What Determines the Total Acceleration Vector at the Top of a Roadway Rise?

Click For Summary
SUMMARY

The discussion focuses on the determination of the total acceleration vector for a car at the top of a roadway rise, as presented in example 4.9 of "Physics for Scientists and Engineers, 6th edition" by Serway and Jewett. The car experiences a constant tangential acceleration of 0.3 m/s² and a radial acceleration calculated using the formula v²/r, resulting in -0.0720 m/s². Participants clarify that while radial acceleration is a kinematic quantity derived from speed and radius, gravitational acceleration does not directly contribute to the total acceleration vector at this point due to the upward normal force from the road. The conversation emphasizes the distinction between acceleration as a geometric concept and force as a physical one.

PREREQUISITES
  • Understanding of kinematic equations, specifically radial and tangential acceleration.
  • Familiarity with the concepts of normal force and gravitational force.
  • Knowledge of circular motion principles, including the formula for radial acceleration (v²/r).
  • Basic physics concepts from "Physics for Scientists and Engineers, 6th edition" by Serway and Jewett.
NEXT STEPS
  • Study the derivation and application of radial acceleration in circular motion.
  • Explore the relationship between forces acting on an object and its acceleration.
  • Review the concepts of normal force and gravitational force in different motion scenarios.
  • Examine example problems involving tangential and radial acceleration in physics textbooks.
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of motion on curved paths.

TRAyres
Messages
4
Reaction score
0
Howdy all, I had a quick question:

An example problem in my physics book (Physics for Scientists and Engineers, 6th edition, Serway and Jewett) is going over tangential and radial acceleration (it is example 4.9, if you've got a copy lying around).

The question is as follows:
A car exhibits a constant acceleration of .3 m/s^2 parallel to the roadway. The car passes over a rise in the roadway such that the top of the rise is shaped like a circle of radius 500m. At the moment the car is at the top of the rise, its velocity vector is horizontal and has a magnitude of 6.0 m/s. What is the direction of the total acceleration vector for the car at this instant?

If someone requests the picture, I can use my scanner to help the discussion along, just let me know.

My question comes from their use of the radial acceleration - they plugged the tangential speed (6 m/s) into v^2/r, it is in the negative radial direction, so acceleration(radial)=-.0720m/s^2.

That is the tangential acceleration coming from moving in a circle at a constant speed. Yeah. But if this car was on Earth, wouldn't we add that to the acceleration due to gravity, which is also in the negative radial direction? That is how I did the problem, then looked at their answer and was confused as to why the hell they wouldn't include acceleration due to gravity here.

Thanks for the help all!
 
Physics news on Phys.org
TRAyres said:
My question comes from their use of the radial acceleration - they plugged the tangential speed (6 m/s) into v^2/r, it is in the negative radial direction, so acceleration(radial)=-.0720m/s^2.
OK.
That is the tangential acceleration coming from moving in a circle at a constant speed.
You mean the radial acceleration.
Yeah. But if this car was on Earth, wouldn't we add that to the acceleration due to gravity, which is also in the negative radial direction? That is how I did the problem, then looked at their answer and was confused as to why the hell they wouldn't include acceleration due to gravity here.
No, the radial acceleration is a kinematic quantity that you calculate based on the given information (speed and radius). If the car were in free fall, then its acceleration would be g downward. But it's not. Gravity is not the only force acting on the car--the road pushes up, negating much--but not all--of the force of gravity.

What if the car were just traveling along a horizontal road with no bump in the road? What would its vertical acceleration be? Would you add g in that case?
 
Hi TRAyres! :smile:

I'll just add this to what Doc Al says:

Acceleration is geometry.

Force is physics.

Once you know that a body moves in a certain way, then its acceleration is a matter of geometry, and has nothing to do with forces. :smile:
 
Hot damn, thank you both! Now I'm genuinely glad I asked.
 
The vertical acceleration comes from gravity and the normal force. Their vector sum will be (v^2/r)
 

Similar threads

Undergrad Total acceleration at the bottom of a rolling wheel
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Weight is less at equator than poles -- Acceleration vectors involved?
  • · Replies 8 ·
Replies
8
Views
2K
Determine the magnitude of its radial acceleration for ball
  • · Replies 7 ·
Replies
7
Views
4K
Finding radial & tangential acceleration at a point
  • · Replies 7 ·
Replies
7
Views
6K
Tangential, Radial and total acceleration
  • · Replies 1 ·
Replies
1
Views
2K
Tangential and radial acceleration
  • · Replies 23 ·
Replies
23
Views
8K
Undergrad Intuitive explanation of the acceleration vector
  • · Replies 2 ·
Replies
2
Views
4K
Uniform Circular Motion: Tension Force at Top of Circle
  • · Replies 4 ·
Replies
4
Views
1K
Tangential and Radial components of acceleration and tension
  • · Replies 3 ·
Replies
3
Views
25K
Tangential and Radial Acceleration
  • · Replies 3 ·
Replies
3
Views
5K