Radius from Radial Acceleration

[bbaker77]

An unbanked circular highway curve on level ground make a turn of 90 degree. The highway carries traffic at 60 mph, and the centripetal force on a vehicle is not to exceed 1/10 of its weight. What is the minimum length of the curve in miles?

I am working towards the arc contained within the angle theta which is 90 degrees. I have easily determined that of course, that arc is 25% of the circumference. I am trying then to find the radius. I have worked backwards here, fiddling with Ar=V^2/R as well as MA = mv^2/r. I am stuck though. Not really looking for the answer, just a shove in the right direction as that I would REALLY like to get this one on my own. I just don't have the physics brain.

 

[turdferguson]

Youre on the right track. Fc < MG/10. R must be greater than something

 

[bbaker77]

With Fc being the centripetal force = Mass(Gravity)/10? Thats assuming a mass then, since I don't know it, right?

 

[turdferguson]

Right, but it will cancel out as you suspect

 

[bbaker77]

Because of the force of friction.. I seem to be getting more lost than I was now.

 

[turdferguson]

They ask for centripetal force, which is a sum of forces. You don't need to split it up any further. Like I said, mv^2/r < mg/10. Note the mass on both sides. No arc length, no friction, but make sure to convert to SI

 

[bbaker77]

Ah. Told you I have no capacity for physics. Or sleep these days.

 

[bbaker77]

I figure a curve (arc) length of no less than 7.36 miles based on my work. Wow. There is no way that is right. Thats a heckuva curve. (the problem calls for the old british system. I would rather work SI, trust me.)