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

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The discussion revolves around calculating the speed of a pebble that is stuck in a tire tread before it flies out tangentially. The pebble's mass is 24.6 grams, and the tire exerts a maximum radial friction force of 19.3 N. The user attempts to apply the formula a = v^2 / r but arrives at an incorrect final speed of 16.9 m/s. There is confusion regarding the calculations, prompting a request for assistance and a reference to a similar problem for further clarification. The thread highlights the challenges of applying physics equations accurately in practical scenarios.
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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.
 

Thread 'Errors and significant figures'

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Thread 'A cylinder connected to a hanging mass'

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Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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