-->

Motion In Straight Line

Question
CBSEENPH11017851

An artificial satellite of mass 300 kg is revolving in an orbit at a height equal 500km from the surface of the earth. Find the kinetic energy, potential energy and total energy of satellite. (Take g = 9.8 m/s2 at the surface of the earth)

Solution

Mass of the satellite = 300 kg
Height  = 500 km, from the surface of the Earth
Here, we have
r = R + h
   = 6.4 x 106 + 500 x 103
   = 7.0 x 10m
m = 300 kg;
M = 6 x 1024 kg;
G = 6.67 x 10-11 N m2 kg-2

i) K.E of satellite =
 1 half space mv squared space equals space 1 half space straight m space GM over straight r

space space space space space space space space space space space space space space equals space 1 half cross times 300 straight x open parentheses fraction numerator 6.67 space straight x 10 to the power of negative 11 end exponent space straight x space 6 space straight x space 10 to the power of 24 over denominator 7 space straight x space 10 to the power of 6 end fraction close parentheses

space space space space space space space space space space space space space equals space 8.7 space straight x space 10 to the power of 9 space straight J
ii right parenthesis space straight P. straight E space equals space minus space fraction numerator straight G space straight M space straight m over denominator straight r end fraction

space space space space space space space space space space space equals space fraction numerator negative left parenthesis 6.67 space straight x space 10 to the power of negative 11 end exponent right parenthesis space straight x space left parenthesis space 6 space straight x 10 to the power of 24 right parenthesis space straight x space 300 over denominator 7 space straight x space 10 to the power of 6 end fraction

space space space space space space space space space space equals space minus 17.4 space straight x space 10 to the power of 9 space straight J

iii right parenthesis straight T. straight E space equals space straight K. straight E space plus space straight P. straight E space

space space space space space space space space space space space equals 8.7 space straight x space 10 to the power of 9 space plus space left parenthesis negative 17.4 space straight x space 10 to the power of 9 right parenthesis space

space space space space space space space space space space space equals space minus 8.7 space straight x space 10 to the power of 9 space straight J