Respuesta :
Answer:
The required work done is [tex]6.5\times10^{9}\ J[/tex]
Explanation:
Given that,
Mass of each satellites = 940 kg
Altitude of A = 4500 km
Altitude of B = 11100 km
We need to calculate the potential energy
Using formula of potential
[tex]U_{A}=-\dfrac{Gm_{A}m_{E}}{r_{A}}[/tex]
Put the value into the formula
[tex]U_{A}=-\dfrac{6.67\times10^{-11}\times940\times5.98\times10^{24}}{6.38\times10^{6}+4.50\times10^{6}}[/tex]
[tex]U_{A}=-3.44\times10^{10}\ J[/tex]
We need to calculate the potential energy
Using formula of potential
[tex]U_{B}=-\dfrac{Gm_{B}m_{E}}{r_{A}}[/tex]
Put the value into the formula
[tex]U_{B}=-\dfrac{6.67\times10^{-11}\times940\times5.98\times10^{24}}{6.38\times10^{6}+11.10\times10^{6}}[/tex]
[tex]U_{B}=-2.14\times10^{10}\ J[/tex]
We need to calculate the value of [tex]k_{A}[/tex]
Using formula of [tex]k_{A}[/tex]
[tex]k_{A}=-\dfrac{1}{2}U_{A}[/tex]
Put the value into the formula
[tex]k_{A}=\dfrac{1}{2}\times3.44\times10^{10}[/tex]
[tex]k_{A}=1.72\times10^{10}\ J[/tex]
We need to calculate the value of [tex]k_{B}[/tex]
Using formula of [tex]k_{B}[/tex]
[tex]k_{B}=-\dfrac{1}{2}U_{B}[/tex]
Put the value into the formula
[tex]k_{B}=\dfrac{1}{2}\times2.14\times10^{10}[/tex]
[tex]k_{B}=1.07\times10^{10}\ J[/tex]
We need to calculate the work done
Using formula of work done
[tex]W=\Delta K+\Delta U[/tex]
[tex]W=(k_{B}-k_{A})+(U_{B}-U_{A})[/tex]
[tex]W=(-\dfrac{U_{B}}{2}+\dfrac{U_{A}}{2})+(U_{B}-U_{A})[/tex]
[tex]W=\dfrac{1}{2}(U_{B}-U_{A})[/tex]
Put the value into the formula
[tex]W=\dfrac{1}{2}\times(-2.14\times10^{10}+3.44\times10^{10})[/tex]
[tex]W=6.5\times10^{9}\ J[/tex]
Hence, The required work done is [tex]6.5\times10^{9}\ J[/tex]
