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Mechanical Energy 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 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 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. Springs and Conservation The spring force is conservative. • U = ½ kx2 The total energy is 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. • E = ½ mv2 + ½ kx2 • Initially, there is no bumper • E = ½ mv2 = 980 kJ v x • Afterward, there is no speed • E = ½ kx2 = 980 kJ • x = 0.84 m Energy Conversion 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 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