Messed up classical mechanics problem:

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Discussion Overview

The discussion revolves around a classical mechanics problem involving a person walking in a bus that is accelerating and then cruising at a constant speed. Participants explore concepts of potential energy, kinetic energy, and the work done by the person relative to the bus's motion.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant describes feeling as if they gained potential energy while walking in the bus due to the bus's acceleration.
  • Another participant suggests that the potential energy may have been transferred to the bus, but expresses uncertainty about this idea.
  • A different viewpoint indicates that when the bus reaches constant velocity, the person would feel a forward motion due to the difference in forces applied while walking.
  • Some participants argue that the work done by the person while walking is not wasted, as it helps them keep up with the bus's acceleration.
  • There is a discussion about whether the energy gained is potential or kinetic, with some asserting it is kinetic energy since the person is moving at the same speed as the bus after sitting down.
  • One participant emphasizes that the engine of the bus must compensate for the extra force exerted by the person while walking, affecting the bus's acceleration.
  • Another participant questions the concept of potential energy in a non-constant acceleration frame, suggesting it complicates the understanding of energy transfer in this scenario.
  • There are conflicting views on whether the work done by the person contributes to the bus's energy or if it solely increases their own kinetic energy.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the nature of energy transfer and the effects of walking in an accelerating bus. The discussion remains unresolved, with no consensus on the definitions or implications of potential and kinetic energy in this context.

Contextual Notes

Participants highlight the complexity of energy transfer in non-inertial reference frames and the implications of varying acceleration on the concepts of potential and kinetic energy. There are unresolved assumptions regarding the definitions of energy in this scenario.

  • #31
In Curl's initial statement, there is no change in potenial energy (gravitational or otherwise). The work done by Curl while walking to the front of the bus while it is accelerating is increasing his kinetic energy.
If he were sitting in his seat during the acceleration (the easier way), the force exerted by his seat back acting through the distance the bus accelerated would do the work necessary to increase Curl's kinetic energy.
 
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  • #32
Curl said:
This is really simple but I can't figure it out. I was on a bus when I thought of this:

Say I'm sitting in the back of a bus which is traveling on a flat surface, and accelerating with a constant acceleration (forward). Now I get up from my seat in the back and make my way to the front of the bus and take a seat at the front. Shortly after I sit down, the bus stops accelerating and is cruising at constant speed.
When I was walking (say at constant rate relative to the floor of the bus) I felt like I was doing work against a "fictitious" gravity force, so it felt like I gained some "potential" energy. Now that the bus is not accelerating anymore, it seems like that potential is gone and some energy is lost. Where did it go?
Curl, how fast do you estimate the bus' instantaneous velocity was when you started? How much was it when you sat down again, and how many seconds elapsed in between?
 

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