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Chapter 11: Q. 29 (page 288)
Two ice skaters, with masses of and , are at the center of a diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier skater reaches the edge in , how long does the lighter skater take to reach the edge?
It will take
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A particle of mass m is at rest at t = 0. Its momentum for is given by kg m/s, where t is in s. Find an expression for , the force exerted on the particle as a function of time.
Two blocks of wood are apart on a frictionless table. A bullet is fired at toward the blocks. It passes all the way through the first block, then embeds itself in the second block. The speed of the first block immediately afterward is . What is the speed of the second block after the bullet stops in it?
You have been asked to design a 鈥渂allistic spring system鈥� to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block and stops in the block. The spring鈥檚 maximum compression d is measured.
a. Find an expression for the bullet鈥檚 speed in terms of m, M, k, and d.
b. What was the speed of a data-custom-editor="chemistry" bullet if the block鈥檚 mass is data-custom-editor="chemistry" and if the spring, with data-custom-editor="chemistry" , was compressed by data-custom-editor="chemistry" ?
At the center of a 50-m-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds on to a 60 kg skater who had been heading west at 3.5 m/s.
a. How long will it take them to glide to the edge of the rink?
b. Where will they reach it? Give your answer as an angle north of west
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 鈭哖y, the change of momentum in the vertical direction, in terms of dm and dvy. 鈭哖y 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鈥攁gain pay attention to signs; m is decreasing鈥攖o 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鈥檚 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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