Solving Centripetal Acceleration for Banked Turns

AI Thread Summary
The discussion focuses on solving problems related to centripetal acceleration in banked turns. One problem involves calculating the minimum coefficient of static friction needed for a car rounding a 100 m radius curve at 30 m/s, given that it's banked for 16 m/s. Participants emphasize the importance of drawing free-body diagrams to visualize the forces acting on the car, specifically the normal force and weight, and suggest using Newton's second law to set up equations for the x- and y-directions. Another problem addresses the required wing tilt angle for a small airplane executing a horizontal turn at 250 km/h with a 1900 m turning radius. The conversation encourages showing attempts at solving these problems for better assistance.
FortyFeet
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Hey there. I took Physics B last year, but for some reason we never covered the banked turns when it comes to centripetal acceleration. So I need a bit of help on these two:

A curve with a 100 m radius on a level road is banked at the correct angle for a speed of 16 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction needed between the tires and the road to prevent skidding?

and...

Aircraft experience a lift force (due to the air) that is perpendicular to the plane of the wings and to the direction of flight. A small airplane is flying at a constant speed of 250 km/h. At what angle from the horizontal must the wings of the airplane be tilted for the plane to execute a horizontal turn from east to north with a turning radius of 1900 m?

Thanks =D
 
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Welcome to PF FortyFeet. We will help you but you must show some attempts at the problems first.

FortyFeet said:
A curve with a 100 m radius on a level road is banked at the correct angle for a speed of 16 m/s.
Thanks =D

Draw a little diagram with the two forces acting up on the car. "at the correct angle" means that the car will not tend to slip so it will not experience any frictional forces when going around the bend. This means only the normal force and weight are acting on the car.

Decompose the normal force into its x- and y-components.

Set the two force equations up in the x- and y-directions using Newton's second law. Post your two equations so that we can help you.
 
andrevdh said:
Draw a little diagram

haha.. Sounds quite funny calling it 'little'. It's supposed to be a free-body diagram ah?
 
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