Conservation of Mechanical Energy
Most recent answer: 03/07/2016
- Emily (age 15)
California, USA
All of these questions are doable by setting initial total mechanical energy = final total mechanical energy.
And knowing that Potential energy due to gravity is mgh mass times "g" times height above a reference level.
Potential energy in a spring is (1/2) k d^2 where k = spring stiffness and d is the amount the spring is compressed or extended.
And Kinetic energy is (1/2) mass times speed^2
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Here's an example problem: a 4 kg mass is placed on a 80 Newton/meter spring and compressed 30 cm = 0.3 meters. Before it is released the system has energy (1/2) 80 (.3)^2 = 36 Joules. After the spring releases it has no energy; all the energy is then in the mass's Kinetic energy = (1/2) M V^2. We solve for V and get about 4.2 m/sec. We can take this further and ask then (if the speed is straight upwards), how far does it go? It should go to a height given by 36 Joules = mg h, so h is about 0.9 meters as the kinetic energy is converted to gravitational potential energy
Richard
p.s. For other readers considering asking for help with standard school problems, we do this very, very rarely. MW
(published on 03/07/2016)