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Energy conservation
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To the extent that there are no forces that lead to convert mechanical energy into heat, the sum of all the energies of all the particles in the system is constant. This occurs even when elastic shocks occur that transfer energy between particles without being lost or won.
ID:(1294, 0)
Energy conservation
Description
To the extent that there are no forces that lead to convert mechanical energy into heat, the sum of all the energies of all the particles in the system is constant. This occurs even when elastic shocks occur that transfer energy between particles without being lost or won.
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Calculations
Variable
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Equation
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Equations
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 }$ |
(ID 9903)
Examples
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 }$ |
(ID 9903)
ID:(1294, 0)