The largest rocket ever launched was the Saturn V, which carried missions to the moon. The total mass of the rocket and payload was 2,800,000 kg. What was the minimum thrust in Newtons the engines needed to provide to launch the rocket?
Details and assumptions
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The rocket has to apply a force equal to the gravitational force acting on it, so
Force of gravity = mass * acceleration = 2 , 8 0 0 , 0 0 0 k g × ( 9 . 8 ) m / s 2 = 2.74E+7 Newtons
the mass of rocket is 2,800,000 and the g=-9.8 . so the force is
F=mg, F=2800000*9.8=2.74E+7
Gravity force is m g, if rocket want to fly it needs to get acceleration a=9.81m/s2^, so 2nd Newton's law says F=m a=9.8m/s^2*2.800.000kg=2.74E+7N
F = m.a F = 2.800.000 . 9,8 = 2.74.10^7
The only force that the rocket needs to overcome is the force of the gravity of the Earth.
The force of gravity of Earth, by F = m a , is 2 , 8 0 0 , 0 0 0 k g ⋅ 9 . 8 s 2 m = 2 7 , 4 0 0 , 0 0 0 N . The rocket has to have a thrust at least this. Thus, the minimum thrust the engines needed to provide to launch the rocket is 2 7 , 4 0 0 , 0 0 0 N = 2 . 7 4 ⋅ 1 0 7 N .
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Using F = m a , we have F = 2 8 0 0 0 0 0 × 9 . 8 = 2 . 7 4 4 × 1 0 7