Cornering on a Smooth Surface

[mangolucy]

Homework Statement

A car of mass m = 1000kg is driven round a smooth circular track of radius r = 250m and takes a time T = 30s to complete one lap. At what angle theta must the track be banked to counteract the tendency of the car to slip sideways?

Relevant Equations

w = 2pi/T
mrw^2 = Nsin theta
mg = Ncos theta
where N is the normal force perpendicular to the track, g = 9.81 ms^-2, and theta is the angle between the track and the horizontal plane.

I have tried to rearrange these equations to get a value of theta but somehow I didn't get the right answer. I am required to put my final answer in degrees.

 

[berkeman]

Welcome to PF.

Can you say in words what each one of those equations represent? What would you want to set equal to balance the forces on the car going around the circular banked track?

Also, it would help if you could upload a sketch that you have made showing the Free Body Diagram (FBD) of the car on the banking -- that will show the forces that you need to balance. Use the "Attach files" link below the Edit window to upload a JPEG or PDF of your sketch. Thanks.

 

[haruspex]

Homework Statement: A car of mass m = 1000kg is driven round a smooth circular track of radius r = 250m and takes a time T = 30s to complete one lap. At what angle theta must the track be banked to counteract the tendency of the car to slip sideways?
Relevant Equations: w = 2pi/T
mrw^2 = Nsin theta
mg = Ncos theta
where N is the normal force perpendicular to the track, g = 9.81 ms^-2, and theta is the angle between the track and the horizontal plane.

I have tried to rearrange these equations to get a value of theta but somehow I didn't get the right answer. I am required to put my final answer in degrees.

Please post your answer - maybe it is right. In case it isn't, it will save time if you also post your working.