Understanding Tension in a Vertical Pendulum: Calculation and Explanation

[Joza]

I know this may sound very simple, but I am actually a bit confuses about it.

Say, in a pendulum swinging in a vertical plane. How does one calculate the tension in the string ( no mass) ,which is connected to a bob (mass m), at various points, say like and angle beta with the vertical?

I know its a very simple idea, but it is actually confusing me. I think I am doing it wrong. If someone could run thru it quickly, I mite see my mistake.

Cheers guys

 

[waht]

Draw a free body diagram of the bob. What forces are acting on it? The sum of all forces in X direction equals zero and like wise in Y direction. Once you derive the magnitude of the tension in X and Y direction, how would you calculate the magnitude of that vector?

 

[Joza]

Would the sum in x direction be zero since the pendulum is swinging? Isn't it acceleration in a horizontal direction?

 

[Doc Al]

Haven't we discussed this at length in your other thread?

I told you several times what to do. Did you try it?

(Also: Don't post the same question in multiple threads!)

 

[Joza]

This is actually a different question

It's a bit different but no matter how I try it my answer is wrong. I must be seriously flawed somewhere

 

[Doc Al]

I would not conclude that you were seriously flawed, but your approach may well be.

As always, identify the forces and apply Newton's 2nd law. Hint: The acceleration has a radial and a tangential component. Treat them separately.

 

[Joza]

Thanks, I'll try that in a second. But just to give you an idea of my reasoning, say the pendulum passes through the vertical.

My diagram says there are 2 forces on the bob, weight acting down, and tension in string acting upward. And these 2 should be equal in magnitude. Is THIS right?

 

[Doc Al]

My diagram says there are 2 forces on the bob, weight acting down, and tension in string acting upward.

This is right.

And these 2 should be equal in magnitude.

This is wrong.

Hint: What's the acceleration? Hint 2: What kind of motion is this?

 

[Joza]

Circular?

So my equation for the sum of y forces would be:

T - mg = (m(v)^2)/R ??

 

[Doc Al]

Right!

 

[Joza]

Hoorah!

Ok so that's for the vertical position, and it seems straight forward, I just forgot about the acceleration. But what about say at an angle theta with the vertical?

 

[Doc Al]

Analyze force components parallel to the string. Apply Newton's 2nd law. (Sound familiar?) Hint: Find the speed.

 

[Joza]

But if that angle is its maximum, won't speed be zero?

 

[Doc Al]

But if that angle is its maximum, won't speed be zero?

Sure, if the angle is the maximum angle. (But you just said angle theta. ) I trust you can solve your earlier problem now?