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

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The discussion revolves around calculating the speed of a car when a pebble flies out of its tire tread. The pebble, weighing 1.2 g, is held by a maximum static friction force of 3.6 N while the car accelerates. The initial calculations involve using torque and angular acceleration, but there is confusion regarding the application of these concepts. One participant suggests treating the friction force as a centripetal force, leading to the conclusion that the car's speed is 34 m/s when the pebble dislodges. The conversation emphasizes the importance of correctly interpreting forces in rotational motion to solve the problem effectively.
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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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