Question

A tetherball leans against the smooth, frictionless post to which it is attached. The string is attached to the center of the ball. If the string is L = 1.20 m long and the ball has a radius of r = 0.150 m with mass m = 0.250 kg , what is the magnitude T of the tension in the rope and what is the magnitude FP of the force the pole exerts on the ball?

Answer 1

So Vgravity = Xtension since it's not moving. And there's a right-triangle which you use pythagorean theorem.

Let's start with Vgravity. Using F=ma, Do you know the force of gravity of the ball?

Answer 2

I see you went offline instantly...

If you ever get back. You can find the force of gravity using F = ma:
Gravity = (0.25kg) * (9.8m/s^2)
Then you know that gravity = Y-component of the tension of the string. (Sorry I had a typo in my post above, it should be Vgravity = Ytension)

To find the T, you need to know Xtension. You can use trig to find the angle.
Angle = cos^-1( 0.15/12)

Once you have the angle, apply it to the force diagram I drew on the right.
sin(Angle) = ytension / T

And that's how you solve for T.

Answer 3

Oh and FP is basically just X-component of the force.
You can easily find that with trig.

tan(Angle) = ytension/xtension

where xtension = FP