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

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Discussion Overview

The discussion revolves around the determination of the total acceleration vector of a car at the top of a roadway rise, specifically addressing the roles of tangential and radial acceleration, as well as the influence of gravity. Participants explore the implications of these accelerations in the context of a physics problem involving a car moving over a circular rise.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the omission of gravitational acceleration when calculating the total acceleration vector, suggesting that it should be included alongside radial acceleration.
  • Another participant clarifies that radial acceleration is a kinematic quantity derived from speed and radius, and emphasizes that gravity is not the only force acting on the car.
  • A different viewpoint suggests that acceleration can be understood geometrically, independent of forces, indicating a conceptual distinction between acceleration and force.
  • One participant notes that the vertical acceleration results from the vector sum of gravitational force and the normal force acting on the car.

Areas of Agreement / Disagreement

Participants express differing views on whether gravitational acceleration should be included in the total acceleration calculation. There is no consensus on this matter, as some argue for its inclusion while others maintain that it is not necessary in this context.

Contextual Notes

The discussion highlights the complexity of analyzing forces and accelerations in non-linear motion, with participants referencing specific conditions and assumptions related to the problem scenario.

TRAyres
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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!
 
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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)
 

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