Centripetal Force Problems: Banked Road Formula & Frictional Force Calculation

[pb23me]

Homework Statement

prob1) For a car traveling with a speed v around a curve of radius r, determine a formula for the angle at which a road should be banked so that no friction is required.
prob2)Calculate the frictional force needed for a 900kg car traveling around a 500m radius curve at 25m/s, if the car is to continue moving in a circle and not slide. Assume an unbanked curve.

Homework Equations

The Attempt at a Solution

I pretty much know how to do both of these problems there is only one thing that I am confused about.When drawing the force diagrams do you break mg up into components or do you break N up into components? On the first prob i believe my instructor said that you wouls have to break N up into x and y components,Then on the second prob we broke mg up into x and y components?This is very confusing to me and i don't know when I am supposed to break mg up and when to break N up?

 

[PhanthomJay]

This is a good question where one can easily get confused. For the first case, draw a free body diagram of the forces acting on the car...its weight acts straight down, and the normal force acts perpendicular to the banked road surface. The centripetal direction of the curve's radius is along the horizontal x axis. Since you are interested in centripetal forces and centripetal acceleration, you'll want to break up your Normal force into its horizontal x and vertical y components. The weight force will have no x component, which is a good thing.

For part 2, the weight and normal forces act in a vertical direction, and only the friction force acts in the horizontal (centripetal) direction, so you son't have to break up any forces into components, since they already are given in their x or y directions, which is nice.

Note that on many inclined plane problems , where it is convenient to choose the x-axis as parallel to the slope of the plane, then you want to break up the weight force into components parallel and perpendicular to the plane. It takes a lot of practice to get familiar with all this.

 

[ehild]

The force is vector quantity. Draw those forces, gravity and normal force. The resultant has to be equal to the centripetal force, which is horizontal and points to the centre of the circle the car travels along. Maybe you can find the angle without breaking up the forces. If you stuck to the breaking up, you can choose the coordinate system as you like.

ehild

 

[pb23me]

ok thanks, but for the second problem i meant to write: If the car is traveling along and the road is banked at 13 degrees, and there is no friction, at what velocity would the car begin to slide? If I am remembering correctly it seems as though my professor broke up the mg component for this one.Thaat doesn't really make sense to me because this problem seems very similar to the first one.

 

[PhanthomJay]

ok thanks, but for the second problem i meant to write: If the car is traveling along and the road is banked at 13 degrees, and there is no friction, at what velocity would the car begin to slide? If I am remembering correctly it seems as though my professor broke up the mg component for this one.Thaat doesn't really make sense to me because this problem seems very similar to the first one.

It is similar, except now you have a third force to deal with., the friction force. Nevertheless, the process is the same, break up the normal force and the friction force into their horizonal x and vertical y components. mg stays as is. In either case, you need to then use Newton 1 in the vertical direction, and Newton 2 in the horizonatl direction, to solve the problems. There are a bunch of sin,cos, tan to deal with, and you may have misunderstood your professor's explanation on force components.