Banked Curves

[ssiding]

Can you please help me out with banked curve problems? I can't determine how its free body diagram would look. I know that the Fc is pointing towards the center, and so is the frictional force, so is the fact that the cars momemtun is pushing the car out of a circular motion thats being negated by the Fc(centripedal force) and Ff(frictional force).
??
Thanks

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[Doctura]

Can you please help me out with banked curve problems? I can't determine how its free body diagram would look. I know that the Fc is pointing towards the center, and so is the frictional force, so is the fact that the cars momemtun is pushing the car out of a circular motion thats being negated by the Fc(centripedal force) and Ff(frictional force).
??
Thanks

Centripetal force is the net force, and it is the vector sum of the frictional force, the force of gravity, and the normal force. On the first free body diagram, I labeled the frictional force, the normal force, and the gravitational force. On the second, I labeled the resultant vector (the centripetal force).

The idea behind a banked curve: When turning, there is a force that is perpendicular to the motion of the car on the tire. On a flat surface, this is countered by the frictional force of the road. When speeds are increased, the frictional force between the tire and the road is not enough to keep a car from spinning out, so the road is banked. The banked roadway permits some of the gravitational force to add to the frictional force pointing down the bank.

I hope this helps.

 

[FutureScaresMe]

so does that mean:

component of Ff in the x dir = Ff*cos(&#920
component of Fg in the x dir = Fg*sin(&#920*cos(&#920

Fc = Ff *cos(&#920 + Fg*sin(&#920*cos(&#920

 

[Doctura]

so does that mean:

component of Ff in the x dir = Ff*cos(&#920
component of Fg in the x dir = Fg*sin(&#920*cos(&#920

Fc = Ff *cos(&#920 + Fg*sin(&#920*cos(&#920

It's not quite that simple. The normal force is not actually just mg cos theta because of the nature of the car driving on the bank (on the free body diagram, into the page). I think this website explains it better than I could try to on a post.

http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular Motion/banked_with_friction.htm