Acceleration question (circular motion)

Click For Summary
SUMMARY

The acceleration of a car traveling around a sharp curve at a constant speed of 60 km/h differs from that of a car navigating a gentle curve at the same speed. This difference arises because the rate of change in direction is greater for a sharp turn, resulting in higher centripetal acceleration. The relevant formula for calculating this acceleration is ac = v2/r, where v is the velocity and r is the radius of the curve. As the radius decreases with sharper turns, the acceleration increases, leading to a higher risk of losing traction.

PREREQUISITES
  • Understanding of centripetal acceleration
  • Familiarity with the formula ac = v2/r
  • Basic knowledge of circular motion dynamics
  • Concept of friction in vehicle dynamics
NEXT STEPS
  • Research the implications of radius changes on centripetal acceleration
  • Explore the role of friction in vehicle stability during turns
  • Study the effects of speed on vehicle handling in circular motion
  • Learn about the physics of skidding and loss of traction in sharp turns
USEFUL FOR

Physics students, automotive engineers, and anyone interested in the dynamics of vehicle motion and safety during turns.

SmallPub
Messages
19
Reaction score
0

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?
 
Physics news on Phys.org
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?
 
  • Like
Likes   Reactions: 1 person
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?
 
  • Like
Likes   Reactions: 1 person
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!
 

Similar threads

Friction direction change in a inclined circular bend (car on a road)
  • · Replies 11 ·
Replies
11
Views
1K
Acceleration in uniform circular motion is uniform or non-uniform?
  • · Replies 55 ·
2
Replies
55
Views
3K
Find the acceleration in circular motion
  • · Replies 6 ·
Replies
6
Views
2K
Problem with the power of car
  • · Replies 3 ·
Replies
3
Views
1K
Circular motion — the acceleration is not constant?
  • · Replies 1 ·
Replies
1
Views
2K
Help with question on motion: Avoiding a rear-end collision
  • · Replies 6 ·
Replies
6
Views
3K
Kinematics, curvilinear motion (a couple of questions)
  • · Replies 30 ·
2
Replies
30
Views
2K
How Do You Calculate Race Car Acceleration and Power Output?
  • · Replies 20 ·
Replies
20
Views
2K
What actually is the centripetal acceleration formula?
  • · Replies 28 ·
Replies
28
Views
3K
Circular Motion Questions (energies, forces, angular velocities, etc.)
  • · Replies 2 ·
Replies
2
Views
2K