# Turning the Corner Circular Motion

• VidaMarie01
In summary, the problem involves determining the maximum speed a car can take a banked curve without sliding, given the mass of the car, coefficient of static friction, and the angle of the curve. To solve this problem, a free body diagram must be drawn, with the weight force and normal force acting on the car, as well as the friction force that is parallel to the surface and helping to keep the car from sliding. The net force in the r direction is equal to nsin(16) plus the maximum static frictional force, and the net force in the z direction is equal to ncos(16) minus the weight force.
VidaMarie01
I am not sure where to start for this problem:
A concrete highway curve of 80m is banked at a 16degree angle. What is the max speed with which a 1600kg rubber-tired car can take this curve without sliding?

I know the static coefficient of friction of rubber on concrete is 1.
I know that the max static friction=coefficient of static friction x normal force.

Draw a free body diagram for the car on the banked curve. The sum of the forces acting on the car must be horizontal and the magnitude of that net force must be what is making the car travel in a circular path.

Step 1: Draw a free body diagram. The easiest way for this problem is to take the reference frame of the car.

OlderDan said:
Draw a free body diagram for the car on the banked curve. The sum of the forces acting on the car must be horizontal and the magnitude of that net force must be what is making the car travel in a circular path.

I did this and I have the weight force down and the normal force going northwest, the angle of it equal to 16degrees, and then I think I also have a static friction force, but I'm not sure...do I put this right on the r axis, going left??

so I would have the F(net)in the r direction=nsin(16) + max static frictional force?

and the F(net) in the z direction=ncos(16)-w?

Am I setting this up right?

VidaMarie01 said:
I did this and I have the weight force down and the normal force going northwest, the angle of it equal to 16degrees, and then I think I also have a static friction force, but I'm not sure...do I put this right on the r axis, going left??

so I would have the F(net)in the r direction=nsin(16) + max static frictional force?

and the F(net) in the z direction=ncos(16)-w?

Am I setting this up right?
The friction force is parallel to the surface. In this case it helping to keep the car from slipping up the bank, so it is down the the bank. It has horizontal and vertical components, as do the other forces.

## 1. What is turning the corner circular motion?

Turning the corner circular motion is a type of motion where an object moves in a circular path while simultaneously changing direction. This can occur when an object is moving along a curved path, such as a roller coaster, or when an object is rotating around a fixed point, such as a spinning top.

## 2. What causes turning the corner circular motion?

The primary cause of turning the corner circular motion is centripetal force, which is the force that pulls an object towards the center of its circular path. This force is necessary to keep the object moving in a curved path, as it counteracts the object's tendency to move in a straight line due to inertia.

## 3. How does the speed of an object affect turning the corner circular motion?

The speed of an object can greatly impact turning the corner circular motion. As an object's speed increases, the centripetal force required to keep it moving in a curved path also increases. If the speed is too low, the object may not have enough centripetal force to stay on its circular path and will instead fly off in a straight line.

## 4. What is the difference between turning the corner circular motion and uniform circular motion?

Turning the corner circular motion and uniform circular motion are similar in that both involve an object moving in a circular path. However, turning the corner circular motion also involves a change in direction, while uniform circular motion remains constant. In other words, turning the corner circular motion has an acceleration component, while uniform circular motion does not.

## 5. How is turning the corner circular motion useful in real life?

Turning the corner circular motion has many practical applications in everyday life. Some examples include car tires turning around a bend, satellites orbiting around Earth, and swinging a tennis racket. Understanding this type of motion is also crucial in fields such as engineering, physics, and astronomy.

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