Area under graph of 'energy versus time' graph

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SUMMARY

The discussion centers on the interpretation of the area under an 'energy versus time' graph, particularly when the graph features a horizontal line indicating zero power. It is established that while power is the rate of energy conversion, the area under the curve can still hold significance in contexts such as Hamiltonian-Lagrangian mechanics, where it relates to action. The conversation also clarifies that two lines with the same slope represent the same power, but their absolute energy levels can differ, impacting energy dissipation. The key takeaway is that zero power indicates no change in energy, not the absence of energy itself.

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  • Understanding of basic physics concepts such as energy, power, and work.
  • Familiarity with energy versus time graphs and their interpretations.
  • Knowledge of Hamiltonian-Lagrangian mechanics.
  • Basic principles of rotational dynamics and angular momentum.
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  • Research Hamiltonian-Lagrangian mechanics and its applications in physics.
  • Explore the relationship between energy, power, and work in classical mechanics.
  • Study the implications of energy versus time graphs in various physical systems.
  • Investigate the role of angular momentum in rotational dynamics.
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Students and professionals in physics, particularly those studying mechanics, energy systems, and anyone interested in the mathematical interpretation of physical concepts in energy versus time graphs.

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.
 
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