Download conservation laws in physics

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CONSERVATION LAWS IN PHYSICS
1. Up to this point we have dealt only with Newton’s laws of dynamics:
a)


 F  ma


b) FAB   FBA
(First and second laws)
(Third law).
2. We now turn to a discussion of the conservation laws of physics:
a) conservation of energy
b) conservation of linear momentum
c) conservation of angular momentum
3. We will use Newton’s laws to derive these important conservation theorems (or
laws). It is important to understand that we will not “prove” the conservation laws,
but simply derive them as consequences of Newton’s laws.
4. A conservation law or theorem states that a certain defined quantity remains
constant no matter what changes may occur. This quantity has the same numerical
value before and after the changes occurred. For example, forces may act on an
object between some initial and final time, or between some initial or final position,
but certain quantities have the same value in the final state as it had in the initial
state.
5. The application of these conservation laws allows us to reach certain conclusions
about the state of an object without the need for a detailed analysis of all of the
various forces acting on it in a given situation in the course of its motion. The
quantities: kinetic energy, work, potential energy, linear momentum, and angular
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momentum, will be defined, and Newton’s laws will be used to derive various
conclusions about them. The use of the conservation laws will enable us to solve
certain dynamical problems more easily than by the direct application of Newton’s
laws.
6. The first conservation theorem that will be considered is the law of conservation
of energy. As far as we know, this is an exact law that governs all natural
phenomena; no exceptions to this principle have yet to be discovered.
7. We have such confidence in the conservation of energy principle, that it has been
used as the basis for other discoveries. For example, there is a nuclear process called
beta decay in which involves the decay of a neutron (zero charge) into a proton (+1
charge unit), an electron (1 change unit), and a uncharged particle called an antineutrino   . In a typical beta decay carbon-14 is transformed into nitrogen-14:
C  147 N  e   .
14
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8. When the energies involved in this reaction were considered, it appeared that there
was less energy after the reaction than before the reaction. Enrico Fermi in 1931
suggested that another particle, the anti-neutrino, might be involved in beta decay
and account for the missing energy. Because neutrinos have no charge and nearly
zero mass (still disputed), they are extremely difficult to detect. Neutrinos were
detected experimentally in 1956 by Cowan and Reines.
9. There is no complete understanding of what energy is. The energy concept was
extended to include heat in the 18th century. It was later extended by Einstein to
include mass in 1905. Nonetheless, we have formulas for calculating it, and find that
no matter what happens, its numerical value is always the same.
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WORK AND ENERGY
1. Work and energy are words that have certain common meanings, e.g.,
a) energy is the ability to do work, and
b) the work done on an object can increase or decrease its energy
2. As physics concepts, these terms are given very specific definitions that may differ
from our common understanding of the terms. For example, according to the physics
definition, a person at rest holding a heavy object is actually doing no work.
Someone employed to hold a heavy object for some period of time would certainly
argue that this was work. Work is done, however, when a person lifts the object off
of the ground.
3. In physics, work requires force and displacement in the direction of the force.
Forces acting in a direction perpendicular to the displacement of an object do no
work on it. For example, suppose a box is pushed across a frictionless horizontal
surface by a horizontal force F. Work is performed only by the applied force F, and
no work is done by gravity w or the normal force N.
N
F
mg
4. The physics definition of energy also may be different from our everyday
meaning. We might consider an object that is at rest to have no energy. However,
according to physics definitions, objects can have a form of energy due to its
position, even if it is not moving. The energy of a moving object is called kinetic
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energy and the energy due to position is called potential energy. Potential energy is
produced when an object is lifted up and converted back to kinetic energy when it is
released and falls back. Work is one mechanism for transforming energy from one
form to another.
5. The pile driver demonstration shown in the picture provides an
excellent illustration of the connection between work and energy.
A mass m is lifted and then released. It falls back down and
crushes a pop can. In terms of work and energy, this involves the
following processes:
a) Work is done by some external agent to lift the mass
b) The work done on the object is stored as potential energy
m
c) When the object is released, the potential energy is converted
into kinetic energy because gravity does work on it
d) The kinetic energy is used to do work to crush the pop can.
pop