Minimum static friction problem

In summary, the conversation discusses a problem regarding a banked circular highway curve and the minimum coefficient of friction required for cars to safely navigate the turn. The problem is solved using the equation angle = tan^-1((v^2)/gR), where v is velocity, g is the acceleration of gravity, and R is the radius of the curve. The individual is having trouble solving for static friction without the weight or mass of the car, but it is pointed out that the mass of the car will drop out of the final solution when worked out algebraically. The conversation concludes with a suggestion to solve the problem algebraically before plugging in numbers.
  • #1
AwesomeMan
1
0
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.
 
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  • #2
AwesomeMan said:
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.
 
  • #3


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.
 

FAQ: Minimum static friction problem

What is the minimum static friction problem?

The minimum static friction problem is a physics concept that involves determining the minimum amount of force required to move an object at rest. It is based on the principle of static friction, which is the friction that exists between two surfaces when they are not in motion relative to each other.

How is the minimum static friction problem solved?

The minimum static friction problem is typically solved using the equation Fs = μsN, where Fs is the maximum static friction force, μs is the coefficient of static friction, and N is the normal force between the two surfaces. By setting the applied force equal to the maximum static friction force, the minimum amount of force required to overcome static friction can be determined.

What factors affect the minimum static friction?

The coefficient of static friction and the normal force are the two main factors that affect the minimum static friction. The coefficient of static friction depends on the nature of the surfaces in contact and their roughness, while the normal force is determined by the weight of the object and the force applied to it.

How does the minimum static friction problem relate to real-life situations?

The minimum static friction problem is relevant in many real-life situations, such as pushing a heavy object, driving a car, or walking on a slippery surface. In each of these cases, the minimum static friction must be overcome in order to initiate motion.

Can the minimum static friction be greater than the applied force?

No, the maximum static friction force can never be greater than the applied force. This is because the applied force is the force needed to overcome static friction and initiate motion. If the maximum static friction force was greater, the object would remain at rest.

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