Answered: The total mechanical energy of an…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter8: Conservation Of Energy

Section: Chapter Questions

Problem 24PQ: A block is placed on top of a vertical spring, and the spring compresses. Figure P8.24 depicts a...

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The total mechanical energy of an object is the sum of its potential energy (U) and it’s kinetic energy (K). In the absence of friction, total energy is conserved. When a popper is launched straight up, the initial U is defined to be a form of elastic potential energy, Us, which converts to kinetic energy, K=(1/2)mv^2, where m is the mass of the popper and v is the muzzle speed of the popper, prior to leaving the ground. When the popper reaches its maximum height, h, the final K is zero and Ug=mgh, where g is the acceleration due to gravity. Conservation of energy gives that the initial K is equal to the final U after the popper has popped and leaves the ground. Using the information given, determine the spring constant (k) of the popper, using mechanical energy (Ei=Ef) Mass: 0.0150kg Initial Height: 1m Measured Distance: 0.020m Final Height: 0.408m Initial Spring Compression: 0.050m Final Spring Compression: 0m Final Velocity: 0m/s I know the correct answer is 69.6, I’m just not sure how to get there.

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