# Archived Rolling Motion, Pebble stuck in a Tire by Static Friction

#### lila.haj

1. 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.

2. Homework 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).

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#### CWatters

Homework Helper
Gold Member
I believe the approach suggested by the OP gives the correct answer.

F=(mv^2)/r
Rearrange for v...
V=SQRT(Fr/m)
= SQRT(3.6*0.38/0.0012)
= 33.76m/S

This is the Velocity of the top of the wheel. The Velocity of the car is half that..

33.76/2=16.88m/S

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