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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.

  • physics -

    IT depends on your assumptions. Think on those.

  • physics -

    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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