InterviewSolution
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InterviewSolution
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An artificial satellite in the presence of frictional forces will move into an orbit closer to the earth and may have increased kinetic energy. Explain this. |
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Answer» `E` (total Energy)`=1/2mv^(2)+(-(GMm)/r)` where `m` is the mass of the satellite `M=`mass of the earth and `r=` radius of the orbit. Being the dynamics of circlar motion, `(GMm)/(r_(2))=(mv^(2))/r` or `v^(2)=(GM)/r` Hence `E=(-1)/2(GM)/r m=-1/2 mv^(2)=-k` (kinetic energy) `E_(i)` (initial energy) `=-1/2(GM)/(r_(0))` `E_(f)` (final energy) `=-1/2(GM)/r` By the principle of conservation of energy `E_(i)=E_(f)+W`( work done by frictional force) `implies-1/2(GM)/(r_(0))=1/2(GM)/r+W` or `1/2 GM(1/r-1/(r_(0)))=W ` (a positive quantity) `:. 1/rgt1/(r_(0))` or `rltr_(0)` Also, `K_(0)=-K+W` or `K-K_(0)=W` (a positive quantity) `:. KltK_(0)` |
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