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there are 2 formulas for escape vel,in what condition should we use the first formula and where should we use the second? |
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Answer» уσυ нєℓρ !!! when SATELLITE is at earth surface thentotal energy = PE + KEPE = -GMm/R , (KE)i = ? (M is mass of earth )TE = (KE)i - GMm/R .....1 (R is radius of earth) when satellite escapes from earths gravitational field then it reaches to infinity ...total energy finally = TE = KE + PEPE = GMm/r ( r is infinity )PE = 0 , (KE)F = ?TE = (KE)f + 0 = (KE)f .............2 since energy is conserved so eq 1 equals eq 2-GMm/R + (KE)i = (KE)f (KE)i = GMm/R + (KE)f .................3from this eq we can see that if (KE)f is 0 then (KE) intial is minimum value of energy should be GIVEN to satellite so that it escapes out...now , (KE)i = mv2/2 , (KE)f = 0 , putting these VALUES in eq 3 we getv = (2GM/R)1/2this is the required RESULT... |
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