Centripetal force of a car on a curve

In summary, a 600 kg car with a speed of 30 m/s is going over a banked curve with a radius of 120m at a 25 degree angle. The coefficient of static friction between the car and the road is 0.3. To find the normal force, the forces acting on the car can be broken down into x and y components. Using the equations F(centripetal) = (mv^2)/r and F(static) = mu(normal force), we can set up two equations and solve for the normal force. The friction force operates at the tire/road interface and opposes the force pushing the car up the bank.
  • #1
sheepy
10
0

Homework Statement


A 600 kg car is going over a curve with radius 120m that is banked at angle of 25 degrees with speed of 30 m/s. The coefficient of static friction between car and road is 0.3. What is the normal force?

Homework Equations


F(centripetal)= (mv^2)/r
F(static) = Mu(normal force)

The Attempt at a Solution


I think that the centripetal force is equal to the friction force. So I can just substitute centripetal force for friction. But my teacher also said that is a parallel force but I'm not sure it is. From the free-body diagram, I will get..
F(c)= (Friction + Parallel force) Cos(angle)

I'm actually quite confused ~_~
 
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  • #2
See if this helps - http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/carbank.html#c1

The normal force means the normal force on the back which comes from the component of the weight point normal to the bank and the component of centrifugal force pointing normal to the bank.

The weight points downard (vertically) while the centrifugal/centripetal force points horizontally, but both have components pointing normal to the bank.
 
  • #3
cool, thanks
it makes more sense now..
except how come the friction force is up there? usually my teacher draws it on the other side of the car, like on the same side as the centripetal force. does it matter? since its negative now instead of positive and etc?
 
  • #4
The friction force operates at the contact surface between tires and bank (road surface). It doesn't matter where one draws the arrow, although it should be correctly drawn at the tire/road interface, but the direction should point down the bank since the friction opposes the force which try to push the car up the bank.
 
  • #5
i got: x-component: Nsin25 + mu(N)(cos25) = (mv^2)/r
y-component: Nsin25 - mg - mu(N)(sin25) = 0

i'm not sure how to find N from that since, there's like 2 N's in each equation? and i can't seem to just factor it out...or did i just get the equation wrong entirely?
 

1. What is centripetal force?

Centripetal force is the force that is required to keep an object moving in a circular path. It is always directed towards the center of the circle and is responsible for changing the direction of the object's velocity.

2. How is centripetal force related to a car on a curve?

When a car is moving on a curve, it experiences a centripetal force directed towards the center of the curve. This force is provided by the friction between the tires and the road, which prevents the car from sliding off the curve and helps maintain its circular motion.

3. What factors affect the centripetal force of a car on a curve?

The centripetal force of a car on a curve is affected by the car's speed, mass, and the sharpness of the curve. The greater the speed or mass of the car, the greater the centripetal force needed to keep it on the curve. Additionally, a sharper curve requires a greater centripetal force.

4. How does centripetal force impact a car's stability on a curve?

Centripetal force plays a crucial role in keeping a car stable on a curve. If the centripetal force is not enough to counteract the car's inertia, it may slide off the curve or lose control. This is why it is important to maintain a proper speed and follow the curve's curvature while driving.

5. Can centripetal force cause a car to lose control on a curve?

In certain cases, if the centripetal force is not enough to keep the car on the curve, it can cause the car to lose control and slide off the curve. This can happen if the car is traveling at a high speed, the curve is too sharp, or there are external forces acting on the car (such as a strong side wind). It is important to always drive within the recommended speed limit and take caution while approaching curves to avoid losing control due to insufficient centripetal force.

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