Effective acceleration due to gravity in non-inertial frame

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Discussion Overview

The discussion revolves around the concept of effective acceleration due to gravity in a non-inertial frame, particularly in the context of a pendulum system within an accelerating car. Participants explore the implications of fictitious forces and the relationship between apparent and true forces in non-inertial frames.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes a pendulum system in an accelerating car and seeks clarification on the concept of effective gravity, specifically the vector sum of fictitious and gravitational forces.
  • Another participant suggests an Insight article as a resource for understanding the topic.
  • A participant expresses confusion about the relationship between apparent force and true force, questioning whether apparent acceleration can ever equal zero in a non-inertial frame.
  • There is a correction regarding the formulation of net force, with a participant emphasizing that net force equals mass times acceleration (F_net = ma).
  • Clarifications are made regarding the definitions of measured acceleration and the acceleration of the non-inertial frame.
  • A participant reiterates the relationship between net force, true force, and apparent force in a linearly accelerating reference frame.
  • Another participant argues that one cannot conclude that apparent acceleration is always zero, citing everyday experiences with objects in non-inertial frames.
  • A later reply discusses the indistinguishability of being at rest in an elevator versus being in free space under acceleration, relating this to the perception of weight.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of apparent acceleration and its implications in non-inertial frames. There is no consensus on whether apparent acceleration can be considered zero, and the discussion remains unresolved regarding the implications of fictitious forces.

Contextual Notes

Participants reference definitions and relationships between forces that may depend on specific assumptions about the system being analyzed. The discussion includes unresolved mathematical steps and varying interpretations of the concepts involved.

Lost1ne
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Take some sort of system accelerating with respect to an inertial reference frame: let's take a spherical mass on the end of a string forming a simple pendulum with the ceiling of a car, and allow that car to accelerate uniformly.

Could someone share with me how they interpret the concept of a geffective where we take the vector sum of the fictitious force and the gravitational force acting on the mass? I don't feel as if I'm understanding it at a level that I would like to.
 
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I'm missing something elementary here. If F_apparent = F_true - mA and A comes from F_true = mA, then we may reach the conclusion that a_apparent equals zero always. I've realized that I also used your way of thinking in the article where we add on the fictitious forces and then make the claim that our object of interest is not accelerating in our non-inertial reference frame. But, looking back at this, doesn't it not make sense for a_apparent to undisputedly equal zero? We view numerous objects accelerating through our non-inertial reference frame daily.
 
Lost1ne said:
...and A comes from F_true = mA,
No, F_net = ma.
 
A.T. said:
No, F_net = ma.
Aha. "a" is the measured acceleration of our object/system of interest from our inertial reference frame, and "A" is the acceleration of our *non-inertial reference frame with respect to our *inertial reference frame.
 
Lost1ne said:
Aha. "a" is the measured acceleration of our object/system of interest from our inertial reference frame, and "A" is the acceleration of our *non-inertial reference frame with respect to our *inertial reference frame.
Lets stick to lower case with subsctpt:

Fnet = Ftrue + Fapparent = mabody

Where for a linearly accelerating reference frame:

Fapparent = -maframe
 
Lost1ne said:
But, looking back at this, doesn't it not make sense for a_apparent to undisputedly equal zero? We view numerous objects accelerating through our non-inertial reference frame daily.
That is all correct. One is (by definition) at rest and remains at rest with respect to one's frame of reference. If you are in an elevator you will not be able to tell the difference between the following two cases: (a) The elevator is at rest near the surface of the Earth; (b) the elevator is in free space accelerating with acceleration g (relative to an inertial frame) in a direction from your feet to your head. In either case if you are standing on a bathroom scale, it will display what you know to be your true weight.
 

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