Download Mechanical Energy

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
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