REMARKS The other solution, d =-0.437 m, can be rejected because d was chosen to
ID: 1777912 • Letter: R
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REMARKS The other solution, d =-0.437 m, can be rejected because d was chosen to be a positive number at the outset. A change in the acrobat's center of mass, say, by crouching as she makes contact with the springboard, also affects the spring's compression, but that effect was neglected. Shock absorbers often involve springs, and this example illustrates how they work. The spring action of a shock absorber turns a dangerous jolt into a smooth deceleration, as excess kinetic energy is converted to spring potential energy QUESTION Is it possible for the acrobat to rebound to a height greater than her initial height? Explain (Select all that apply.) Yes. Elastic energy is always present in the spring and can give the acrobat greater height than Yes. The acrobat can provide mechanical energy by pushing herself up while in contact with the No. There is no external source of energy to provide the potential energy at a greater height. initially springboard Yes. The acrobat can bend her knees while falng and then straighten them as if jumping when bouncing upward again No. The kinetic energy that the acrobat gains on the way down is converted entirely back into potential energy when she reaches the initial height. Consider whether the acrobat standing on the ground, without any spring at all, could jump to a greater height than she had initially when simply standing in place. Then apply the same idea to what the acrobat could try on a trampoline PRACTICE IT Use the worked example above to help you solve this problem. A 50.9 kg circus acrobat drops from a height of 1.93 meters straight down onto a springboard with a force constant of 6.59 x 103 N/m, as shown in the figure. By what maximum distance does she compress the spring? 54 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m EXERCISE HINTS: GETTING STARTED I'M STUC! An 7.31 kg block drops straight down from a height of 0.75 m, striking a platform spring having a force constant of 9.90 x 102 N/m. Find the maximum compression of the spring Do not neglect the change in gravitational potential energy after the block hits the spring. mExplanation / Answer
1st question : The correct options are 3rd and 5th
2nd question : Let the spring compress by a length x. Let us consider the compressed configuration as the datum with respect to which we will determine the potential energy
From conservation of energy, potential energy will be converted to energy in springboard
50.9*9.8*(1.93+x) = (0.5*6.59*103*x2)
962.7226+498.82x=3295x2
x = 0.62m
answer is 0.62m
3rd question : The approach is very similar to 2nd question .
7.31*9.8*(0.75+x) = 0.5*9.9*100x2
Or, 71.638x+53.7285=495x2
x = 0.41 m
Answer is 0.41m
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