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A rocket has a mass of `2 xx10 ^(4)` kg of which half is fuel Assume that the fuel is consumed at a constant rate as the rocket is fired and there is contact thrust of `5 xx 10^(6)` N neglecting air resistance and any possible variation of g comput (i) the intial acceleration (ii) acceleration just when the whole fuel is consumed . |
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Answer» Here, mass of rocket `m = 2xx 10^(4) kg` mass of fuel `m = (1)/(2) (2xx10^(4)) kg = 10^(4) kg` upthrust `= 5 xx 10^(6) N` (i) Net force on the rocket F = up thrust - weight (mg) `5 xx 10^(6) -2xx 10^(4) xx 10` ` = 10^(5) (50 -2) = 48 xx 10^(5) ` `:.` Initial acceleration `= (F)/(m) = (48xx 10^(5))/(2xx10^(4)) = 240 m//s^(2) ` When the fuel has been completly exhausted , remaining mass of rocket F = upthrust - weight (m' g) `5 xx 10^(6) - 10^(4) xx 10 = 49 xx 10^(5) ` `:.` Acceleration = `(F)/(m) = (49 xx 10^(5))/(10^(4)) = 490 m//s^(2)` . |
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