Tension and Centripetal Acceleration?

Question

Two wires are tied to the 500 g sphere shown in figure. The sphere revolves in a horizontal circle at a constant speed of 8.30 m/s.

What is the tension in the upper wire?

What is the tension in the lower wire?

This is a link to the figure:

http://session.masteringphysics.com/problemAsset/1000599/6/knight_Figure_07_61.jpg

Answer 1

Consider components of force on the sphere in the horizontal and vertical directions. Let T_u denote the tension in the upper wire and let T_l denote the tension in the lower wire.

The horizontal components of tension supply the centripetal force:

mv²/r = T_u cos 30º + T_l cos 30º

The sphere does not accelerate in the vertical direction, so the net force in the vertical direction is zero:

T_u sin 30º = mg + T_l sin 30º

m and v are given, and r can be determined from your diagram.

Solve for T_u and T_l