Acceleration question (circular motion)

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Homework Help Overview

The discussion revolves around the acceleration of a car traveling at a constant speed of 60 km/h while navigating different types of curves—sharp versus gentle. Participants explore the relationship between the curvature of the path and the resulting acceleration, particularly in the context of circular motion.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss whether the acceleration differs between sharp and gentle curves, with one suggesting that the rate of change in direction affects acceleration. Others introduce equations related to circular motion to analyze the situation further.

Discussion Status

There is active engagement with the concepts, including the introduction of relevant equations. Participants are questioning how changes in the curve's sharpness affect the variables in the equations, and some guidance has been provided regarding the implications of sharper bends on acceleration.

Contextual Notes

Participants are considering the effects of friction in relation to sharper curves, with some uncertainty about how friction behaves under these conditions. The discussion reflects a mix of assumptions and interpretations regarding the physics involved.

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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

None

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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