Acceleration question (circular motion)

In summary, the acceleration of a car will not be the same when traveling around a sharp curve at a constant speed of 60 km/h compared to traveling around a gentle curve at the same speed. This is because when turning sharply, the car's direction changes quickly, resulting in a higher acceleration. This can be confirmed using the formula ac = v^2/r, where a smaller radius (sharper curve) will result in a larger acceleration. The car is also more likely to slide off the road and crash on a sharper bend due to a decrease in friction, which can cause it to lose control.
  • #1
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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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  • #2
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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  • #3
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
 
  • #4
The first one looks good. Can you see what would happen to the variables in that equation if the corner became sharper?
 
  • #5
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
 
  • #6
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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  • #7
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.
 
  • #8
Right idea, but there's no real reason for the friction to decrease, it's more likely to remain constant...
 
  • #9
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!
 

1. What is circular motion?

Circular motion is a type of motion in which an object follows a circular path around a fixed point, also known as the center of rotation. This type of motion is often seen in objects such as planets orbiting around a star or a child riding a merry-go-round.

2. What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences while moving in a circular path. It is always directed towards the center of rotation and its magnitude is given by the equation a = v^2/r, where v is the velocity of the object and r is the radius of the circular path.

3. How is centripetal acceleration related to force?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it. In circular motion, the centripetal acceleration is caused by a centripetal force that is directed towards the center of rotation and keeps the object moving in a circular path.

4. Can an object have centripetal acceleration without changing its speed?

Yes, an object can have centripetal acceleration without changing its speed. This is because acceleration is a vector quantity and consists of both magnitude and direction. In circular motion, the direction of the velocity is constantly changing, resulting in a non-zero acceleration even if the speed remains constant.

5. What is the difference between centripetal and centrifugal force?

Centripetal force is the force that acts towards the center of rotation, while centrifugal force is the apparent outward force that an object experiences when moving in a circular path. Centrifugal force is a fictitious force and does not actually exist, whereas centripetal force is a real force that keeps the object moving in a circular path.

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