Circular Motion Regarding Car Sliding on a Curve

[Neek 007]

Homework Statement

What is the maximum speed at which a car can negotiate a level curve of 100m without sliding if the coefficient of static friction is .70?

Homework Equations

F_fr≤ coefficient of frictionF_n
F=ma
F_c=mv²/r
Cir.=2pir
I know there are a couple more, but I'm not sure which ones.

The Attempt at a Solution

I know mass is not a factor here.
I think I'm supposed to plug in a formula into another formula. I'm thinking to plug in the force of friction formula(first formula) into F=ma.

 

[Redbelly98]

Homework Statement

What is the maximum speed at which a car can negotiate a level curve of 100m without sliding if the coefficient of static friction is .70?

Homework Equations

F_fr≤ coefficient of frictionF_n
F=ma
F_c=mv²/r
Cir.=2pir
I know there are a couple more, but I'm not sure which ones.

The Attempt at a Solution

I know mass is not a factor here.
I think I'm supposed to plug in a formula into another formula. I'm thinking to plug in the force of friction formula(first formula) into F=ma.

Yup, that would work. And here's a couple of questions to help you along:

1. What else is F_n eqivalent to? (If you have to, draw a force diagram to help figure this out.)
2. What is a, given that the car is moving in a circle as it moves around the curve?

 

[Neek 007]

Ah, thank you so much. I got the right answer, 26.2 m/s.

 

[sorra54]

Ah, thank you so much. I got the right answer, 26.2 m/s.

Ok. I'm doing a small assignment about drifting at the moment! I can see that you figured out something, that might be similar to drifting.

My assignment is as following:

Describe some aspects of the phenomena drifting you'll find interesting, being a requirement that you use math, and or physics to explain.

Could you guys maybe help me out a little bit on this one?

 

[rwisz]

I would approach this problem by first understanding the physical principles involved. In this case, circular motion and friction are the key concepts. The maximum speed at which a car can negotiate a curve without sliding can be determined by considering the forces acting on the car.

The first step would be to calculate the centripetal force required to keep the car moving in a circular path. This can be done using the formula Fc=mv^2/r, where m is the mass of the car, v is its velocity, and r is the radius of the curve.

Next, we need to consider the maximum force of static friction that the tires can exert on the road. This is given by the formula Ffr≤ μFn, where μ is the coefficient of static friction and Fn is the normal force between the tires and the road. In this case, the normal force is equal to the weight of the car, which is given by the formula Fn=mg.

Therefore, we can set up the following inequality to determine the maximum speed:

Ffr≤ μFn
mv^2/r ≤ μmg

Solving for v, we get:

v ≤ √(μrg)

Substituting the given values of μ=0.70, r=100m, and g=9.8 m/s^2, we get the maximum speed as:

v ≤ √(0.70*100*9.8) = 26.38 m/s

Therefore, the maximum speed at which the car can negotiate the curve without sliding is approximately 26.38 m/s or 95.0 km/h. It is important to note that this is the theoretical maximum speed and in reality, other factors such as the condition of the road surface and the driver's skill can affect the actual speed at which the car can safely negotiate the curve.