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Chapter 7: Q32P (page 318)
A certain motor is capable of doing 3000 J of work in 11 s . What is the power output of this motor?
The power output of this motor is 272.2 W.
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Describe a situation in which it would be appropriate to neglect the effects of air resistance.
You drop a single coffee filter of mass 1.7 g from a very tall building, and it takes 52 s to reach the ground. In a small fraction of that time the coffee filter reached terminal speed. (a) What was the upward force of the air resistance while the coffee filter was falling at terminal speed? (b) Next you drop a stack of five of these coffee filters. What was the upward force of the air resistance while this stack of coffee filters was falling at terminal speed? (c) Again assuming that the stack reaches terminal speed very quickly, about how long will the stack of coffee filters take to hit the ground?
A horizontal spring鈥攎ass system has low friction, spring stiffness and mass. The system is released with an initial compression of the spring of and an initial speed of the mass of.
(a) What is the maximum stretch during the motion?
(b) What is the maximum speed during the motion?
(c) Now suppose that there is energy dissipation of 0.01 J per cycle of the spring鈥攎ass system. What is the average power input in watts required to maintain a steady oscillation?
Question: Figure 7.48 is a portion of a graph of energy terms vs, time for a mass on a spring, subject to air resistance. Identify and label the three curves as to what kind of energy each represents. Explain briefly how you determined which curve represented which kind of energy.
Question: Design a 鈥渂ungee jump鈥� apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. You have cords that are10m long, and these cords stretch in the jump an additional 24mfor a jumper whose mass is 80kg, the heaviest adult you will allow to use your bungee jump (heavier customers would hit the ground). You can neglect air resistance. (a) Make a series of five simple diagrams, like a comic strip, showing the platform, the jumper, and the two cords at various times in the fall and the rebound. On each diagram, draw and label vectors representing the forces acting on the jumper, and the jumper鈥檚 velocity. Make the relative lengths of the vectors reflect their relative magnitudes. (b) At what instant is there the greatest tension in the cords? How do you know? (c) What is the jumper鈥檚 speed at this instant? (d) Is the jumper鈥檚 momentum changing at this instant or not? (That is, isnonzero or zero?) Explain briefly. (e) Focus on this instant, and use the principles of this chapter to determine the spring stiffnessfor each cord. Explain your analysis. (f) What is the maximum tension that each cord must support without breaking? (g) What is the maximum acceleration (in g鈥檚) that the jumper experiences? What is the direction of this maximum acceleration? (h) State clearly what approximations and estimates you have made in your design.
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