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

AI Thread Summary
A 1.2 g pebble is held in place by a maximum static friction force of 3.6 N in a 0.76 m diameter tire as the car accelerates. The problem involves determining the car's speed when the pebble dislodges. The correct approach uses the centripetal force equation, leading to the calculation of velocity without dividing by 2. The final calculations yield a speed of approximately 38 m/s, indicating the importance of accurately applying the physics principles involved. Understanding the relationship between static friction and centripetal force is crucial for solving similar problems.
lila.haj
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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
Fc=(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).
 
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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
 

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