Radius from Radial Acceleration

In summary, the minimum length of the unbanked circular highway curve on level ground is approximately 7.36 miles. The curve must contain an angle of 90 degrees and carry traffic at 60 mph, with the centripetal force on a vehicle not exceeding 1/10 of its weight. The formula used to determine the minimum length is mv^2/r < mg/10, with the mass being cancelled out. The problem can be solved using SIAh or the British system, with the former being preferred.
  • #1
bbaker77
5
0
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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  • #2
Youre on the right track. Fc < MG/10. R must be greater than something
 
  • #3
With Fc being the centripetal force = Mass(Gravity)/10? Thats assuming a mass then, since I don't know it, right?
 
  • #4
Right, but it will cancel out as you suspect
 
  • #5
Because of the force of friction.. I seem to be getting more lost than I was now.
 
  • #6
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
 
  • #7
Ah. Told you I have no capacity for physics. Or sleep these days.
 
  • #8
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.)
 

Related to Radius from Radial Acceleration

What is radial acceleration?

Radial acceleration is the acceleration experienced by an object moving along a curved path. It is directed towards the center of the circle or curve.

What is the formula for radial acceleration?

The formula for radial acceleration is ar = v^2/r, where ar is the radial acceleration, v is the velocity, and r is the radius of the circle or curve.

How does radial acceleration affect an object's motion?

Radial acceleration changes the direction of an object's velocity, causing it to continuously turn towards the center of the circle or curve. It also increases as the object's speed increases or as the radius of the curve decreases.

How does radial acceleration relate to centripetal acceleration?

Radial acceleration is another term for centripetal acceleration, which is the acceleration directed towards the center of a circle or curve. However, centripetal acceleration can also refer to any force that causes an object to move in a circular path, while radial acceleration specifically refers to the change in velocity.

Can radial acceleration be negative?

Yes, radial acceleration can be negative if the object is slowing down or moving in the opposite direction of the curve. In this case, the acceleration is directed away from the center of the circle or curve.

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