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

1. Mar 4, 2013

### lila.haj

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. 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).

2. Mar 4, 2013

### 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.

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