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Ejemplo de Energías
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Variable
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Equation
To be used
Equations
As the gravitational force is
| $ F_g = m_g g $ |
with $m$ representing the mass. To move this mass from a height $h_1$ to a height $h_2$, a distance of
| $ V = m g ( h_2 - h_1 )$ |
is covered. Therefore, the energy
| $ dW = \vec{F} \cdot d\vec{s} $ |
with $\Delta s=\Delta h$ gives us the variation in potential energy:
$\Delta W = F\Delta s=mg\Delta h=mg(h_2-h_1)=U_2-U_1=\Delta V$
thus, the gravitational potential energy is
| $ V = - m_g g z $ |
(ID 3245)
En el caso el stico (resorte) la fuerza es
| $$ |
con
| $ dW = \vec{F} \cdot d\vec{s} $ |
\\n\\nLa diferencia\\n\\n
$\Delta x = x_2 - x_1$
\\n\\ncorresponde al camino recorrido por lo que\\n\\n
$\Delta W=k,x,\Delta x=k(x_2-x_1)\displaystyle\frac{(x_1+x_2)}{2}=\displaystyle\frac{k}{2}(x_2^2-x_1^2)$
y con ello la energ a potencial el stica es
| $ V =\displaystyle\frac{1}{2} k x ^2$ |
(ID 3246)
When an object moves from a height $h_1$ to a height $h_2$, it covers the difference in height
$h = h_2 - h_1$
thus, the potential energy
| $ V = - m_g g z $ |
becomes equal to
| $ V = m g ( h_2 - h_1 )$ |
(ID 7111)
Examples
At the surface of the planet, the gravitational force is
| $ F_g = m_g g $ |
and the energy
| $ dW = \vec{F} \cdot d\vec{s} $ |
can be shown to be
| $ V = - m_g g z $ |
(ID 3245)
To lift an object from height $h_1$ to a height $h_2$, energy is required, which we will call gravitational potential energy
| $ V = - m_g g z $ |
and which is proportional to the gained height:
| $ V = m g ( h_2 - h_1 )$ |
(ID 7111)
The elongation $\Delta x$ of a spring is calculated as the difference between its original position $x_1$ and its current position $x_2$, which is expressed as
| $ V =\displaystyle\frac{1}{2} k ( x_2 ^2- x_1 ^2)$ |
It is commonly defined that if a spring is stretched, the elongation is positive, and if it is compressed, it is negative.
(ID 7112)
En el caso el stico (resorte) la fuerza es
| $$ |
la energ a
| $ dW = \vec{F} \cdot d\vec{s} $ |
se puede mostrar que en este caso es
| $ V =\displaystyle\frac{1}{2} k x ^2$ |
(ID 3246)
ID:(686, 0)