The mass of a spaceship is 1000 kg. It is to | vedclass

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(A) The energy required to launch an object of mass $m$ from the earth's surface to infinity (free space) is equal to the gravitational potential ener

Vedclass · Accepted Answer

$6.4 	imes 10^{10} \ J$

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(A) The energy required to launch an object of mass $m$ from the earth's surface to infinity (free space) is equal to the gravitational potential energy at the surface,which is given by the formula: $E = \frac{GMm}{R}$.Since the acceleration due to gravity at the surface is $g = \frac{GM}{R^2}$,we can write $GM = gR^2$.Substituting this into the energy equation: $E = \frac{(gR^2)m}{R} = mgR$.Given values: $m = 1000 \ kg$,$g = 10 \ m/s^2$,and $R = 6400 \ km = 6.4 	imes 10^6 \ m$.Calculating the energy: $E = 1000 	imes 10 	imes 6.4 	imes 10^6 = 6.4 	imes 10^{10} \ J$.

The mass of a spaceship is $1000 \ kg$. It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth) are $10 \ m/s^2$ and $6400 \ km$ respectively. The required energy for this work will be

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