How fast will the pebble be travelling with respect to the center of the wheel

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SUMMARY

The problem involves calculating the tangential speed of a 24.6 g pebble embedded in a 28.7 in tire, subject to a maximum radial friction force of 19.3 N. The equation used is derived from Newton's second law, where the centripetal force equals the mass times the tangential velocity squared divided by the radius. The correct calculation yields a tangential speed of 16.9 m/s, but the user indicated this answer was incorrect, suggesting a potential miscalculation or misunderstanding of the parameters involved.

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Homework Statement



A 24.6 g pebble is stuck in the thread of a 28.7 in tire. If the tire can exert an inward radial friction force of up to 19.3 N on the pebble, how fast will the pebble be traveling with respect to the center of the wheel when it flies out tangentiall?

Homework Equations



a = v^2 / r

The Attempt at a Solution



I got:

19.3 N = (m*v^2)/r => v^2 = (19.3 * r) / m = (19.3N * 0.36449 m) / 0.0246 kg = 16.9 m/s = final answer = INCORRECT ?

This problem is supposed to be easy, but I don't know what I'm doing wrong here. Anyone?
 
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I can't see what's wrong with it.
 

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