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ENG102_SL8(1)

# ENG102_SL8(1) - DATE ENG102 Solution to homework set#8 DUE...

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DATE: November 16, 2011 DUE: November 22 (at or before 4:30), 2011 ENG102, Solution to homework set #8. 1. A rocket has before the start a mass m (0) = 4 × 10 3 kg. The exhaust velocity of the combustion products is u = 3 . 0 km/s. How much mass should be ejected per second if the rocket at its start from the surface of the earth should have an acceleration of g vertically upwards? We look at the change dp in the total momentum p in a an infitesimal time slice dt : dp = m dv - v dm f - ( u - v ) dm f = - mg dt (1) where dm f is the amount of fuel burnt in the time dt and dv is the change in velocity of the rocket. Thus, we have ma = um f - mg = mg (2) m f = 2 mg u = 26 . 19kg / s (3) 2. Let us assume that we have another rocket ready to go vertically upwards from the earth. Let us furthermore assume that the rocket engine burns its fuel such that the mass of the rocket with fuel decreases according to m = m 0 exp( - bt ) . Determine the minimum value of b such that the rocket can lift itself from the ground. Insert values u = 3 km/s and m 0 = 4000 kg.

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