Download Chapter 8 Potential Energy and Conservative Forces

Chapter 8 Potential Energy and
Conservative Forces
Section 8-1
• Conservative forces are: 1) path independent and 2) have associated potential
energy functions. 1) means that conservative forces do zero work along closed
paths. For any conservative force, 2) means that we can write a potential energy
function (i.e., energy may be stored through the action of the force) for an object
that depends on the object's position or location. Examples are : gravity and the
spring force.
• Nonconservative forces are path dependent, i.e. the work done by a
nonconservative force depends on the precise path followed by an object. That
work may be either positive, negative, or zero depending on the force and the path.
Nonconservative forces do not store energy. Examples are: friction, tension,
muscular force, etc.
Section 8-2
• When a conservative force does work, it shows up as a change in the corresponding
potential energy: Wc = –∆U = Ui – Uf.
• In the case of gravity the potential energy is U = mgy. Determining the
gravitational potential energy of an object requires setting a zero height location.
The choice of that location is up to you but, once chosen, needs to be used
consistently throughout the problem. Remember – only differences in U will be
important when applying conservation of energy. In particular, when the height
doesn't change (e.g. horizontal motion), ∆U = 0.
• Only the initial position and final position determine an object's change in
gravitational potential energy (∆U). The path taken by the object is not important as
far as ∆U is concerned.
1
• For a spring, U = 2 k x2, where x is the spring's displacement.
Section 8-3
• Energy is always conserved when all different forms of energy are included.
Mechanical energy (E = U + K) is conserved only when no frictional (or other nonconservative) forces are acting on an object. Then: Ei = Ui + Ki = Uf + Kf = Ef.
Section 8-4
• When present, work done by nonconservative forces should be included by writing:
Uinitial + Kinitial + Wnc = Ufinal + Kfinal
The work done by friction is always negative, so the total final mechanical energy
(Ufinal + Kfinal) will be smaller than the total initial mechanical energy (Uinitial +
Kinitial) by just the amount of work done by friction.
• Conservation of energy is built upon the observation that energy can be
transformed, but not destroyed. For example, a falling object converts U to K.
• When applying conservation of energy, the mass of the object may not be needed.
This is true when Wnc = 0 and only v or h is being solved for. Even when Wnc is not
zero, the mass may cancel if it appears explicitly (e.g., in the frictional force).
Otherwise the mass will be required, as it will when calculating a specific kinetic or
potential energy.
Section 8-5
• A graph of potential energy versus position (or displacement) combined with a
knowledge of the total energy of an object can be used to determine kinetic energy
(using conservation of energy). For example:
U
E = U+K
K
U
x
turning points