Centripetal Acceleration & Frictional Force

[amaryllia]

Homework Statement

A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve having a radius of 75.0 m?

Homework Equations

Fc = m(v^2/r)

Fc = net centripetal force
m = mass
v = tangenital speed
r = radius

The Attempt at a Solution

The answer I got is what is in the back of my book, but I am unsure if I took the right path to get to the answer and if my reasoning is sound. Any feedback would be greatly appreciated!

In a free body diagram of this problem the only force acting in the radial direction is the force of static friction keeping the car on the road. Although the problem does not state this directly, I'm assuming that the truck is taking the second curve of radius 75.0 m under the same road conditions as the first curve. If this is true, then the net centripetal force would be equal in both curves (the force of static friction is the same on both curves).

If Fc = m(v^2/r) and Fc is the same in both situations, then I can set m(v^2/r) of the first curve equal to the second, getting:
m(v1^2/r1) = m(v2^2/r2)
where v1 = tangenital velocity of curve 1 = 32.0 m/s
r1 = radius of curve 1 = 150 m
v2 = unknown solving for
r2 = radius of curve 2 = 75 m

I can cancel out mass, and get:
32^2/150 = v2^2/75

For a solution, I get v2 = 22.6 m/s.

 

[rock.freak667]

Yes both your method and reasoning are correct.