Minimum speed for a ball to complete a vertical loop of radius 2.25 m

[liz777]

Homework Statement

A ball has a radius of 2.25 m. What is the slowest speed of the ball at the bottom which will just make it around at the top of the path?

The Attempt at a Solution

I don't even know where to start with this problem. I don't understand it. Any help would be greatly appreciated!

 

[quantumdude]

I don't even know where to start with this problem. I don't understand it.

Neither do I, because you didn't type in the entire problem statement. I'm guessing that the ball is tethered to a rope of radius 2.25 m, but that's just a guess. Please type in the problem statement exactly as it appears on your assignment.

 

[liz777]

oh sorry...here it is:

When one spins a ball in a circular path which has a radius of 2.25 m, what is the slowest speed of the ball at the bottom which will just make it around at the top of the path?

 

[quantumdude]

You should begin by drawing a free body diagram of the ball at the top of its path. Then write down Newton's second law for the ball at that point. That's how you start all dynamics problems at this level.

 

[liz777]

ok, I drew a diagram and I think I understand. Gravity pulls down on the ball, which is the acceleration so:
v^2=gr
=(9.8)(2.25)

Is this correct?

 

[quantumdude]

Right, just remember to take the square root. You found $v^2$, not $v$.

 

[liz777]

ok, thank you! :) I understand it.