Velocity of a Car Skidding: Solving for Maximum Speed on a Circular Turn

[mortho]

[SOLVED] Velocity of a car skidding

Homework Statement

A 2.20 103 kg car rounds a circular turn of radius 30.0 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.8, how fast can the car go without skidding?

Homework Equations

Fcentripital=ma
a=v2/t
v=2πr/t

The Attempt at a Solution

So i used F=ma and substituted F with Coefficient*mass*gravity and for ma i used
m 2πr/t and solved for t. Then i used the t for the velocity equation and solved it. I got 24.0 m/s but it was wrong. What did i do wrong?

 

[hage567]

a=v2/t

I believe you mean this $$a = \frac{v^2}{r}$$

It's r for radius in the denominator, NOT t for time. This is centripetal acceleration here.

Try to solve it again.

 

[mortho]

Thank you soo much for pointing that out but I'm having algebra problems, so if i used
v2/r but i have no velocity so i use 2πr\t but then i have two divisions, i know this probably is a very stupid question but I'm really bad at math. so how would i put that equation to equal to t. Would it be (coefficient*m*g)/m(2πr2) ? The answer i got was completely ridiculous so I'm guessing it's wrong.

 

[hage567]

but i have no velocity so i use 2πr\t but then i have two divisions

But you are trying to find velocity, so there is no need to substitute something in for it. You don't need to find the time, either. Just equate the frictional force into the first equation listed in your "relevant equations" and the proper term for "a". Solve for v.

 

[mortho]

Thanks. i feel so retarded now that you said that. I got carried away trying to find time that i didn't even realize i was looking for velocity in the first place. So i solved for it and got 15.3 m/s correct?

 

[hage567]

Looks reasonable to me.

 

[mortho]

Thank you!

 

[hage567]

You're welcome.