Minimum static friction problem

[AwesomeMan]

The problem reads:

A banked circular highway curve is designed for traffic moving
at 60 km/h. The radius of the curve is 200 m. Traffic is moving
along the highway at 40 km/h on a rainy day. What is the
minimum coefficient of friction between tires and road that will
allow cars to take the turn without sliding off the road?
(Assume the cars do not have negative lift.)

I managed to solve for the angle of the bank through the equation
angle = tan^-1((v^2)/gR). Where v=velocity, g=the acceleration of gravity,
and R=the radius of the curve.

My trouble is that after I solve for the angle I cannot think of anyway to solve for static friction without the weight or mass of the car. Am I thinking in the wrong direction to believe that i need the mass of the car?

It would be very appreciated if someone could point me in the right direction on this problem. Thanks.

 

[Doc Al]

My trouble is that after I solve for the angle I cannot think of anyway to solve for static friction without the weight or mass of the car. Am I thinking in the wrong direction to believe that i need the mass of the car?

While it may seem that you need the mass of the car (for example, how else can you find the weight = mg?), if you actually work it out the mass of the car will drop out of the final solution. Give it a try.

Don't rush to "plug in numbers" right away. Work it out algebraically, using symbols. Once you've done the algebra, then plug in numbers and calculate.

 

[wais]

The minimum coefficient of friction needed for the cars to take the turn without sliding off the road can be calculated using the formula μ = tanθ, where μ is the coefficient of friction and θ is the angle of the bank. In this case, we have already solved for the angle of the bank using the given information, which is 21.8 degrees. Now, we can simply plug this value into the formula to get the minimum coefficient of friction needed.

μ = tan(21.8) = 0.39

So, the minimum coefficient of friction needed between the tires and the road is 0.39. This means that the tires must have a good grip on the road in order for the cars to safely take the turn without sliding off. The mass or weight of the car is not needed in this calculation because it is already taken into account in the formula for the angle of the bank. Keep in mind that this solution assumes that the cars do not have any negative lift, which would affect the calculations. I hope this helps guide you in the right direction.