# Tension in a rope on frictionless pulley

1. ### simon360

15
1. The problem statement, all variables and given/known data

A 4kg object is palced on a table with a coefficient of friction of 0.2, and attached to a rope. This rope is run through a frictionless pulley, and attached to an 8kg weight. What is the tension in the rope?

2. Relevant equations

F=ma
F of friction = (coefficient of friction)(Force normal)

3. The attempt at a solution

Force normal of weight = 8(9.8) = 78.4
Force normal of object = 4(9.8) = 39.2
Force of friction on object = 0.2(39.2)

I don't know where to go from here, and I have an exam tomorrow. Help would be greatly appreciated, obviously :P

Thanks, I hear you guys are the best for quick physics help ;)

### Staff: Mentor

Apply Newton's 2nd law to each mass, then combine the two equations.

3. ### simon360

15
So add both forces from F=ma together?

### Staff: Mentor

Not sure what you mean. What I mean is: Apply F=ma to each mass separately. You'll end up with two equations that you will solve together.

What forces act on each mass?

5. ### simon360

15
Well, the weight is pulling the object because it is hanging off the table, through the pulley...

### Staff: Mentor

What pulls on the object is the tension in the string. (Of course that tension also pulls up on the weight.)

7. ### simon360

15
Ahh, I think I get it (but physics has confused me from the start, so bear with me). The tension is essentially a net force?

### Staff: Mentor

No. "Net force" just means the total force on an object. The tension is just one of several forces.

9. ### simon360

15
Alright, I'll be honest, I still don't get it :(

This was a quick question I came up with to demonstrate what I need to know. What would be the tension? Then I could figure out how to actually get it.

### Staff: Mentor

Start by applying Newton's 2nd law to the hanging mass. What forces act on it?

11. ### simon360

15
Gravity times its own weight, and the object on the table (which I presume can act as friction). Anything I'm missing?

The object on the table is also prone to friction, and the weight that is hanging pulls back on it.

### Staff: Mentor

Stick to the forces acting on the hanging mass. Yes, its weight is one force. What's the other? (Forget about the object on the table for the moment. We'll analyze that one next.)

13. ### simon360

15
I can't think of any, unless you mean the rope/tension itself.

### Staff: Mentor

Of course I mean the rope tension!

There are two forces acting on the hanging mass: The rope tension, which acts up; the weight, which acts down.

Now apply Newton's 2nd law.

15. ### simon360

15
Haha, thought that would be too easy :P

The force down = 8(9.8) = 78.4 N

Not sure how to deal with the rope tension, tbh...

### Staff: Mentor

The rope tension is unknown, so just call it T. (You'll end up solving for it.)

17. ### simon360

15
Oh, ok.

So the net force is F down - T

### Staff: Mentor

The net force on the hanging mass is $T - m_2 g$, where $m_2$ equals 8 kg.

19. ### simon360

15
Alright, so essentially just the reverse: T - 78.4.

### Staff: Mentor

OK, now apply Newton's 2nd law.