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Section 5–3: Conservation of Energy
Coach Kelsoe
Pages 173–178
• Identify situations in which
conservation of mechanical energy
is valid.
• Recognize the forms that
conserved energy can take.
• Solve problems using conservation
of mechanical energy.
Conserved Quantities
• When we say that something is
conserved, we mean that is
remains constant.
• Mass is an entity that is conserved.
If a light bulb is dropped on the
floor, no matter how it shatters, the
total mass of the debris is the
same as the intact bulb.
• Energy is also an entity that is
Mechanical Energy
• The description of the motion of
many objects involves a
combination of kinetic and
potential energy as well as
different forms of potential energy.
• The pendulum of a clock is a great
example of kinetic and potential
energy. At the top of its swing, the
pendulum has only PEg, but at the
very bottom has only KE.
Mechanical Energy
• Mechanical energy is the sum of
kinetic energy and all forms of
potential energy associated with
an object or group of objects.
• Don’t let the term “mechanical
energy” confuse you. It is simply
energy that is not nuclear,
chemical, internal, or electrical.
• Nuclear, chemical, internal, and
electrical energy is called
nonmechanical energy.
Mechanical Energy
• The total amount of mechanical
energy can be found from
– ME = KE + ΣPE
• Mechanical energy is often
conserved (in the absence of
– MEi = MEf
– ½mvi2 + mghi = ½mvf2 + mghf
Sample Problem
• Conservation of Mechanical
Starting from rest, a child zooms down
a frictionless slide from an initial
height of 3.00 m. What is her speed
at the bottom of the slide? Assume
she has a mass of 25.0 kg.
Sample Problem Solution
• 1. Identify givens and unknowns:
– h = hi = 3.00 m
– m = 25.0 kg
– vi = 0.0 m/s
– hf = 0 m
– vf = ?
Sample Problem Solution
• 2. Choose the correct equation.
– Since the slide is considered
frictionless, mechanical energy is
conserved. KE and PEg are the only
forms of energy present.
– KE = ½mv2
– PEg = mgh
– The zero level chosen for our
situation is the bottom of the slide.
Because the child ends at the zero
level, the final PEg = 0.
Sample Problem Solution
• 2. Choose the correct equation
– The initial PEg at the top of the slide
= mgh.
– Because the child starts at rest, the
initial KE at the top is zero.
– Therefore the final kinetic energy is
• ½mvi2 + mghi = ½mvf2 + mghf OR
• mghi = ½mvf2
• ghi = ½vf2
Sample Problem Solution
• 3. Calculate
– ghi = ½vf2
– (9.81 m/s2)(3.00 m) = ½vf2
– vf2 = (2)(9.81 m/s2)(3.00 m)
– vf = √58.86 m2/s2
– vf =7.67 m/s
In the Presence of Friction
• Mechanical energy is not
conserved in the presence of
• For example, as a sanding block
slides across a piece of wood,
energy (in the form of heat) is
dissipated into the block and
• Energy is ALWAYS conserved, but
it isn’t always conserved in its
current form.
• Mechanical energy