Physics Circular Motion

Question

An engineer is trying to determine the maximum speed at which a vehicle travel around the curve without skidding. She know the coefficient of friction between the wheels and the road is 0.75 when the road is dry and 0.35 when the road is wet. She knows that the mass of the vehicle does not matter, but completes her calculations for a 900kg car.

Answer questions for the case when the car is traveling at the maximum speed that will allow it to navigate the in both wet and dry conditions.

Should she perform her calculations with the coefficient of friction for wet or day pavement?

In this case, what is the car's centripetal acceleration?

m/s2

In this case, what is the car's speed?

m/s

mph

Could vehicles, obeying a speed limit of 65mph, navigate the curve on wet or dry pavement?

Answer 1

You really need the radius of curvature to solve this. If we leave the value as R for the radius, we would solve for the case with the lowest coefficient of friction (low coefficient corresponds to less friction).

On an unbanked curve, the only force providing the centripetal force is friction (which is why you would skid off if going too fast!).

since centripetal force is Fc = m ac

and friction can be expressed as μN, so on an unbanked curve where normal is equal and opposite to weight, Ff = μmg

set those equal to each other

m ac = μmg

ac = μg = 0.35 x 9.81 = 3.43 m/s^2

There are two ways to solve for velocity. If you hadn't already found acceleration, you would set centripetal force equal to friction as follows:

mv^2/R = μmg

Since we already know centripetal acceleration, we can solve using ac = v^2/R. As I noted the problem did not provide the radius, so I will leave it as R

3.4335 = v^2/R

3.4335R = v^2

sqrt(3.4335R) = v

Obviously, you can't solve further without radius.

But, for example, say the radius was 250 m

v = sqrt (3.4335 x 250) = 29 m/s (2 s.f.)

in km/h = 105 km/hr or 65 mph.