Solving Tension & Pulley Homework Problem

[jegues]

Homework Statement

See figure.

Homework Equations

$$\sum F_{y} = 0$$
$$\sum F_{x} = 0$$

The Attempt at a Solution

I can't see how to solve this. The only thing I can think of is the vertical forces of both sides of the pulley are going to equal the gravitational force of the mass in and that the two x components on each side of the rope will cancel.

I don't have the magnitude on the right hand side of the pulley and on the left hand side I don't have the magnitude or the angle. How do we solve this?

Thanks in advance.

 

[tiny-tim]

Hi jegues!

The question doesn't say that the pulleys are frictionless, but I think you'd better assume they are.

If so, then the tension T will be the same all the way along the rope.

 

[jegues]

If the tension is constant across the pulley, then isn't it just like ignoring the pulley and pulling on the rope directly?

See my FBD to get what I'm trying to say.

 

[tiny-tim]

Hi jegues!

No, because there's three arrows, one up-left, and two up-right, all with magnitude T.

 

[jegues]

because there's three arrows, one up-left, and two up-right, all with magnitude T

Thank you tiny-tim, with that I was able to solve it.

But for a conceptual clarification of why there is two up-right, is it because of the 2nd pulley the cord passes over?

Thanks again!

 

[tiny-tim]

No, it's because there's two ropes on the right …

you have to add the tensions (they happen to be the same, but if they weren't, you'd still add them)

 

[jegues]

But it's the same rope passing over the pulley, the tension should remain constant so why isn't it simply T instead of 2T?

 

[tiny-tim]

The weight doesn't know they're the same rope.