# Area under graph of 'energy versus time' graph

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??

mfb
Mentor
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.

haruspex
Homework Helper
Gold Member
2020 Award
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.

Except, angular momentum is a vector. ∫energy.dt will necessarily be a scalar.

Could be a magnitude

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.
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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