How to find max velocity in curve

In summary, the maximum speed of a car successfully passing through a curve with a radius of 230 meters and a friction value of 0.87 can be found using the equation a = r * w^2, where a is the centripetal acceleration, r is the curve radius, and w is the angular velocity. The correct answer is 44 m/s, and the time and mass of the car are not necessary for finding the answer. The limiting factor for the car's speed around the curve is the centripetal force, which can be found using the equation F = m * v^2 / r, where m is the mass of the car and v is its velocity. Drawing a force diagram can aid in understanding the
  • #1
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Homework Statement


Curve radius is 230 meters and friction value between car tires and road is 0.87. Find the maximum speed of a car that wants to successfully pass through that curve.

Homework Equations


Friction force = k * N
Perimeter of a circle = 2 * pi * r
F = m * g
w = (f-f0)/t
a = r * w^2

The Attempt at a Solution


I know how to solve this exercise when I have the mass of a car and the time of travel. In this situation I tried to assign variables X and Y to both mass and time, but still didn't manage to find the correct answer.

PS. Correct answer should be 44 m/s.
 
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  • #2
pacman. said:

Homework Statement


Curve radius is 230 meters and friction value between car tires and road is 0.87. Find the maximum speed of a car that wants to successfully pass through that curve.


Homework Equations


Friction force = k * N
Perimeter of a circle = 2 * pi * r
F = m * g
w = (f-f0)/t
a = r * w^2

The Attempt at a Solution


I know how to solve this exercise when I have the mass of a car and the time of travel. In this situation I tried to assign variables X and Y to both mass and time, but still didn't manage to find the correct answer.

PS. Correct answer should be 44 m/s.

I don't see the time of travel in the problem statement.

What do you think would limit the speed of the car driving around the curve (if it wanted to stay on the road!)?
 
  • #3
This problem is independent of mass and time, neither are required to find the answer. Drawing a force diagram might help you.
 
  • #4
better question ...
What you think is giving centripetal force to turn the curve ?
 
  • #5


To find the maximum velocity in a curve, we need to consider the forces acting on the car and the centripetal acceleration of the car.

First, we need to calculate the maximum friction force that the tires can provide. This can be done using the formula F = k * N, where k is the coefficient of friction and N is the normal force. In this case, the normal force is equal to the weight of the car, which can be calculated using the formula F = m * g, where m is the mass of the car and g is the acceleration due to gravity (9.8 m/s^2). Therefore, the maximum friction force is equal to k * m * g.

Next, we need to calculate the centripetal acceleration of the car. This can be done using the formula a = r * w^2, where r is the radius of the curve and w is the angular velocity of the car. The angular velocity can be calculated using the formula w = (f-f0)/t, where f is the final angle of the car's rotation and f0 is the initial angle of the car's rotation, and t is the time it takes for the car to complete the curve. In this case, we can assume that the final angle is 2*pi, since the car completes one full rotation, and the initial angle is 0. Therefore, the angular velocity is equal to 2*pi/t.

Finally, we can use the formula F = m * a to equate the maximum friction force to the centripetal force. This will give us the maximum speed of the car, which is equal to the square root of (r * w^2 / k). Plugging in the values given in the problem, we get:

v = sqrt(230 * (2*pi/t)^2 / 0.87) = 44 m/s

Therefore, the maximum speed of the car that can successfully pass through the curve is 44 m/s.
 

1. What is the formula for finding maximum velocity in a curve?

The formula for finding maximum velocity in a curve is v = √(gr), where v is the maximum velocity, g is the acceleration due to gravity, and r is the radius of the curve.

2. How does the angle of the curve affect the maximum velocity?

The angle of the curve does not directly affect the maximum velocity, but it does affect the radius of the curve. A sharper curve with a smaller radius will require a lower maximum velocity to maintain safe turning.

3. What other factors besides velocity can affect a car's ability to navigate a curve?

Other factors that can affect a car's ability to navigate a curve include the car's mass and weight distribution, the condition of the tires and brakes, and external forces such as wind or road conditions.

4. Can you determine the maximum velocity in a curve without knowing the radius?

No, the radius of the curve is an essential component in the formula for maximum velocity. Without knowing the radius, it is not possible to accurately calculate the maximum velocity in a curve.

5. How can I use the calculation of maximum velocity in a curve to improve my driving?

Knowing the maximum velocity in a curve can help you determine the appropriate speed to enter the curve and maintain control of your vehicle. It can also aid in predicting and avoiding potential accidents or loss of control in the curve.

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