Centripetal acceleration question: car moving around banked curve

In summary: When your feet touch the surface, they do not move (relative to the surface), but you can move forward as you constantly switch between both feet.
  • #1
gokuls
35
0
If the wheels and tires of a car are rolling without slipping or sliding when turning, the bottom of the tire is rest against the road at each instant, so the force of friction is the static friction. Essentially if you are moving around a banked curve and the car is not skidding, then friction will be calculated by using coefficient of static friction. Why though? Isn't the car moving?
 
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  • #2
The point of the tire in contact isn't moving- it is constantly changing as the tire rotates, but it is not skidding so it uses static rather than kinetic friction.
 
  • #3
schaefera said:
The point of the tire in contact isn't moving- it is constantly changing as the tire rotates, but it is not skidding so it uses static rather than kinetic friction.

I still don't understand. Could you elaborate a bit more? Alright the car is not skidding, but I still don't understand.
 
  • #4
Like schaefera said, you will use the static friction coefficient as the point of the tire in contact with road is not moving against the road. The wheels TURN and so the point in contact changes. Of course the previous point in contact moves but not against the road. So since the point is not moving but only changing its position that too not against the road, each point will have μ as the static friction co-efficient.
 
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  • #5
gokuls said:
Essentially if you are moving around a banked curve and the car is not skidding, then friction will be calculated by using coefficient of static friction.
Not quite, The coefficient of static friction just tells you what the maximal static friction force is, that the contact could transmit. The actual transmitted force of static friction can be less than that.

gokuls said:
Alright the car is not skidding, but I still don't understand.
No skidding = no relative horizontal movement between the contact patches. The tire contact point moves on a cycloid. Around contact time it moves only vertically:

http://en.wikipedia.org/wiki/Cycloid
 
  • #6
Static friction occurs when there is no slipping between the surfaces. If the tyres don't slip, then this is what you use.
 
  • #7
Compare it with walking: When your feet touch the surface, they do not move (relative to the surface), but you can move forward as you constantly switch between both feet.
 
  • #8
mfb said:
Compare it with walking
bike-wheel-out-of-boots.jpg
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that causes an object to move in a circular path. It is always directed towards the center of the circle and its magnitude is dependent on the object's speed and the radius of the circle.

2. How is centripetal acceleration related to a car moving around a banked curve?

In the case of a car moving around a banked curve, centripetal acceleration is responsible for keeping the car moving in a circular path. The force that creates this acceleration is the friction between the tires and the road, which is directed towards the center of the curve.

3. What factors affect the magnitude of centripetal acceleration in a car on a banked curve?

The magnitude of centripetal acceleration in a car on a banked curve is affected by the speed of the car, the mass of the car, and the angle of the banked curve. The higher the speed and mass of the car, the greater the centripetal acceleration needed to maintain the circular motion. The angle of the banked curve also plays a role, as a steeper angle requires a greater centripetal acceleration to counteract the force of gravity.

4. How is centripetal acceleration different from tangential acceleration?

Centripetal acceleration is the acceleration that causes an object to move in a circular path, while tangential acceleration is the acceleration that causes an object to change its speed along a straight line. In the case of a car on a banked curve, centripetal acceleration is responsible for keeping the car moving in a circular path, while tangential acceleration is responsible for increasing or decreasing the car's speed.

5. What is the formula for calculating centripetal acceleration in a car on a banked curve?

The formula for calculating centripetal acceleration in a car on a banked curve is a = v^2/r, where a is the centripetal acceleration, v is the velocity of the car, and r is the radius of the curve. This formula can also be written as a = ω^2r, where ω is the angular velocity of the car.

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