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Chapter 11: Q. 37 (page 288)
A rocket in deep space has an exhaust-gas speed of 2000 m/s. When the rocket is fully loaded, the mass of the fuel is five times the mass of the empty rocket. What is the rocket’s speed when half the fuel has been burned?
The speed of the rocket when half fuel is burned is .
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Section 11.6 found an equation for vmax of a rocket fired in deep space. What is vmax for 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 ∆Py, the change of momentum in the vertical direction, in terms of dm and dvy. ∆Py is 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 vmax for 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?
A golf club continues forward after hitting the golf ball. Is momentum conserved in the collision? Explain, making sure you are careful to identify “the system.”
FIGURE P11.71 shows a collision between three balls of clay. The three hit simultaneously and stick together. What are the speed and direction of the resulting blob of clay?
a. Write a realistic problem for which this is the correct equation.
b. Finish the solution of the problem, including a pictorial representation.
A ball is dropped from a height of , bounces on a hard floor, and rebounds to a height of . FIGURE P11.41 shows the impulse received from the floor. What maximum force does the floor exert on the ball?
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