Solving a Car's Travel in a Flat Circle - Can You Help?

In summary, the question asks for the radius of a car traveling in a flat circle at a certain instant with a velocity of 18 m/s west and a total acceleration of 2 m/s2 at 46 degrees north of west. The correct formula to use is a = v2/R, taking the component of the acceleration as sin(46). The linear speed is 18 m/s and the calculated radius is 162 m.
  • #1
Xamfy19
60
0
The question is :
A car travel in a flat circle of radius R. At a certain instant the velocity of the car is 18 m/s west and the total acceleration of the car is 2 m/s2 at 46 degrees north of west. What is R?

I simply used a = v2/R and obtained 162 m. I suspected the question should be more complicated than I thought. Can anyone help. Thanks.
 
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  • #2
The formula u applied is for an so u have to take the component which is in the direction of radius or it shoul be radial component of acceleration. and velocity should be the tangential velocity
 
Last edited:
  • #3
thanks, maybe more info needed

I took cos(46) of 2 m/s2 and used for the formula. It's not the correct answer. Do I need to figure out the linear speed? (apparently it is not 18 m/s)?
Thanks alot.
 
  • #4


Originally posted by Xamfy19
I took cos(46) of 2 m/s2 and used for the formula. It's not the correct answer. Do I need to figure out the linear speed? (apparently it is not 18 m/s)?
The linear speed is 18 m/s, nothing wrong with that.

Draw a picture of what's happening and you will see that you took the component of the acceleration incorrectly.
 
  • #5
should be sin instead of cos

I guess I've mistaken the direction 46 degrees north of west as west of north. I have just tried again and it worked. Thanks alot.
 

1. How do you calculate a car's travel in a flat circle?

To calculate a car's travel in a flat circle, you will need to know the car's speed, the radius of the circle, and the time it takes to complete one full circle. You can then use the formula: distance = (speed * time) / 2πr, where r is the radius of the circle. This will give you the total distance traveled by the car in one complete circle.

2. What factors can affect a car's travel in a flat circle?

There are a few factors that can affect a car's travel in a flat circle, such as the car's speed, the radius of the circle, any friction or resistance on the surface, and the car's handling and steering capabilities. These factors can impact the distance traveled and the time it takes to complete one full circle.

3. How can you improve a car's travel in a flat circle?

To improve a car's travel in a flat circle, you can make changes to the car's design and mechanics, such as increasing the car's horsepower or improving its handling and steering. You can also choose a smooth surface to minimize friction and resistance, and ensure that the car is properly maintained and in good condition.

4. Can a car travel in a perfect flat circle?

Technically, no car can travel in a perfect flat circle, as there will always be some variations in the surface and external factors that can affect the car's movement. However, with the right conditions and adjustments, a car can come very close to traveling in a flat circle.

5. Why is it important to understand a car's travel in a flat circle?

Understanding a car's travel in a flat circle can help with various aspects of car design and performance, such as improving handling and steering, optimizing speed and efficiency, and ensuring safety. It can also be a useful concept in fields such as physics and engineering.

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