How Does Normal Force Change as a Car Accelerates on a Banked Curve?

In summary: In that case, the car would end up moving in a straight line instead of following the curve. In summary, the conversation discusses the normal force and its relationship with weight and friction in a car's motion around a banked curve. It is explained that the normal force gradually increases as the car accelerates, causing a centripetal force that allows it to change direction. The ground provides the necessary force through its contact with the car's wheels. The importance of the normal force in maintaining the car's motion on the curve is emphasized.
  • #1
Yh Hoo
73
0
hello good morning. Let look at the two diagram.
(back view)

In STATIC, a car is remauning static at a bank curve and its force diagram is as follows. for this case, the normal force is smaller than the weight of the car and friction exists in the directiin perpendicular to car.

In MOTION, the car is moving into the screen and is surrounding a banked curve. now what i am so surprised with is that THE MECHANISM OF FORCE CHANGING. if we inspect a car changes it state from.diagram 1 to 2, we wil actually realize that the normal force gradually increases until its vertical component Ncos(∠) is equal to the mg and balances the weight of the car. meanwhile there is an unbalanced component that causes centripetal force ,Nsin(∠) . Can anyone explain to me the actual mechanism of this changes in normal force?? or correct me if i am wrong.
 

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  • #2
Why did you not include the friction force in the "motion" diagram?

You mean you start with the car stationary on a banked curve and then it accelerates around the curve?
In order to accelerate the car must experience a net unbalanced force. The mechanism for this is the wheels contact with the ground. As it accelerates around the corner, it will have an increasing centripetal component - which comes from the reaction from the ground ... so the normal force must increase.

The mechanism is that the car has to push against the ground in order to change direction and the ground is fixed in place so it must push back - just the same as the normal force knows exactly how hard to push on the car in the stationary case.

Another way to think about this is to consider what would happen if the ground did not push hard enough against the car to make it turn.
 
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1. What is banked curve circular motion?

Banked curve circular motion refers to the motion of an object, such as a car or a roller coaster, traveling on a curved path along a banked surface. This type of motion involves both a horizontal and vertical component, as the object experiences both centripetal and gravitational forces.

2. How does the banking angle affect the motion of an object on a banked curve?

The banking angle, or the angle at which the banked surface is tilted, plays a crucial role in determining the speed at which an object can safely travel on a banked curve. A steeper banking angle allows for higher speeds, as it provides more centripetal force to counteract the object's inertia and prevent it from slipping or sliding off the curve.

3. What factors determine the ideal banking angle for a banked curve?

The ideal banking angle for a banked curve depends on several factors, including the object's speed, mass, and radius of the curve. The centripetal force required to keep the object moving along the curve must be equal to the gravitational force pulling the object towards the center of the curve. Therefore, the ideal banking angle can be calculated using the formula tanθ = v^2/rg, where θ is the banking angle, v is the object's speed, r is the radius of the curve, and g is the gravitational acceleration.

4. How does friction play a role in banked curve circular motion?

Friction between the object and the banked surface plays a crucial role in maintaining the object's motion along the curve. Without friction, the object would not be able to experience the necessary centripetal force to stay on the curve. However, too much friction can also cause the object to slow down or even slide off the curve if the banking angle is not steep enough.

5. Can banked curves be used in other applications besides transportation?

Yes, banked curves can be used in various other applications, such as in amusement park rides, circular tracks for motorsports, and even in some industrial machinery. The principles of banked curve circular motion can be applied in any situation where an object needs to maintain a constant speed while traveling along a curved path.

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