6. +)-3 points SerCpg 5AED 10 My Notes Ask Your Teach EXAMPLE 5.10 Circus Acroba

Question

6. +)-3 points SerCpg 5AED 10 My Notes Ask Your Teach EXAMPLE 5.10 Circus Acrobat 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 103 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 0 as the point of maximum compression, so the final gravitational potential compress. energy is zero. This choice also means that the initial position of the acrobat is y h + 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 SOLUTION Use conservation of mechanical (1) (KE + PE® + PEs), = (KE + PE® + PEs)f energy.

Explanation / Answer

m = mass of block = 6.03 kg

h = height = 0.85 m

k = force constant = 1200 N/m

assuming the point where the sping is compressed to as the reference to measure height

using conservation of energy

PE at Top = spring potential energy

mg (h + x) = (0.5) k x2

6.03 x 9.8 (0.85 + x) = (0.5) (1200) x2

x = 0.343 m

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