Physics 220

You are a highway engineer who wants to design a freeway segment that has a radius of curvature of 500 m. The road is to be banked so that cars travelling at 25 m/s have no friction on the tires. What should the bank angle be?

Side view

Draw a free body diagram showing all the forces acting on the car. Then decide on the direction of the acceleration and draw it in your diagram too. Hint: where is the center of the circle?

Now choose your coordinates.

Fill out the table showing the components of the forces in terms of their magnitudes.

Force

x-component

y-component

n

nsinq

ncosq

W

0

-mg

Sum of force components

å Fx = nsinq

å Fy = ncosq - mg

Acceleration

a = mv2/r

0

Now apply Newton's second law. You should have two equations in terms of two unknowns. (Hint: the mass of the car should be considered a known quantity.) Eliminate the one unknown you don't want to find the angle of the bank.

nsinq = mv2/r

ncosq - mg = 0

Eliminate n by dividing:

tanq = v2/rg = (25 m/s)2/(500 m)(10 m/s2) = 0.125

So

q = 7