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Mechanical Energy

Mechanical Energy. Net Work. The work-energy principle is D K = W net . The work can be divided into parts due to conservative and non-conservative forces. Kinetic energy D K = W con + W non. d. F f. F g. Kinetic and Potential Energy.

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Mechanical Energy

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  1. Mechanical Energy

  2. Net Work • The work-energy principle is DK = Wnet. • The work can be divided into parts due to conservative and non-conservative forces. • Kinetic energy DK = Wcon + Wnon d Ff Fg

  3. Kinetic and Potential Energy • Potential energy is the negative of the work done by conservative forces. • Potential energy DU = -Wcon • The kinetic energy is related to the potential energy. • Kinetic energy DK = -DU+ Wnon • The energy of velocity and position make up the mechanical energy. • Mechanical energy Emech = K + U

  4. Conservation of Energy • Certain problems assume only conservative forces. • No friction, no air resistance • The change in energy, DE = DK + DU = 0 • If the change is zero then the total is constant. • Total energy, E = K + U = constant • Energy is not created or destroyed – it is conserved.

  5. The spring force is conservative. U = ½ kx2 The total energy is E = ½ mv2 + ½ kx2 A 35 metric ton box car moving at 7.5 m/s is brought to a stop by a bumper. The bumper has a spring constant of 2.8 MN/m. Initially, there is no bumper E = ½ mv2 = 980 kJ Afterward, there is no speed E = ½ kx2 = 980 kJ x = 0.84 m Springs and Conservation v x

  6. A 30 kg child pushes down 15 cm on a trampoline and is launched 1.2 m in the air. What is the spring constant? Initially the energy is in the trampoline. U = ½ ky2 Then the child has all kinetic energy, which becomes gravitational energy. U = mgh The energy is conserved. ½ ky2 = mgh k = 3.1 x 104 N/m Energy Conversion

  7. Solving Problems • There are some general techniques to solve energy conservation problems. • Make sure there are only conservative forces and kinetic energy in the problem • Identify all the potential and kinetic energy at the beginning • Identify all the potential and kinetic energy at the end • Set the initial and final energy equal to one another next

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