# UCM problem

#### ffrpg

The problem reads, A boy whirls a stone in a horizontal circle, 1.6m above the ground, by means of a string. The radius of the circular motion is 1.0m. The string breaks and the stone hits the ground 5.0m from the point directly below where the string broke. What was the magnitude of the centripetal acceleration of the stone while it was experiencing circular motion, before the string broke?

I used the formula a=v^2/r. I started off by trying to find v by using the formula v = squareroot of rg. So v=sqrt(1.0)(9.81). After finding v I used the formula T= 2 pi r/ v. I didn't get the right answer. I've looked through my book, and can't find an example similar to this. I don't know how to use the other info given to me, like knowing the circle was 1.6m above the ground and knowing that it landed 5.0m away.

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#### Tom Mattson

Staff Emeritus
Gold Member
Originally posted by ffrpg
I used the formula a=v^2/r.
Yes, that's right.

I started off by trying to find v by using the formula v = squareroot of rg. So v=sqrt(1.0)(9.81).
That is not right.

You have to solve a projectile motion problem to find v. That is how you use the information given about the stone landing 5.0m away. If you call the breaking point of the string the origin (0m,0m), then the stone lands at the point (-1.6m,5.0m). The only unknown in the projectile motion problem is vi, the speed with which the stone left its circular path. That is also the speed it had in its orbit.

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