A model rocket engine has an average thrust of 5.26 N. It has an initial mass of

Question

A model rocket engine has an average thrust of 5.26 N. It has an initial mass of 25.4 g, which includes fuel mass of 13.1 g. The duration of its burn is 1.90 s. (Assume all the fuel is consumed.) (a) What is the average exhaust speed of the engine? m/s (b) This engine is placed in a rocket body of mass 54.0 g. What is the magnitude of the final velocity of the rocket if t were to be fired from rest in outer space by an astronaut on a spacewalk? Assume the fuel burns at a constant rate. m/s Need Help? Read It

Explanation / Answer

Given,

Fuel burn rate = dM / dt = 13.1 g / 1.90 s = 6.89 x10-3 kg/s

(a) thrust, P = -V dM/dt

5.26  = - V x 6.89 x 10-3 kg/s

V = - 762.9 m/s

(b) Vfinal -Vinitial = V ln (Minitial/Mfinal)

Vfinal - 0 = 762.90 x ln [ {54 + 25.4}/{54 + 25.4 - 13.1} ]

Vfinal = 137.56 m/s

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