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Chapter 7: Q2CP (page 289)
How many joules of energy can you store in a spring whose stiffness is, 0.6 N/m by starting from a relaxed spring and stretching it 20cm?
A spring having0.6 N/m stiffness and starting to stretch it from a relaxed position upto 20 cm can store0.012 J of energy.
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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.
of boiling water (temperature , heat capacity ) are poured into an aluminum pan whose mass is 1050 g and initial temperature (the heat capacity of aluminum is ).
(a) After a short time, what is the temperature of the water?
(b) What simplifying assumptions did you have to make? (1) The thermal energy of the water doesn't change. (2) Thermal energy of the aluminum doesn't change. (3) Energy transfer between the system (water plus pan) and the surroundings was negligible during this time. (4) The heat capacities for both water and aluminum hardly change with temperature in this temperature range.
(c) Next you place the pan on a hot electric stove. While the stove is heating the pan, you use a beater to stir the water, doing 29541 J of work and the temperature of the water and pan increases to . How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?
You lift a heavy box. We鈥檒l consider this process for different choices of system and surroundings.
(a) Choose the box as the system of interest. What objects in the surroundings exert significant forces on this system?
(b) Choose you and the box as the system of interest. What objects in the surroundings exert significant forces on this system?
(c) Choose you, the box, and the Earth as the system of interest. What objects in the surroundings exert significant forces on this system?
Question: A mass of 0.3 Kghangs motionless from a vertical spring whose length is 0.8 mand whose unstretched length is 0.65 m. Next the mass is pulled down so the spring has a length of 0.9 mand is given an initial speed upward of 1.2 m/s. What is the maximum length of the spring during the following motion? What approximations or simplifying assumptions did you make?
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?
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