Banked Frictionless Curve, and Flat Curve with Friction

In summary, the conversation discusses a problem involving a car of mass 1200 kg traveling at 40.0 km/hour on a banked turn covered in ice with an angle of theta. The goal is to find the radius of the turn assuming the car continues in uniform circular motion. The attempt at a solution involves using the formula Fc = FN sin(theta) = m(v^2/r) to solve for r, but the answer is rejected due to the normal force not being equal to the weight of the car. The question arises about the value of FN and the possibility of another missing value in the equation. Further discussion suggests breaking down FN into vertical and horizontal components, with the horizontal component providing the centripetal acceleration and
  • #1
Digitalx04
4
0

Homework Statement


A car of mass M = 1200 kg traveling at 40.0 km/hour enters a banked turn covered with ice. The road is banked at an angle theta, and there is no friction between the road and the car's tires.

What is the radius r of the turn if [tex]\theta[/tex] = 20.0 degrees (assuming the car continues in uniform circular motion around the turn)?


The Attempt at a Solution



I believe that [tex]F_{c}[/tex] = [tex]F_{N}[/tex] sin ([tex]\theta[/tex]) = m([tex]\frac{v^{2}}{r}[/tex])

Using this I solved for r, which is my missing variable and came up with:

r = [tex]\frac{v^{2}}{F_{N}sin\theta}[/tex]

Using this formula I get
r = [tex]\frac{11.1^{2}}{9.8 sin 20}[/tex]

but when I submitted this answer it told me the normal force is not equal to the weight of the car.

My questions are what is the [tex]F_{N}[/tex] value and am I missing another value in my equation?
 
Physics news on Phys.org
  • #2
Break down Fn into vertical and horizontal components. You already saw that the horizontal component provides the centripetal acceleration; what does the vertical component do?
 
  • #3


Thank you for your question. I can provide you with an explanation for the concept of a banked frictionless curve and a flat curve with friction.

A banked frictionless curve is a curved surface that is tilted at an angle, known as the bank angle, to facilitate the motion of an object, in this case, a car. The bank angle is designed to provide a force, known as the normal force, that helps to keep the car moving in a circular motion around the curve. In this scenario, the normal force is the only force acting on the car, as there is no friction between the tires and the road. This means that the car will continue in uniform circular motion around the curve, without any acceleration or deceleration.

On the other hand, a flat curve with friction is a curved surface with a coefficient of friction between the tires and the road. This coefficient of friction provides a force that opposes the motion of the car, causing it to slow down. In this case, the car is not in uniform circular motion, as it experiences a change in velocity due to the force of friction.

Now, let's take a look at your attempt at solving the problem. Your equation is correct, but you are missing the value for the normal force. The normal force is the force that the banked surface exerts on the car, perpendicular to the surface. In this scenario, the normal force is not equal to the weight of the car, as the car is not on a flat surface. To find the value of the normal force, you can use the equation F_{N} = mg cos\theta, where m is the mass of the car, g is the acceleration due to gravity, and \theta is the bank angle.

Once you have the value for the normal force, you can substitute it into your equation to solve for the radius r. I hope this helps clarify the concept of a banked frictionless curve and a flat curve with friction. Keep up the good work with your studies!
 

1. What is banked frictionless curve?

Banked frictionless curve is a type of curved track or road that is designed to allow objects, such as vehicles, to travel around the curve with minimal friction. This is achieved by tilting the curve towards the center, which helps to balance the centrifugal force acting on the object.

2. How does a banked frictionless curve work?

A banked frictionless curve works by tilting the curve towards the center, which helps to balance the centrifugal force acting on the object. This allows the object to travel around the curve with minimal friction, making it easier to maintain control and stability.

3. What is flat curve with friction?

A flat curve with friction is a type of curved track or road that does not have any banking or tilting towards the center. This means that the centrifugal force acting on the object is not balanced, which can result in higher levels of friction and make it more difficult to maintain control and stability while traveling around the curve.

4. How does a flat curve with friction differ from a banked frictionless curve?

A flat curve with friction differs from a banked frictionless curve in that it does not have any banking or tilting towards the center. This means that the centrifugal force acting on the object is not balanced, which can result in higher levels of friction and make it more difficult to maintain control and stability while traveling around the curve.

5. What are the advantages of using a banked frictionless curve?

There are several advantages of using a banked frictionless curve, including: reducing friction and wear on tires or other moving parts, allowing for higher speeds and smoother travel around the curve, and providing better control and stability for vehicles or other objects traveling around the curve.

Similar threads

  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
547
  • Introductory Physics Homework Help
2
Replies
68
Views
4K
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
766
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
699
  • Introductory Physics Homework Help
Replies
4
Views
7K
Back
Top