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finding the radius of a curve

 
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Oct16-04, 05:01 PM   #1
 

finding the radius of a curve


can someone please help me, i can't figure out where the angle on the free body diagram for this problem. i was thinking of using newton's second law with a = v(squared)/R would this work?

A car goes around a curve on a road that is banked at an angle of 27.0°. Even though the road is slick, the car will stay on the road without any friction between its tires and the road when its speed is 23.0 m/s. What is the radius of the curve?
 
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Oct16-04, 05:11 PM   #2
 
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Do the forces analysis and find which force component is working as the centripetal force.
 
Oct16-04, 05:46 PM   #3
 
well there is no friction force so the only thing pushing it to the center would be the acceleration, is that right?
 
Oct16-04, 06:04 PM   #4
 
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finding the radius of a curve


Actually it will be a component of the normal force, try to draw all the forces on our particle, Normal and weight.
 
Oct16-04, 06:39 PM   #5
 
oh ok so
sumF = Ncosθ = m ((v^2)/R)

sumFy = Nsinθ - mg = 0

i used this and i solved for R = (v^2)/cotθ but i didn't get the correct answer. can you please tell me what i did wrong?
 
Oct16-04, 06:43 PM   #6
 
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[tex] Ncos\theta = mg[/tex]

[tex] Nsin\theta = ma_{c}[/tex]

Look at the triangle....
 
Oct16-04, 06:48 PM   #7
 
oh i get it. its R = (v^2)/(tanθ g)
thank you for your help!
 
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