Calculating coefficient of static friction without a mass.

In summary, the car requires a coefficient of static friction of 0.3 to ensure it does not slip on a road with a radius of 70m.
  • #1
Gheret
11
0

Homework Statement


A car is traveling at 30m/s around a bend of radius 70m. What coefficient of static friction between the tires and the road is required to ensure the car will not slip?


Homework Equations





The Attempt at a Solution


I know that the centripetal acceleration is a=30^2/70
and I know that this acceleration has to be canceled out by the frictional force for the car to not slip, but I am not sure out to calculate frictional force F=mA without a mass for the car.
 
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  • #2
Gheret said:
but I am not sure out to calculate frictional force F=mA without a mass for the car.
Maybe you don't need the actual mass. Try calling the mass 'm' and see what happens.

(Tip: Solve things symbolically as much as possible. Only use the calculator at the end.)
 
  • #3
Doc Al said:
Maybe you don't need the actual mass. Try calling the mass 'm' and see what happens.

(Tip: Solve things symbolically as much as possible. Only use the calculator at the end.)

I'm guessing that since mass will not change and the two forces have to be equal the m will cancel out but I still do not know how to calculate the acceleration into Newtons for this situation.
 
  • #4
Gheret said:
I'm guessing that since mass will not change and the two forces have to be equal the m will cancel out
You're right. But no need to guess: Try it and see!
but I still do not know how to calculate the acceleration into Newtons for this situation.
I assume that you mean you cannot calculate the force in Newtons. True, without the mass, you cannot calculate the force. So what? You can figure out the coefficient of friction, which is all you need.
 
  • #5
I'm sorry but I am totally lost now..
What I have done so far: F(r)=mv^2/r=F(fr)
F(r) being centripetal force and F(fr) being frictional force.
But I do not know the equation for calculating coefficient of static friction.

Thanks for helping me out.
 
  • #6
Gheret said:
But I do not know the equation for calculating coefficient of static friction.
How does the maximum static friction force relate to the normal force between surfaces?
 
  • #7
Oh I was completely ignoring normal force!
F=u(9.8m/s^-2)m
mv^2/r=u(9.8m/s^-2)m
(30)^2/70=u(9.8)

Right?
 
  • #8
Right!

(This assumes that the road is flat--no banking angle.)
 
  • #9
You have been the best help.
Thank you for not just telling me the answer cause now I have actually learned how to solve these for myself. :smile:

Thank you!
 

1. How do you calculate coefficient of static friction without a mass?

To calculate the coefficient of static friction without a mass, you need to measure the force required to move an object and the normal force acting on the object. Then, divide the force by the normal force to get the coefficient of static friction.

2. What is the formula for calculating coefficient of static friction without a mass?

The formula for calculating coefficient of static friction without a mass is μs = F/N, where μs is the coefficient of static friction, F is the force required to move the object, and N is the normal force acting on the object.

3. Can the coefficient of static friction be negative when calculated without a mass?

No, the coefficient of static friction cannot be negative when calculated without a mass. It is always a positive value as it represents the ratio of the force required to move an object to the normal force acting on the object.

4. Why is it important to calculate coefficient of static friction without a mass?

Calculating the coefficient of static friction without a mass is important as it helps determine the maximum force that can be applied to an object before it starts to slide. This information is crucial in designing structures and ensuring their stability.

5. Are there any limitations to calculating coefficient of static friction without a mass?

Yes, there are limitations to calculating the coefficient of static friction without a mass. The calculated value may not be accurate if the surface conditions or the angle of the surface is not taken into account. Additionally, this calculation only applies to stationary objects and does not take into account the dynamic friction that occurs when an object is already in motion.

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