will indeed be 4N (and your other method doesn't work because you are not taking into account the force the boy exerts).
If somewhere on S2 then it will depend exactly where on S2.

He holds S1, but I still don't understand how the forces will work.

 

[haruspex]

He holds S1, but I still don't understand how the forces will work.

So add that force, and note that the tensions will be different each side of where that force is applied.

 

[Eitan Levy]

So add that force, and note that the tensions will be different each side of where that force is applied.

So on the left side it would be 9N and on the right side 6N?

 

[haruspex]

So on the left side it would be 9N and on the right side 6N?

If the boy holds S1 at the top, yes. But he might be holding it half way up one side.