Area under graph of 'energy versus time' graph

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Discussion Overview

The discussion centers around the interpretation of the area under an 'energy versus time' graph, particularly in relation to power, energy conversion, and the implications of different slopes on the graph. Participants explore theoretical aspects, potential applications in mechanics, and the significance of absolute energy values.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the meaning of the area under a horizontal line in an energy-time graph, suggesting that if power is zero, then no energy should be used.
  • Another participant argues that the area under the graph may not have a meaningful value unless considered in the context of quantum mechanics and phase shifts.
  • There is a discussion about whether two lines with gentle upward slopes represent the same power, with a participant noting that absolute energy values are meaningless in classical physics.
  • One participant suggests that the area under the curve could have relevance in Hamiltonian-Lagrangian mechanics, as action has units of energy multiplied by time.
  • Another participant points out that while angular momentum shares units with energy-time, it is a vector quantity, whereas the integral of energy over time is a scalar.
  • A participant clarifies that no power implies no change in energy, indicating that the energy of a system remains constant over time.
  • Another participant disputes the idea that energy dissipated is the same for two systems with the same power, suggesting that while energy gained is the same, the percentage change may differ.

Areas of Agreement / Disagreement

Participants express differing views on the significance of the area under the graph and the implications of power and energy in various contexts. There is no consensus on the interpretation of absolute energy values or the relationship between power and energy dissipation.

Contextual Notes

Participants highlight limitations in understanding the implications of energy-time graphs, particularly regarding the definitions of energy and the context of classical versus quantum mechanics.

chewchun
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Lets say i have a horizontal line which is above the x-axis in a 'energy versus time' graph.
Since gradient is zero,power is zero.
From what i have known,power is the rate at which energy is converted or work is done.
If power is zero,no work is done or no energy is converted,then what is the area below the horizontal line? No power is done,means no energy should be used?

Second question.If both line have a gentle,upward sloping gradient,power is the same right?
But what is one of the line is way up,while another line is just above the x-axis.
They both have the same power but the energy dissipated is different.Why is this so??
 
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I do not think the area in an energy-time-graph has a meaningful value, unless you think about quantum mechanics and phase shifts.

Second question.If both line have a gentle,upward sloping gradient,power is the same right?
Which lines where? The same slope in the same graph corresponds to the same power somewhere.

But what is one of the line is way up,while another line is just above the x-axis.
Absolute energy is meaningless in classical physics. You can define "0" wherever you want.
 
The area under a curve in an energy vs. time graph might find some meaning in Hamiltonian-Lagrangian mechanics. Action has units of Energy*time. When finding the path taken by a physical particle, you might have to find that quantity. It also might find use in rotational dynamics...since angular momentum has the same units.
 
Reptillian said:
It also might find use in rotational dynamics...since angular momentum has the same units.
Except, angular momentum is a vector. ∫energy.dt will necessarily be a scalar.
 
haruspex said:
Except, angular momentum is a vector. ∫energy.dt will necessarily be a scalar.

Could be a magnitude :approve:
 
chewchun said:
No power is done,means no energy should be used?
Wrong ! No power means there is no CHANGE in energy thus the energy of a system remains constant with respect to time.
chewchun said:
They both have the same power but the energy dissipated is different.

Wrong ! The energy gained by both systems is exactly the same with time, however the percentage change will be different.
 
Last edited:

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