physics problem?

Question

A car is to make a turn without skidding on an unbanked curve with a radius of 90 meters. If the coefficient of friction is 0.64, what is the maximum speed of the car can have?

Answer 1

First step is to break everything down. We'll define r as radius, which equals 90m. Since I can't make the appropriate greek symbol in this font, we'll use u for coefficient of friction, which equals 0.64. Now, we will be using M as a place-holder for mass (with any luck, it will cancel out at some point). You're looking for the absolute value of the tangential velocity (in other words, the car's speed), and we'll use v to denote this. Also, g is going to represent the acceleration due to gravity.

Centripital force is equal to M(v^2)/r

The only force which would provide a centripital acceleration is the force of friction on the tires.

Frictional force is equal to u*N, where N is the normal force of the object against the surface.

In this case, N = Mg. Plugging this in, we get that the frictional force is equal to uMg.

Since the frictional force IS the centripital force, we can say uMg = M(v^2)/r

Now, M cancels out and we're left with ug = (v^2)/r

Solving for v gives us v = sqrt[r*u*g]

Plugging in 90 for r, 0.64 for u, and 9.8 for g, we get v = 24.76 m/s. The absolute value of v is still 23.76, so that is your speed.

Answer 2

Ffric=ma
umg=mv^2/r
.64(9.8) = v^2/90

and solve for v.

Answer 3

v= sqr( r*u*g)

v= sqr(90m * .64 * 9.8m/s^2)
v= 23.76m/s