Car Rounding Curve: Acceleration Calculation with C=2piR

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In summary, a car with a constant speed of 30 m/s rounds a level curve with a radius of 100 meters. The acceleration of the car can be calculated using the equation C = 2piR, which results in a circumference of 628m. However, the acceleration cannot be determined without knowing the direction of the velocity, which is changing as the car goes around the curve. It is important to review the concept of acceleration in circular motion in order to solve this problem.
  • #1
Austin Gibson
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Homework Statement


A car rounds a level curve of radius 100 meters at a constant speed of 30 m/s.
What is the magnitude of the acceleration of the car?

Homework Equations


C = 2piR

The Attempt at a Solution


I calculated the circumference as 628m. Besides that, I'm ignorant of the procedure to solve this.
 
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  • #2
Austin Gibson said:
1. A car rounds a level curve of radius 100 meters at a constant speed of 30 m/s.
What is the magnitude of the acceleration of the car?

Homework Equations


C = 2piR[/B]

The Attempt at a Solution


I calculated the radius as 628m. Besides that, I'm ignorant of the procedure to solve this.[/B]
What have you learned about cars going around curves? Do they accelerate?
The radius is given as 100 m. You cannot claim that it is 628 m. Please pay attention to what you are doing.
 
  • #3
I intended to type "circumference" instead of "radius." This is the first time I encountered this type of question. My initial estimation was the acceleration would be zero if the speed is constant.
 
  • #4
Austin Gibson said:
I intended to type "circumference" instead of "radius." This is the first time I encountered this type of question. My initial estimation was the acceleration would be zero if the velocity is constant.
The speed is constant but not the velocity. Velocity has direction which in this case is changing. Speed has no direction. The speedometer in a car indicates the speed but it does not indicate in which direction the car is moving; that's why it's called a "speedometer".

Does the question make more sense now? This problem must be related to a section in your textbook, notes or material covered in class. What is the acceleration when something goes around in a circle?
 
  • #5
Yes, I understand the distinction now because acceleration is the change in velocity rather than speed. Unfortunately, we never reviewed this subject in class. Gravity is vertically holding the car to the earth. That seems irrelevant if it's horizontally turning a corner.
 
  • #6
Austin Gibson said:
Yes, I understand the distinction now because acceleration is the change in velocity rather than speed. Unfortunately, we never reviewed this subject in class. Gravity is vertically holding the car to the earth. That seems irrelevant if it's horizontally turning a corner.
Since you didn't review this in class, you should review it on the web. Just do a web search for the title of this thread and you will see a wealth of useful information out there, videos, tutorials, worked out examples, etc. Happy hunting.
 

1. How is acceleration calculated when rounding a curve in a car?

Acceleration when rounding a curve in a car can be calculated using the formula A = v²/R, where A is the acceleration, v is the velocity, and R is the radius of the curve.

2. What is the significance of C=2piR in the calculation?

C=2piR is the circumference of the curve and is used in the calculation to determine the distance traveled around the curve. It is an important factor in understanding the forces acting on the car while rounding the curve.

3. How does the velocity of the car affect the acceleration when rounding a curve?

The velocity of the car has a direct impact on the acceleration when rounding a curve. The higher the velocity, the greater the acceleration will be, and vice versa. This is because a higher velocity requires a greater force to maintain the car's position on the curve.

4. Is there a maximum safe speed for rounding a curve in a car?

Yes, there is a maximum safe speed for rounding a curve in a car. This speed is determined by factors such as the radius of the curve, the friction between the tires and the road, and the car's center of gravity. Exceeding this safe speed can result in loss of control and potential accidents.

5. How does the radius of the curve affect the acceleration when rounding a curve in a car?

The radius of the curve directly affects the acceleration when rounding a curve in a car. A smaller radius requires a tighter turn, resulting in a higher acceleration, while a larger radius allows for a wider turn and a lower acceleration. This is because a smaller radius increases the centripetal force acting on the car.

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