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.
2 answers
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.
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.
2 answers