How Fast Is the Car Moving When the Pebble Flies Out of the Tire Tread?

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Homework Help Overview

The problem involves a pebble embedded in the tread of a tire, with the context centered on determining the speed of a car at the moment the pebble dislodges due to static friction. The subject area includes concepts from dynamics and rotational motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between static friction and the forces acting on the pebble, with some questioning the relevance of torque in this context. There are attempts to apply equations of motion and centripetal force to find the speed of the car.

Discussion Status

Some participants have provided calculations and alternative interpretations of the forces involved, while others express uncertainty about the assumptions being made. There is no explicit consensus on the approach, but a potential direction has been suggested regarding the treatment of forces.

Contextual Notes

Participants note the challenge of determining the distance the pebble travels along the circular path, which is critical for solving the problem. There is also mention of the maximum static friction force and its implications for the motion of the pebble.

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Homework Statement



A 1.2 g pebble is stuck in a tread of a .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?

Homework Equations


alpha=net Torque/I=FR/MR^2

so: (3.6)(.38)/(.0012)(.38^2)=7895 rad/s^2

now my plan is to use s=R * theta to find theta (where s is the distance the pebble travels along the circular pathway), plug that value into wf^2=wi^2 + 2alpha * theta and then use the value I get for Wf in equation v=wr to get v. but the problem is I don't know how to find s because I don't know what distance the pebble travels along the circular pathway. Can someone please help? Thank you :)


The Attempt at a Solution

 
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sona1177 said:
A 1.2 g pebble is stuck in a tread of a .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?

Homework Equations


alpha=net Torque/I=FR/MR^2

so: (3.6)(.38)/(.0012)(.38^2)=7895 rad/s^2
I'm not quite sure what is meant by your above calculations, :rolleyes:, But I don't think the 3.6 N should be assumed to be a tangential force. In other words, I don't the solution has anything to do with torque.
now my plan is to use s=R * theta to find theta (where s is the distance the pebble travels along the circular pathway), plug that value into wf^2=wi^2 + 2alpha * theta and then use the value I get for Wf in equation v=wr to get v. but the problem is I don't know how to find s because I don't know what distance the pebble travels along the circular pathway. Can someone please help? Thank you :)
I would approach this problem treating the 3.6 N as being directed radially. I.e., think centripetal force. :wink:
 
Hi okay so F=mv^2/r that means 3.6=.0012 * v^2/.038. V=34 m/s. Is this correct? Thank you so much for all your help!
 
That seems much better to me. :approve:
 
Thanks! :)
 

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