Student Workbook for Physics for Scientists and Engineers: A Strategic Approach, Vol 1. (Chs 1-21)
4th Edition
ISBN: 9780134110646
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 11, Problem 84EAP
Section 11.6 found an equation for vmaxof a rocket fired in deep space. What is vmaxfor a rocket fired vertically from the surface of an airless planet with free-fall acceleration g? Referring to Section 11.6, you can write an equation for ?Pythe change of momentum in the vertical direction, in terms of dm and dvy. ?Pyis no longer zero because now gravity delivers an impulse. Rewrite the momentum equation by including the impulse due to gravity during the time dt during which the mass changes by dm. Pay attention to signs! Your equation will have three differentials, but two are related through the fuel burn rate R. Use this relationship—again pay attention to signs; m is decreasing—to write your equation in terms of dm and dvy. Then integrate to find a modified expression for vmax, at the instant all the fuel has been burned.
a. What is vmaxfor a vertical launch from an airless planet? Your answer will be in terms of mR, the empty rocket mass: mF0, the initial fuel mass; vex, the exhaust speed; R, the fuel burn rate; and g.
b. A rocket with a total mass of 330.000 kg when fully loaded burns all 280,000 kg of fuel in 250 s. The engines generate 4.1 MN of thrust. What is this rocket’s speed at the instant all the fuel has been burned if it is launched in deep space? If it is launched vertically from the earth?
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Chapter 11 Solutions
Student Workbook for Physics for Scientists and Engineers: A Strategic Approach, Vol 1. (Chs 1-21)
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