Radius from Radial Acceleration

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Homework Help Overview

The discussion revolves around calculating the minimum length of a circular highway curve given specific conditions related to speed and centripetal force. The subject area includes concepts of circular motion and forces acting on vehicles in motion.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to relate the arc length of a circular curve to its radius using centripetal force equations. They express uncertainty in their understanding of the physics involved and seek guidance without wanting a direct answer.

Discussion Status

Participants are engaging in a back-and-forth exploration of the problem, with some providing hints about the relationships between forces and the radius. There is acknowledgment of the need to convert units and a recognition that mass will cancel out in the equations, but no consensus has been reached on the correct approach or solution.

Contextual Notes

The problem is framed within the context of a real-world scenario involving a highway curve, and participants note the preference for working in SI units despite the problem being stated in the British system. There is also mention of constraints regarding the maximum allowable centripetal force relative to weight.

bbaker77
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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.
 
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Youre on the right track. Fc < MG/10. R must be greater than something
 
With Fc being the centripetal force = Mass(Gravity)/10? Thats assuming a mass then, since I don't know it, right?
 
Right, but it will cancel out as you suspect
 
Because of the force of friction.. I seem to be getting more lost than I was now.
 
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
 
Ah. Told you I have no capacity for physics. Or sleep these days.
 
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.)
 

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