Acceleration question (circular motion)

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The acceleration of a car differs when navigating sharp versus gentle curves at the same speed due to the rate of change in direction. A sharper turn results in a smaller radius, which increases the centripetal acceleration, as described by the formula ac = v^2/r. This means that the car experiences greater acceleration on a sharp curve compared to a gentle one. Additionally, while friction remains constant, the likelihood of sliding off the road increases on sharper bends due to the higher acceleration demands. Understanding these dynamics is crucial for safe driving in varying road conditions.
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Homework Statement

will the acceleration of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Homework Equations

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The Attempt at a Solution

No the acceleration will not be the same because when you are turning the car sharply so you are changing your direction right away. If you are turning at a gentle curve at the same speed you are changing your direction not as fast as a sharp turn so the acceleration would be different. Am I correct?
 
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You are correct. There is an equation you could use to confirm your answer. If you assume that while the car travels around the bend it is briefly in circular motion, what formula could you use to describe the acceleration?
 
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BOYLANATOR said:
You are correct. There is an equation you could use to confirm your answer. If you assume that while the car travels around the bend it is briefly in circular motion, what formula could you use to describe the acceleration?

I was thinking ac = v^2/r , ac= 4∏^2r/T^2

But I am not sure
 
The first one looks good. Can you see what would happen to the variables in that equation if the corner became sharper?
 
BOYLANATOR said:
The first one looks good. Can you see what would happen to the variables in that equation if the corner became sharper?
Would the radius become smaller making the acceleration larger? Correct me if I'm wrong
 
Yes. For a bonus, why is the car more likely to slide off the road and crash on the sharper bend?
 
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BOYLANATOR said:
Yes. For a bonus, why is the car more likely to slide off the road and crash on the sharper bend?
There would be less friction to keep the car on the road, making the car crash.
 
Right idea, but there's no real reason for the friction to decrease, it's more likely to remain constant...
 
BOYLANATOR said:
Right idea, but there's no real reason for the friction to decrease, it's more likely to remain constant...
Ok got it! Thanks for the help!
 

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