Explain the escape energy of a body of mass $m$ lying on the surface of the Earth.
(N/A) The escape energy of a body is defined as the minimum energy required to move the body from the surface of the Earth to infinity,such that its final kinetic energy at infinity is zero.
The gravitational potential energy $U$ of a body of mass $m$ at the surface of the Earth (at distance $R_E$ from the center) is given by:
$U = -\frac{GM_Em}{R_E}$
To move the body to infinity,where the potential energy is zero,we must provide an amount of energy equal to the magnitude of this potential energy.
Therefore,the escape energy $E_e$ is:
$E_e = -U = -\left(-\frac{GM_Em}{R_E}\right) = +\frac{GM_Em}{R_E}$
This energy is typically provided in the form of kinetic energy to the body to allow it to escape the Earth's gravitational pull.
The gravitational potential energy $U$ of a body of mass $m$ at the surface of the Earth (at distance $R_E$ from the center) is given by:
$U = -\frac{GM_Em}{R_E}$
To move the body to infinity,where the potential energy is zero,we must provide an amount of energy equal to the magnitude of this potential energy.
Therefore,the escape energy $E_e$ is:
$E_e = -U = -\left(-\frac{GM_Em}{R_E}\right) = +\frac{GM_Em}{R_E}$
This energy is typically provided in the form of kinetic energy to the body to allow it to escape the Earth's gravitational pull.
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