Work out the tension on a string

[jimmy42]

How can I work out the tension on a string, with some mass at one end? The mass is being spun around?

So, there are three forces Weight (W), acting only in the negative y direction and the centripetal force (C) acting only in the positive x direction. Tension (T) can be viewed as the hypotenuse of the right angle triangle?

So if W = mg and C = mrw^2. What is T?

I could do this using pythagorus' theorem is it were numbers but how to do it with only letters?

Thanks.

 

[PhanthomJay]

I believe you are talking about uniform circular motion in a horizontal circle. There are actually just 2 forces acting on the mass...its weight force acting down, and the tension sttring force acting at an angle relative to the x axis. The centripetal force is the horizontal component of the tension force. You'll need to apply Newton's laws in both the vertical and horizontal direction to solve for T and the angle it makes with the horizontal, assuming r and v are known.

 

[jimmy42]

Thanks, I got this

http://en.wikipedia.org/wiki/File:Centrifugal_governor_forces.PNG

How can i get the equation for tension? Thanks for any help.

 

[PhanthomJay]

Forget the sketch labeled with the 'reactive centrifugal', and even the 2nd sketch is unclear, because it shows a centripetal force which tends to look like a third force, but it is not. There are 2 forces acting on the mass...the tension force in the rod, and its weight. The rod makes a certain angle theta with the horizontal. Use Newton 1 in the y direction to get one equation, and Newton 2 in the x direction to get a second equation. Note please that the horizontal component of the tension force is the centripetal force arising from the centripetal acceleration. Please show an attempt at a solution.

 

[jimmy42]

Yes I got the two forces, so weight (W) = Mg and centripetal force(C) = rw^2. So W acts only in the negative y direction and C only in the positive x direction. Tension is the hypotenuse. So I have a right angle triangle.

I need to somehow add these together to find the Tension, is that right? So I put T= rw^2-mg. I know that is not true but don't know what to do?

Am I on the right track?

 

[PhanthomJay]

Yes I got the two forces, so weight (W) = Mg

yes, that's one of 'em

and centripetal force(C) = rw^2.

No, the other force is the tension force.

So W acts only in the negative y direction and C only in the positive x direction. Tension is the hypotenuse. So I have a right angle triangle.

In the y direction, W acts down and the vertical component of the tension force acts up. What is the vertical component of the tension force in terms of the angle theta? What do these 2 'y' forces sum to, per Newton 1? In the x direction, only the horizontal component of the tension force acts to the right. It IS the net centripetal force in the center-seeking (horizontal) direction. Use Newton 2 in this direction, since a net force results in an acceleration in the direction of that force. Then solve 2 equations with 2 unknowns.

I need to somehow add these together to find the Tension, is that right? So I put T= rw^2-mg. I know that is not true but don't know what to do?

Am I on the right track?

You have to use vector components before you can do your algebraic additions