GOAL Use conservation of mechanical energy to solve a one-dimensional problem in
ID: 2037842 • Letter: G
Question
GOAL Use conservation of mechanical energy to solve a one-dimensional problem involving gravitational potential energy and spring potential energy PROBLEM A 50.0 kg circus acrobat drops from a height of 2.00 meters straight down onto a springboard with a force constant of 8.00 x 10 N/m, as in the figure. By what maximum distance does she compress the spring? STRATEGY Nonconservative forces are absent, so conservation of mechanical energy can be applied. At the two points of interest, the acrobat's initial position and the point of maximum spring compression, her velocity is zero, so the kinetic energy terms will be zero. Choose y O as the point of maximum compression, so the final gravitational potential energy is zero. This choice also means that the initial position of the acrobat is yh + d, where h is the acrobat's initial height above the platform and d is the spring's maximum compression. An acrobat drops onto a springboard, causing it to cmpress SOLUTION Use conservation of mechanical (1) (KE PEg PE, (KEPER+PE,)y energy The only nonzero terms are the initial gravitational potential energay and the 0+mg(h + d) + 0-0+0+½kd2 mg (h + d)-wakd2 (s0.0 kg)(9.80 m/s2)(2.00 m d(8.00 x 10 final spring potential energy. Substitute the given quantities and rearrange the equation into standard N/m)d2 d2 (0.123 m) d 0.245 m2 o d 0.560 m quadratic form. Solve with the quadratic formula. LEARN MOREExplanation / Answer
there is no possibility to move more height than the intial height.
what ever the potential energy at height h is converted into kinetic energy of the person and when it touch the spring the kinetic energy converts into spring potential energy and this spring energy only responsible to push the person again back i.e., restoring force act. so there is addition of mechanical energy so that the person to move more height.
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