Physics Help!!!!?

Question

A curve of radius 155 m is banked at an angle of 24°. At what speed can it be negotiated under icy conditions where friction is negligible?

I think I can get it but i dont know how i am going to use just angle and radius to solve this. I need to somehow get the force to get velocity but i dont have mass. Help?

Answer 1

To follow the curve, there needs to be a centripetal force towards the center. The centripetal force is given by
Fc = m*v^2/r.

The car's weight is given by
W = m*g
The component of the weight that is down the bank of the curve (towards the center of the arc), is given by
Wd = m*g*sin(24).

The down-bank component of weight, Wd, will provide the required centripetal force Fc, if the velocity is right. So
Wd = Fc
m*g*sin(24) = m*v^2/r

See how the mass will cancel out? Solve for v. That's the magic velocity that goes with that amount of bank. The car can be in a major sideways slide and stay on the curve, if the velocity is right.