Question Question about Static Friction and Curves/Banked Curves

[Sports Junky]

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So I have a few theoretical questions about static friction and banked curves in general.

The scenario is simple: A car moves around a banked curve at a fixed velocity (v) with an angle (Theta).

1) What is causing the centripetal acceleration in this case, is it the speed of the car, friction, or both?

2) Would this be the correct equation to determine centripetal acceleration:

Friction Force + Vector Normal Force towards center = mv^2/r

3) Friction points towards the center of the circle, but when would it start to point away from the center? Would it be possible that the velocity decreases to such a point that the car starts to slide towards the center?

Edit: Title should have been 'Quick Question about Static Friction/Banked Curves'.

 

[milski]

Speed cannot cause acceleration.

1) The centripetal acceleration is created by two components - static friction (from the wheels not slipping on the pavement) and normal from the pavement on the car wheels.

2) It is a fairly good estimate for small angles but it is not the exact location. You have to remember that the friction is parallel to the pavement and will have a vertical component. That changes the amount pointed towards the center.(the horizontal component).

3) Yes, it is very, very possible. Been there, done that. Won't drive in the snow with summer tires again. 😀 The weight of the car has a component parallel to the pavement - at low enough speed and high enough incline it is possible that the net force on the car will be towards the center. If you think about it, if the car is stopped, the friction is pointed away from the center - that's what prevents the car from sliding down.

 

[Sports Junky]

Speed cannot cause acceleration.

1) The centripetal acceleration is created by two components - static friction (from the wheels not slipping on the pavement) and normal from the pavement on the car wheels.

2) It is a fairly good estimate for small angles but it is not the exact location. You have to remember that the friction is parallel to the pavement and will have a vertical component. That changes the amount pointed towards the center.(the horizontal component).

3) Yes, it is very, very possible. Been there, done that. Won't drive in the snow with summer tires again. 😀 The weight of the car has a component parallel to the pavement - at low enough speed and high enough incline it is possible that the net force on the car will be towards the center. If you think about it, if the car is stopped, the friction is pointed away from the center - that's what prevents the car from sliding down.

Thank you! So in essence the pavement provides an additional centripetal force since some of it's force is pointing towards the circle. I guess this would mean that increasing the angle and increasing velocity would always increase acceleration.

 

[milski]

In most real life situations most of the centripetal force is provided by the pavement. In the case of a flat road, all of the force is just because of the pavement. Once you start adding bank, you get that extra help from the normal force from the pavement.

Increasing the angle will increase the contribution of the normal to the centripetal force. Increasing the velocity will increase it as absolute value, it may or may not change the proportion of normal:friction contributing to it. (I have to do the math to be sure and I've had enough of that today to want to do it).