finding the radius of a curve

mikep

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?

Pyrrhus

Do the forces analysis and find which force component is working as the centripetal force.

mikep

well there is no friction force so the only thing pushing it to the center would be the acceleration, is that right?

Pyrrhus

Actually it will be a component of the normal force, try to draw all the forces on our particle, Normal and weight.

mikep

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?

Pyrrhus

[tex] Ncos\theta = mg[/tex]

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

Look at the triangle....

mikep

oh i get it. its R = (v^2)/(tanθ g)
thank you for your help!