Calculating the Radius of a Banked Curve Using Newton's Second Law

[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]

$$Ncos\theta = mg$$

$$Nsin\theta = ma_{c}$$

Look at the triangle...

 

[mikep]

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