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Total Energy
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The total energy is the sum of the total kinetic energy and the potential energy where the total kinetic energy is the sum of the kinetic energy of translation and rotation.
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Total Energy
Equation
The total energy corresponds to the sum of the total kinetic energy and the potential energy:
 $ E = K + V $ |
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Energy Conservation
Equation
When we have friction, we observe that bodies heat up, which makes sense to discuss thermal energy. In these cases, the total energy
| $ E = K + V $ |
doesn't seem to be conserved unless we interpret the generated heat as another form of energy. Mohr was the first to realize that the sum of kinetic energy $K$, potential energy $V$, and thermal energy $Q$ is conserved
| $ E = K + U + Q $ |
and there are only conversions between these.
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Total Kinetic Energy
Equation
In a more complex system, the total kinetic energy is equal to the sum of the kinetic energies of the individual parts
| $ K = \displaystyle\sum_i K_i $ |
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Total Potential Energy
Equation
In a more complex system, the total potential energy is equal to the sum of the potential energies of the individual parts
| $ U =\displaystyle\sum_i U_i $ |
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Free falling object
Equation
An object that is raised to a height $h$ gains potential energy
| $ V = m_g g z $ |
If the object begins to fall, the potential energy transforms into kinetic energy,
| $ K_t =\displaystyle\frac{1}{2} m_i v ^2$ |
thus, the speed at which it impacts the ground is:
| $ v =\sqrt{2 g h }$ |
When an object is raised to a height $h$, it gains potential energy
| $ V = m_g g z $ |
If the object starts to fall, the potential energy will transform into kinetic energy:
| $ K_t =\displaystyle\frac{1}{2} m_i v ^2$ |
By the time the object reaches the ground ($h=0$), all the potential energy has been converted into kinetic energy, leading to the equation:
$\displaystyle\frac{m}{2}v^2=mgh$
If the velocity is solved for, it can be obtained as
| $ v =\sqrt{2 g h }$ |
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Video
Video: Total Energy