Newton's Laws - Tetherball on a pole

[Trojanof01]

A tether ball leans against the post to which it is attached (Fig. 5-40). If the string to which the ball is attached is 2.00 m long, the ball has a radius of 0.300 m, and the ball has a mass of 0.400 kg, what are the tension in the rope and the force the pole exerts on the ball? Neglect any friction between the ball and the pole. (The string is attached to the ball such that a line along the string passes through the center of the ball.)

Find the Tention in the Rope

Find the Force of pole on ball

My work:

http://i14.tinypic.com/5xh73pf.jpg

Biggest problem has been trying to set up the free body diagram? Does it look right? How about the answers?

edit: sorry for poor quality, my scanner blows

 

[Doc Al]

Since there's no friction between ball and pole, the force of the pole must be perpendicular to the pole (and ball surface). Redo your FBD.

 

[m2003]

Yes, your free body diagram looks correct. The tension in the rope is the force that the ball exerts on the rope, and it is equal to the force of gravity acting on the ball (0.400 kg x 9.8 m/s^2 = 3.92 N). This is because according to Newton's third law, for every action, there is an equal and opposite reaction. So the tension in the rope is 3.92 N.

The force that the pole exerts on the ball is equal to the centripetal force that keeps the ball moving in a circular motion. This force is given by the equation Fc = mv^2/r, where m is the mass of the ball, v is the velocity of the ball, and r is the radius of the circular motion. In this case, the velocity of the ball is zero since it is leaning against the pole, so the force of the pole on the ball is also zero.

In summary, the tension in the rope is 3.92 N and the force of the pole on the ball is 0 N. This means that the pole is not exerting any force on the ball, but the tension in the rope is keeping the ball in equilibrium.