Posted by J on Wednesday, March 31, 2010 at 12:28pm.
IT depends on your assumptions. Think on those.
A 1000m3 rocket weighing 2.0x10^3 kg is going to be launched into space. On ignition, gas is expelled from the bottom of the rocket at a speed of 2.4x10^3 m/s relative to the rocket. The rate at which the fuel is consumed is 8.02kg/s. Is there a time delay between ignition and take-off? State your assmptions clearly.
The thrust must equal the weight before the rocket will begin to rise.
The thrust F = Vex(P)/g where Vex = the velocity of the exhaust gases = 2400 m/s, p = the propellant consumption rate = 8.02 kg/sec, and g = the acceleration due to gravity = 9.8 m/sec^2.
Therefore, F = 2400(8.02)/9.8 = 1964.08 kg.
2000 - 8.02t = 1964 making t = 4.488 sec.
Therefore, at t = 4.488 sec., the weight of the rocket becomes 2000 - 4.488(8.02) = 2000 - 36 = 1964 kg.
The thrust of the rocket being 1964 kg at that instant, liftoff will initiate at 4.488 sec.
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