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9 September, 21:03

A solid motor has an average thrust of 67,000 N, a specific impulse of 285 sec, and a propellant mass fraction of 0.92. Calculate the total mass of the vehicle for a 42 sec burn time.

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  1. 9 September, 22:45
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    total mass is 1095.096 kg

    Explanation:

    given data

    thrust = 67000 N

    impulse time t = 285 sec

    mass fraction = 0.92

    to find out

    total mass of the vehicle

    solution

    we know here thrust formula that is

    thrust = m * g * t

    put here value and find m

    m = 67000 / 9.8 (285)

    m = 23.988 kg/s

    so here mass fraction is express as

    mass fraction = m * time / (m * time + mf)

    put here time after 42 sec

    0.92 = 23.988 * 42 / (23.988 * 42 + mf)

    (23.988 * 42 + mf) 0.92 = 23.988 * 42

    mf = 87.60 kg

    total mass = mf + m * time

    put here value

    total mass = 87.60 + 23.988 * 42

    total mass is 1095.096 kg
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