Maximum speed of a car in a circular flat track (involves static friction)

In summary, the maximum speed a car can achieve on a circular flat track is determined by factors such as the radius of the track, the coefficient of static friction, and the mass of the car. A larger radius and a higher coefficient of static friction generally result in a higher maximum speed. The coefficient of static friction is a measure of the force required to overcome the friction between the tires and the track surface, and a higher coefficient allows for a higher maximum speed. The maximum speed can be calculated using a formula, but it does not account for external factors. The mass of the car also plays a role in determining the maximum speed, with a heavier car generally having a lower maximum speed, but it may also have more grip.
  • #1
kalisious
13
0

Homework Statement


In a circular flat track of radius 50m, what is the maximum speed car can go without sliding? Assume the coefficient of static friction between the car tire and the road is 0.4.


Homework Equations


Unsure of what equations to use.


The Attempt at a Solution


Unsure of what equations to use to attempt solution.
 
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  • #2
What forces are involved? Write down the appropriate force formulas as a start.
 
  • #3


I can provide a response by using the principles of circular motion and static friction. The maximum speed of a car on a circular flat track without sliding can be determined by considering the centripetal force and the maximum static friction force that can be exerted by the tires on the road.

The centripetal force, which keeps the car moving in a circular path, is given by F = mv^2/r, where m is the mass of the car, v is its velocity, and r is the radius of the track. The maximum static friction force that can be exerted by the tires is given by μsN, where μs is the coefficient of static friction and N is the normal force acting on the car.

In order for the car to move without sliding, the centripetal force must be equal to the maximum static friction force. Therefore, we can set these two equations equal to each other and solve for the maximum speed:

mv^2/r = μsN

v = √(μsN*r/m)

Substituting the given values, we get:

v = √(0.4*mg*50m/m)

v = √(20g) ≈ 20√g ≈ 44.7 m/s

Therefore, the maximum speed that the car can go without sliding on the circular flat track is approximately 44.7 m/s or 160.9 km/h.
 

Related to Maximum speed of a car in a circular flat track (involves static friction)

1. What is the maximum speed a car can achieve in a circular flat track?

The maximum speed a car can achieve in a circular flat track is dependent on several factors, including the radius of the track, the coefficient of static friction between the tires and the track surface, and the mass of the car. In general, the larger the radius and the higher the coefficient of static friction, the greater the maximum speed.

2. How does the radius of the track affect the maximum speed of a car?

The radius of the track is a key factor in determining the maximum speed of a car. This is because a larger radius allows for a wider turn, which means the car can maintain a higher speed without slipping or sliding. In general, a larger radius results in a higher maximum speed.

3. What is the coefficient of static friction and how does it impact the maximum speed of a car?

The coefficient of static friction is a measure of the force required to overcome the static friction between two surfaces in contact. In the context of a car on a circular flat track, a higher coefficient of static friction between the tires and the track surface allows for a higher maximum speed, as it provides more grip and prevents the car from sliding or slipping.

4. Can the maximum speed of a car on a circular flat track be calculated?

Yes, the maximum speed of a car on a circular flat track can be calculated using the formula v = √(μrg), where v is the maximum speed, μ is the coefficient of static friction, r is the radius of the track, and g is the acceleration due to gravity. However, this calculation assumes ideal conditions and does not account for external factors such as air resistance and tire wear.

5. How does the mass of the car affect the maximum speed on a circular flat track?

The mass of the car also plays a role in determining the maximum speed on a circular flat track. A heavier car will generally have a lower maximum speed compared to a lighter car, as it requires more force to overcome the static friction between the tires and the track surface. However, a heavier car may also have more grip due to increased downward force, which can result in a higher maximum speed.

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