A size C5 model rocket engine has an average thrust of 5.26 N, a propellant mass

Question

A size C5 model rocket engine has an average thrust of 5.26 N, a propellant mass of 0.0127 kg, and an initial total mass (propellant + structure) of 0.0255 kg. The duration of its burn is 1.90 s.

(a) What is the impulse of the engine?

(b) What is the speed of the exhaust gases from the engine?

(c) If the C5 engine is placed in a rocket body that has a mass of 0.0535 kg and launched vertically from ground level, what is the velocity of the rocket when all of the propellant is burned? Ignore air resistance, but take into account gravitational force.

Explanation / Answer

(a) impulse    =trust * time   = 5.26 N* 1.90s = 9.994 v

(b)

trust   = - m' * v_ex

V_ex     = trust / m'

Here m'    = rate of change in mass    =( 0.0255 - 0.0127)  /1.9   = 0.0067

V_ex     = trust / m'    = 5.26 / 0.0067   = 785 m/s

(c) velocity    v = v_0   +v_ex ln ( intial mass / final mass)

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