Centripetal Force / Inclined Plane Question

[Dooga Blackrazor]

A car is rounding a 515 m frictionless curve in the highway. If the curve is banked at an angle of 12.0 degrees, what is the maximum speed of the car? (1.5)

I achieved an answer of 32.39 m/s or 116.604 km/h . I used an incline plain to find that Fc = mgsin12 and used that to find the answer along with the Fc = mvsquared / radius formula. I made them equal canceled the mass and solved for V - got the answer above. The answer isn't avaliable so if anyone could check it I would appreciate the assistance.

 

[Pyrrhus]

I suppose we are assuming a circular track?

 

[zwtipp05]

Fc does not equal mg sin 12
It is actually equal to Fn sin 12

It's a common mistake in centripetal force problems to assume that the normal force is equal to the force of gravity, but in fact it is not. I have attached a diagram that is generic to most centripetal force problems. The normal force is actually the resultant of the centripetal force and gravity.

 

[Dooga Blackrazor]

I think we assume a circular track. Thanks - the diagram is pending approval. Is there a formula for Fn in a centripetal force problem?

 

[Pyrrhus]

Actually, the centripetal force is just a role given to forces (components) acting towards the center, not another force...

Now if we assume a circular track of 515m arc length you can find the radius, and then work the FBD to find v

 

[mukundpa]

Normal reaction is to be resolved horizontally and vertically. vertical component balances the weight and horizontal provides the required centripetal force to move the car on the curve.

If the track is frictionless the only speed you get for the car not to slide up or down, what is meant by maximum speed? think....

 

[Dooga Blackrazor]

Oh, I meant a circular track, but I think it is a half of a circle. I think 515 is supposed to be the radius - I could be wrong though.

Maximum speed is Fc = mvsquared / radius formula = by solving for Vsquared you can find the maximum speed (I assume).

 

[zwtipp05]

Yeah, you're on the right track. Try solving it again and post your answer here and I'll let you know what I got when I solved it.