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running shoes are high-tech marvels They enhance performance and protect your body by acting as shock absorbers How do running shoes help you win a race They Upper reduce your energy consumption, as well as allow you to use energy more efficiently Good running shoes must be flexible enough to bend with your feet as you run, support your feet, and hold them in place They must be lightInsert weight and provide traction to prevent slipping and tendons of the foot and leg are a natural cushioning system But operating this system requires the body to use stored energy to contract muscles So if a shoe can be worn that assists a runner s natural cushioning system, the runner does not expend as much of his or her own stored energy The energy the runner saved can be spent to run farther or faster The cushioned midsole uses the law of conservation of energy to return as much of the energy to the runner as possible The runner s kinetic energy transforms to elastic potential energy, plus heat, when the runner s foot hits the running surface If the runner can reduce the amount of energy that is lost as heat, the runner s elastic potential energy can be converted back to useful kinetic energy Bouncy, springy, elastic materials that resist crushing over time commonly are used to create the cushioned midsole Options now range from silicon gel pads to complex fluid-filled systems and even springs to give a runner extra energy efficiency



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focus of running shoe technology centers on the cushioned midsole Outsole that plays a key role as a shockabsorber and performance enhancer Each time a runner s foot hits the ground, the ground exerts an equal and opposite force on the runner s foot This force can be nearly four times a runner s weight, causing aches and pains, shin splints, and damage to knees and ankles over long distances Cushioning is used in running shoes to decrease the force absorbed by the runner As a runner s foot hits the ground and comes to a stop, its momentum changes The change in momentum is p F t, where F is the force on that object and t is the time during which the force acts The cushioning causes the change of momentum to occur over an extended time and reduces the force of the foot on the ground The decreased force reduces the damage to the runner s body





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1 Use Scientific Explanations Use physics to explain why manufacturers put cushioned midsoles in running shoes 2 Analyze Which surface would provide more cushioning when running: a grassy field or a concrete sidewalk Explain why that surface provides better cushioning 3 Research Some people prefer to run barefoot, even in marathon races Why might this be so

A shoe s cushioning system also affects energy consumption The bones, muscles, ligaments, 304

Smith chart applications 119 You can use the Smith chart to plot the performance of such a network with respect to various frequencies Consider the load impedance connected to a 50- transmission line in Fig 4-11 In this case, the resistance is in series with a 22-pF capacitor, which will exhibit a different reactance at each frequency The impedance of this network is 1 Z=R j [475] C or 1 [476] Z = 50 j 2 FC And, in normalized form, Z' = 10 j (2 F C) 50 [477]

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DinkToPdf is a cross-platform oriented library which is the wrapper for the Webkit HTML to PDF library. It uses the WebKit engine to convert HTML to PDF . It will allow us to create a PDF document from our HTML string that we generate in the . NET Core project, or to create a PDF document from an existing HTML page.

2 class Chilis { 3 Chilis(String c, int h) { color = c; hotness = h; } 4 String color; 5 private int hotness; 6 public boolean equals(Object o) { 7 Chilis c = (Chilis)o; 8 if(colorequals(ccolor) && (hotness == chotness)) 9 return false; 10 } 11 // insert code here 12 }

(p 287)

(p 291)

The kinetic energy of an object is proportional to its mass and the square of its velocity The rotational kinetic energy of an object is proportional to the object s moment of inertia and the square of its angular velocity When Earth is included in a system, the work done by gravity is replaced by gravitational potential energy The gravitational potential energy of an object depends on the object s weight and its distance from Earth s surface PE mgh

The reference level is the position where the gravitational potential energy is defined to be zero Elastic potential energy may be stored in an object as a result of its change in shape Albert Einstein recognized that mass itself has potential energy This energy is called rest energy E0 mc2

return true;

(p 293)

50 50 50

thermal energy (p 295) elastic collision (p 298) inelastic collision (p 298)

If no objects enter or leave a system, the system is considered to be a closed system If there are no external forces acting on a system, the system is considered to be an isolated system The total energy of a closed, isolated system is constant Within the system, energy can change form, but the total amount of energy does not change Thus, energy is conserved KEbefore PEbefore KEafter PEafter

Which, inserted independently at line 11, fulfill the equals() and hashCode() contract for Chilis (Choose all that apply) A public int hashCode() { return 7; } B public int hashCode() { return hotness; } C public int hashCode() { return colorlength(); } D public int hashCode() { return (int)(Mathrandom() * 200); } E public int hashCode() { return (colorlength() + hotness); }

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