08_InstSolManual_PDF_Part15 - v ex 5 2 F D m D t 5 2 35 3...

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8.55. Set Up: Use Eq. 8.26. Solve for Solve: Reflect: The acceleration is proportional to the speed of the exhaust gas and to the rate at which mass is ejected. 8.56. Set Up: and The maximum acceleration of the rocket occurs when the mass m is the smallest, just before the fuel runs out. Solve: (a) The thrust is (b) Initially and The maximum acceleration occurs when so (c) After the fuel runs out the thrust suddenly becomes zero and the acceleration suddenly becomes zero. (d) The acceleration becomes zero so the speed is constant, with the value it had just before the fuel ran out. 8.57. Set Up: Initially and Since the shuttle is at the earth’s surface, the gravity force on it must be included. The free-body diagram for the shuttle at liftoff is shown in Figure 8.57. Take to be upward. Figure 8.57 Solve: (a) gives and (b) (c) so Reflect: In part (a) it is important to include the gravity force on the shuttle; the thrust is only 1.75 times its weight.
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Unformatted text preview: v ex 5 2 F D m / D t 5 2 35 3 10 6 N 2 3.8 3 10 3 kg / s 5 9.2 3 10 3 m / s 5 9.2 km / s F 5 2 v ex D m D t D m D t 5 2 230,000 kg 60 s 5 2 3.8 3 10 3 kg / s a 5 F m 2 g 5 35 3 10 6 N 2.04 3 10 6 kg 2 9.80 m / s 2 5 7.4 m / s 2 F 2 mg 5 ma g F y 5 ma y F x y a w 5 mg 1 y F 5 35 3 10 6 N. m 5 2.04 3 10 6 kg a max 5 2 1 1200 m / s 25,000 kg 2 1 2 135 kg / s 2 5 6.48 m / s 2 m 5 25,000 kg a initial 5 2 1 1200 m / s 75,000 kg 2 1 2 135 kg / s 2 5 2.16 m / s 2 m 5 75,000 kg a 5 2 v ex m D m D t . F 5 2 v ex D m D t 5 2 1 1200 m / s 21 2 135 kg / s 2 5 1 1.62 3 10 5 N D m / D t 5 2 135 kg / s. v ex 5 1200 m / s v ex 5 2 a 1 D m D t / m 2 5 2 15.0 m / s 2 1 2 m 160 2 / m 5 2.40 3 10 3 m / s 5 2.40 km / s a 5 2 v ex m D m D t . v ex . D m D t 5 2 m 160 . Momentum 8-15...
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