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1 Solve for speed, y, in terms of height, x Begin by setting PEi KEf 2 How does the equation found in the previous question relate to the power law regression calculated earlier 3 Suppose you want the ball to roll twice as fast on the level part of the track as it did when you released it from the 2-cm mark Using the power law regression performed earlier, calculate the height from which you should release the ball 4 Explain how this experiment only models dropping a ball and finding its kinetic energy just as it hits the ground 5 Compare and Contrast Compare the potential energy of the ball before it is released (step 8) to the kinetic energy of the ball on the level track (step 9) Explain why they are the same or why they are different 6 Draw Conclusions Does this experiment demonstrate conservation of energy Explain
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1 Infer What effect did changing the slope of the inclined plane in steps 2 6 have on the speed of the ball on the level portion of the track 2 Analyze Perform a power law regression for this graph using your graphing calculator Record the equation of this function Graph this by inputting the equation into Y= Draw a sketch of the graph 3 Using the data from step 9 for the release point of 80 cm, find the potential energy of the ball before it was released Use an electronic balance to find the mass of the ball Note that height must be in m, and mass in kg 4 Using the speed data from step 9 for the release point of 80 cm calculate the kinetic energy of the ball on the level portion of the track Remember, speed must be in m/s and mass in kg
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What are potential sources of error in this experiment, and how can they be reduced
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How does your favorite roller coaster demonstrate the conservation of energy by the transfer of potential energy to kinetic energy
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The Physics of Running Shoes Today s
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
Running Shoes as Shock Absorbers Today, much of the
Midsole
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