Banked Curve Safety Speed Problem

In summary, the conversation is about finding the range of speeds at which a car can safely make a curve with a radius of 68m, banked for a design speed of 85km/h. The coefficient of static friction is given as 0.30 for wet pavement. The conversation includes equations involving the normal force, friction force, and velocity, and discusses the effects of friction on the banked curve at different speeds. The solution involves finding the maximum safe speed at which the friction force is equal to 0.3 times the normal force.
  • #1
hanlon
20
0

Homework Statement


A curve of radius 68m is banked for a design speed of 85km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely make the curve?


Homework Equations



1) FNsin(theta) = m*v2/r
2) FNcos(theta) - mg = 0
3) tan(theta) = v2/rg



The Attempt at a Solution



I used the third equation to find (theta) which is 39.9o
but I can't find out how to find Ffr or the range of velocity
I understand that when the car goes slow the frictional force faces up the banked curve and when it goes fast the friction goes down the banked curve but I can't figure out how to solve the question.
 
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  • #2
Hi hanlon! :smile:

(have a theta: θ and a mu: µ :wink:)
hanlon said:
1) FNsin(theta) = m*v2/r
2) FNcos(theta) - mg = 0
3) tan(theta) = v2/rg

but I can't find out how to find Ffr or the range of velocity
I understand that when the car goes slow the frictional force faces up the banked curve and when it goes fast the friction goes down the banked curve but I can't figure out how to solve the question.

When the car is at its fastest safe speed, the friction force will be µsFN, = 0.3FN.

So rewrite 1) and 2) to include the friction …

what do you get? :smile:
 

1. What is a banked curve?

A banked curve is a type of curved road or track that is designed to help vehicles navigate the turn more safely and efficiently. It is sloped or angled towards the inside of the curve, providing a centripetal force that helps keep the vehicle on the road and reduces the need for friction between the tires and the road surface.

2. How is the banking angle of a curve determined?

The banking angle of a curve is determined by the velocity of the vehicle, the radius of the curve, and the coefficient of friction between the tires and the road surface. These factors are used in the formula tanθ = v^2/rg, where θ is the banking angle, v is the velocity, r is the radius, and g is the acceleration due to gravity.

3. Why are banked curves important in racing?

Banked curves are important in racing because they allow vehicles to maintain higher speeds while making turns. This is because the centripetal force provided by the banking reduces the need for friction, allowing for a smoother and faster turn. This can be especially beneficial in high-speed races, such as Formula One.

4. How do banked curves affect the force exerted on a vehicle?

Banked curves affect the force exerted on a vehicle by providing a centripetal force that helps keep the vehicle on the road. This reduces the need for friction between the tires and the road surface, and therefore, reduces the lateral force exerted on the vehicle. This can help prevent accidents and improve the overall stability of the vehicle.

5. Are banked curves always beneficial?

No, banked curves are not always beneficial. They are most effective at higher speeds and can be less effective at lower speeds. Additionally, banked curves may not be suitable for all types of vehicles, such as larger and heavier vehicles or vehicles with different tire configurations. Improperly designed or maintained banked curves can also be dangerous for drivers. It is important for engineers to consider all factors when designing banked curves to ensure their safety and effectiveness.

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