# Max. speed you can drive on a circular hill an still be in Uniform Circular Motion

• Unix
In summary, the top of a circular hill with a radius of 25 meters is being approached by an 1800kg car with a speed of 8.0 m/s. When considering the normal force that the road exerts on the car, it is determined that at a certain speed, the driver will experience a moment of weightlessness. This indicates that the car has exceeded the maximum speed for uniform circular motion on the hill and therefore there is no normal force on the car at that point. The calculated speed for this moment of weightlessness is likely to be "at least" a certain speed.
Unix
Max. speed you can drive on a circular hill an still be in "Uniform Circular Motion"

## Homework Statement

The top of a hill is in the shape of a circle of radius 25 meters.

## Homework Equations

a) What is the normal force that the road exerts on an 1800kg car as it tops the hill with a speed of 8.0 m/s?

b) At what speed would the driver experience a moment of weightlessness as they top the hill?

## The Attempt at a Solution

My question isn't about performing calculations, I just wanted to make sure I am understanding the concept.

In part b, if the driver is experiencing weightlessness, is it correct to say that the car has exceeded the maximum speed that you can have on the hill and still be in "Uniform Circular Motion"? If that's the case then there is no normal force on the car at that point?

Unix said:
In part b, if the driver is experiencing weightlessness, is it correct to say that the car has exceeded the maximum speed that you can have on the hill and still be in "Uniform Circular Motion"? If that's the case then there is no normal force on the car at that point?

Yes that is correct. During normal circular motion, the normal force would be the force that the driver experiences, so if he is weightless then the normal force is zero.

Unix said:

## Homework Statement

The top of a hill is in the shape of a circle of radius 25 meters.

## Homework Equations

a) What is the normal force that the road exerts on an 1800kg car as it tops the hill with a speed of 8.0 m/s?

b) At what speed would the driver experience a moment of weightlessness as they top the hill?

## The Attempt at a Solution

My question isn't about performing calculations, I just wanted to make sure I am understanding the concept.

In part b, if the driver is experiencing weightlessness, is it correct to say that the car has exceeded the maximum speed that you can have on the hill and still be in "Uniform Circular Motion"? If that's the case then there is no normal force on the car at that point?

DOn't forget that when you have calculated a speed for part (b), you answer is likely to be "At least a speed of ... "

## 1. What is Uniform Circular Motion?

Uniform Circular Motion is the motion of an object along a circular path at a constant speed, with a constant radius. This means that the object is constantly changing direction, but its speed remains the same.

## 2. How is the maximum speed determined?

The maximum speed that an object can drive on a circular hill and still be in Uniform Circular Motion is determined by the radius of the circle and the coefficient of friction between the tires and the surface of the hill. It can be calculated using the formula: v = √(rgμ), where v is the maximum speed, r is the radius, g is the acceleration due to gravity, and μ is the coefficient of friction.

## 3. What factors affect the maximum speed in Uniform Circular Motion?

The maximum speed in Uniform Circular Motion is affected by the radius of the circle, the coefficient of friction, and the acceleration due to gravity. A larger radius or a higher coefficient of friction will result in a higher maximum speed, while a higher acceleration due to gravity will decrease the maximum speed.

## 4. Is it possible to drive at a speed higher than the maximum speed and still be in Uniform Circular Motion?

No, it is not possible to drive at a speed higher than the maximum speed and still be in Uniform Circular Motion. If the speed exceeds the maximum, the object will lose contact with the surface and will either fly off the circular path or slide down the hill.

## 5. How is Uniform Circular Motion different from non-uniform circular motion?

In Uniform Circular Motion, the speed remains constant while the direction of motion changes, whereas in non-uniform circular motion, the speed and/or direction of motion changes. This can be seen in objects moving on a race track where the curves have different radii, resulting in varying speeds and directions of motion.

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