Max Speed for Car on Concrete Curve of Radius 80.0m, 19.0^\circ Angle

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In summary, the problem involves a concrete highway curve with a radius of 80.0 m and a banked angle of 19.0^\circ. The goal is to find the maximum speed at which a 1900 kg rubber-tired car can take the curve without sliding, assuming a static coefficient of friction of 1.0 for rubber on concrete. The equation v(max) = sq. rt. (rg*u(coeff. static friction)) was attempted but did not work, and the person asking the question is unsure of how to approach the problem.
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calvinth
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Homework Statement



A concrete highway curve of radius 80.0 m is banked at a 19.0^\circ angle.

What is the maximum speed with which a 1900 kg rubber-tired car can take this curve without sliding? (Take the static coefficient of friction of rubber on concrete to be 1.0.)

The Attempt at a Solution



I used the equation v = sq rt (rg*tan(theta)) but that didn't work, so I used
v(max) = sq. rt. (rg*u(coeff. static friction)) and got 28.8 m/s2, but that didn't work either.

If anyone can tell me what I'm missing or went wrong, I'd greatly appreciate it.
 
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  • #2
If you are trying to use some formula directly, it is the wrong formula.
If you have drawn free body diagram and then tried to get the formula, you have missed something. Show your attempt.
 
  • #3
I'm not really sure how I should approach the problem. Can you tell me how I can start?
 

1. What is the maximum speed for a car on a concrete curve with a radius of 80.0m and an angle of 19.0 degrees?

The maximum speed for a car on a concrete curve with a radius of 80.0m and an angle of 19.0 degrees is dependent on various factors such as the weight and type of the car, the condition of the tires, and the coefficient of friction between the tires and the road surface. However, based on the standard formula for centripetal force, the maximum speed can be calculated to be approximately 32.8 m/s or 73.4 mph.

2. How does the radius of the curve affect the maximum speed of a car on concrete?

The radius of the curve is directly proportional to the maximum speed of a car on concrete. This means that the larger the radius, the higher the maximum speed of the car can be. This is because a larger radius allows for a gentler turn, therefore requiring less centripetal force to keep the car on the curve.

3. What is the significance of the angle in determining the maximum speed of a car on a concrete curve?

The angle of the curve plays a crucial role in determining the maximum speed of a car on concrete. A sharper angle will require a greater centripetal force to keep the car on the curve, therefore limiting the maximum speed. In contrast, a shallower angle will allow for a higher maximum speed as less centripetal force is needed.

4. Can the type of concrete affect the maximum speed of a car on a curve?

Yes, the type of concrete can have an impact on the maximum speed of a car on a curve. Different types of concrete have varying coefficients of friction, which can affect the amount of traction between the tires and the road surface. This, in turn, can affect the maximum speed that a car can safely travel on a curve.

5. How can the maximum speed of a car on a concrete curve be increased?

The maximum speed of a car on a concrete curve can be increased by improving the conditions of the car and the road surface. This can include using high-performance tires with better traction, maintaining proper tire pressure, and using a smoother and more durable concrete for the road surface. Additionally, reducing the weight of the car and increasing the angle of the curve can also help increase the maximum speed.

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