Centripetal acceleration of ball and rope

[blader324]

Homework Statement

An athlete swings a 5 kg ball horizontally on the end of a rope. the ball moves in a circle of a radius .800m at an angular speed of .500rev/second. if the maximum tension the rope can withstand before breaking is 100N, what is the maximum tangential speed the ball can have?

Homework Equations

I think you have to use net forces in the 'y' direction, as well as omega_final^2=omega_intial^2+2alpha(delta theta)

The Attempt at a Solution

i've drawn a free body diagram of the 5kg mass at the bottom of a circle (so that the centripetal acceleration is going directly upwards). i know i have to solve for alpha. can i do that by solving for the acceleration through the net forces in the y direction with the free body diagram?

 

[mgb_phys]

The centredal force acts outward (in the x direction if you like) the weight acts downward (in -y). The tension in the rope is just the force triangle of these two.

 

[blader324]

i thought that at the bottom of the circle, the centripetal acceleration would be going upwards?

 

[mgb_phys]

I assumed horizontal to mean the circle was horizontal, like swinging a hammer throw around your head?

But in any case the centripedal accel always acts outwards away form the axis.

 

[blader324]

oh okay...i think that might help