Mastering Physics: Rolling Motion, Pebble stuck in a Tire by Static Fr

[lila.haj]

Homework Statement

A 1.2 g pebble is stuck in a tread of a 0.76 m diameter automobile tire, held in place by static friction that can be at most 3.6 N. The car starts from rest and gradually accelerates on a straight road. How fast is the car moving when the pebble flies out of the tire tread? I know the answer is 17 m/s however I don't know how to get it.

Homework Equations

v=(2*\pi*R)/T
v=ωR
\alpha=τ/I
I=1/2*M*R²
F_c=(m*v²)/2

The Attempt at a Solution

I tried using the centripetal force equation and rearranged for velocity, using the maximum static friction as my force. I then divided that number by 2 to get the speed in the centre of the wheel (since the speed at the top of the wheel is twice the speed of the vehicle).

 

[lila.haj]

Problem Solved!

I found the solution, I used the centripetal force equation like I explained above, but I did not divide by 2 at the end.

F_c=mv²/r
v=√(F_cr/m)
v=√[(3.6 N)(0.38 m)/(0.0012kg)]
v=33.76388603 m/s
v=38 m/s