Physics question-don't know where to start

Question

A 2000 kg car is traveling on a banked curved icy road. The velocity of the car is 25.0

m/s and the road has a radius of curvature of 500 m. If the car is to travel on the icy

road without sliding, then the angle of the banked road is?

I know which formula to use but don't know how to rearrange it to find the angle.

Answer 1

Assume that the coefficient of friction between the car and road is 0, because the road is icy.

m = 2000 kg, v = 25 m/s, r = 500 m.

First, we have to find the centripetal force required to keep the carve accelerating inward around the bank. using the equation F = mv²/r

Next, we find the angle of the road at which portion of the force of the road on the car inward will equal the force of the centripetal acceleration.

The inward portion of the force on the road is mg*tanθ, thus, equating the two equations gives

1. F = mg*tanθ = mv²/r

cancelling out m and isolating θ, we get

1. θ = tan^-1(v²/rg)

As we can see, the mass of the vehicle ends up not having an influence on the required curvature of the road. Plugging the values above into the deduced equation, we get

1. θ = tan^-1(25²/(500*9.81)) = 7.26º

Answer:

1. θ = 7.26º