How fast is car moving when. .

[sona1177]

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

 

[collinsmark]

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, :uhh:, 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.

 

[sona1177]

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!

 

[collinsmark]

That seems much better to me.

 

[sona1177]

Thanks! :)