LEARN MOREREMARKS The other solution, d = -0.437 m, can be rejected because d was chosen to be a positivenumber at the outset. A change in the acrobat's center of mass, say, by crouching as she makes contactwith the springboard, also affects the spring's compression, but that effect was neglected. Shockabsorbers often involve springs, and this example illustrates how they work. The spring action of a shockabsorber turns a dangerous jolt into a smooth deceleration, as excess kinetic energy is converted to springpotential energy.QUESTION Is it possible for the acrobat to rebound to a height greater than her initial height? Explain.(Select all that apply.)No. The kinetic energy that the acrobat gains on the way down is converted entirely back intopotential energy when she reaches the initial height.Yes. The acrobat can provide mechanical energy by pushing herself up while in contact with thespringboard.Yes. Elastic energy is always present in the spring and can give the acrobat greater height thaninitially.Yes. The acrobat can bend her knees while falling and then straighten them as if jumping whenbouncing upward again.No. There is no external source of energy to provide the potential energy at a greater height.PRACTICE ITUse the worked example above to help you solve this problem. A 49.7 kg circus acrobat drops from aheight of 1.57 meters straight down onto a springboard with a force constant of 6.90 × 10³ N/m, as shownin the figure. By what maximum distance does she compress the spring?mEXERCISEHINTS: GETTING STARTED | I'M STUCK!An 6.37 kg block drops straight down from a height of 0.77 m, striking a platform spring having a forceconstant of 9.50 x 102 N/m. Find the maximum compression of the spring.m EXAMPLE 5.10Circus AcrobatGOAL Use conservation of mechanical energy tosolve a one-dimensional problem involvinggravitational potential energy and spring potentialenergy.PROBLEM A 50.0 kg circus acrobat drops froma height of 2.00 meters straight down onto aspringboard with a force constant of 8.00 x 10³N/m, as in the figure. By what maximum distancedoes she compress the spring?STRATEGY Nonconservative forces are absent,so conservation of mechanical energy can beapplied. At the two points of interest, theacrobat's initial position and the point ofmaximum spring compression, her velocity iszero, so the kinetic energy terms will be zero.Choose y = 0 as the point of maximumcompression, so the final gravitational potentialenergy is zero. This choice also means that the initial position of the acrobat is y; = h + d, where h is theacrobat's initial height above the platform and d is the spring's maximum compression.SOLUTIONUse conservation of mechanical energy.The only nonzero terms are the initialgravitational potential energy and thefinal spring potential energy.Substitute the given quantities andrearrange the equation into standardquadratic form.Solve with the quadratic formula.LEARN MOREh(a)An acrobat drops onto a springboard, causing it tocompress.(b)(1) (KE + PEg + PEs)¡ = (KE + PEg + PEs)ƒ0 + mg (h+ d) + 0 = 0 + 0 + ½kd²mg (h + d) = ½kd²d = 0.560 m(50.0 kg)(9.80 m/s²)(2.00 m + d) = ½(8.00 × 10³N/m)d²d² - (0.123 m) d - 0.245 m² = 0

Name: LEARN MOREREMARKS The other solution, d = -0.437 m, can be rejected b
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Description: LEARN MOREREMARKS The other solution, d = -0.437 m, can be rejected because d was chosen to be a positivenumber at the outset. A change in the acrobat's center of mass, say, by crouching as she makes contactwith the springboard, also affects the spr