Banked Curve with Friction Problem

In summary, the conversation discusses a problem involving centripetal force and a banked curve. The given values are a friction coefficient of 0.49, an angle of 19 degrees, a radius of 46m, and a mass of 1200 kg. The question is how fast the car can take the curve without skidding to the outside. The person asking the question has attempted the problem and shares their calculation of the normal force and friction force. They also mention adding the sine component of weight to the friction force and using it to calculate the velocity, which is incorrect according to their online homework. Another person asks how the normal force was found and reminds the original poster to consider all three forces acting on the car.
  • #1
ruck101
9
0
Hey all! Brand new to PF. Anyway, I'm having trouble with a problem involving centripital force. Here are the givens:

Friction coefficient = .49
Angle = 19 degrees
Radius = 46m
mass= 1200 kg

Question - How fast can the car take the curve without skidding to the outside? Thanks ahead of time!

By the way, yes, I have attempted this problem, just so nobody thinks I'm trying to get my homework done for me. :biggrin:
 
Last edited:
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  • #2
Show us your attempt then. and Welcome to PF!
 
  • #3
Banked Curve

Hehe, guess I should have done that in the first part. Anyway, I drew a freebody diagram and got the Normal Force = 11119 N, and the Friction force = Normal x Coefficient = 5448 N. Is that the only centripital force or is there also the sin component of the weight? I've added sin (mg) and the friction force together and plugged it into V^2= Centripital Force x radius/ mass. And I get the wrong answer, or so my online homework says. I get around 18 m/s.
 
  • #4
How did you find the normal force?

Realize that when the car moves at maximal speed, there are three forces acting on the car: weight, friction (which way does it act?), and the normal force. In the horizontal direction, there is centripetal acceleration; in the vertical direction, equilibrium.
 

1. What is a banked curve with friction problem?

A banked curve with friction problem is a physics problem that involves a car or other object traveling around a curved path with a banked angle and experiencing friction. It is used to demonstrate the principles of circular motion and centripetal force.

2. How do you calculate the banked angle in a banked curve with friction problem?

The banked angle can be calculated using the equation tanθ = v^2/rg, where θ is the banked angle, v is the velocity of the object, r is the radius of the curve, and g is the acceleration due to gravity. This equation takes into account the centripetal force and the gravitational force acting on the object.

3. What is the role of friction in a banked curve with friction problem?

Friction plays a crucial role in a banked curve with friction problem by providing the centripetal force necessary for the object to travel in a curved path. Without friction, the object would not be able to maintain its circular motion and would slide off the curve.

4. How does the speed of the object affect the banked curve with friction problem?

The speed of the object affects the banked curve with friction problem in two ways. First, the faster the object is traveling, the larger the banked angle needs to be in order to keep the object on the curve. Second, the faster the object is traveling, the greater the friction force needed to provide the necessary centripetal force, which can lead to increased wear on tires and other components.

5. What are some real-world applications of a banked curve with friction problem?

Some real-world applications of a banked curve with friction problem include designing banked turns on race tracks and highways, understanding the physics behind roller coasters and other amusement park rides, and analyzing the forces acting on vehicles when taking turns on curved roads.

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