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Lab 4  Conservation of Mechanical Energy
Lab 4  Conservation of Mechanical Energy
Introduction
When a body moves, some things—such as its position, velocity, and momentum—change. It is interesting
and useful to consider things that
do not
change. The total energy is a quantity that does not change; we say
that it is
conserved
during the motion. There are several forms of
energy
with which you may be familiar,
such as solar, nuclear, electrical, and thermal energies. In this experiment you will investigate two kinds of
mechanical energy
:
kinetic energy
and
potential energy
. You will carry out an experiment that demonstrates
the
conservation of the total mechanical energy
of a system.
Discussion of Principles
Conservation of Mechanical Energy
The total mechanical energy
E
of a system is defined as the sum of the kinetic energy
K
and potential energy
U
of the system.
( 1 )
E
=
K
+
U
In the absence of nonconservative forces, such as friction or air drag, the total mechanical energy remains a
constant and we say that mechanical energy is conserved. If
K
1
,
U
1
,
K
2
,
U
2
are the kinetic and potential energies at two different locations 1 and 2 respectively, then the conservation of
mechanical energy leads to the following mathematical expression
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K
1
+
U
1
=
K
2
+
U
2
This can also be expressed in terms of the changes in kinetic and potential energies
( 3 )
Δ
K
+ Δ
U
= 0
where
Δ
K
=
K
2
−
K
1
and
Δ
U
=
U
2
−
U
1
. Conservation of Mechanical Energy is one of the fundamental laws of physics that is also a very powerful
tool for solving complex problems in mechanics.
Kinetic Energy
Kinetic energy
K
is the energy a body has because it is in
motion
. When
work
is done on an object, the result is a change in the
kinetic energy of the object. Energy of motion can be
translational kinetic energy
and/or
rotational kinetic
energy
.
Translational kinetic energy
K
T
is the energy an object has because it is moving from place to place, regardless of whether it is also rotating;
K
T
is related to the mass
m
and velocity or speed
v
of the object by
( 4 )
K
T
=
1
2
mv
2
Rotational kinetic energy
K
R
is the energy an object has because it is rotating, regardless of whether the body as a whole is moving from
place to place.
K
R
is related to the
moment of inertia
I
and
angular velocity
ω
of the object by
( 5 )
K
R
=
1
2
I
ω
2
The angular velocity of a rolling sphere that is not slipping is the velocity (relative to the center of the sphere)
of a point on the circumference, divided by the radius
R
of the sphere.
( 6 )
ω
=
v
R
Just as the mass
m
of a body is a measure of its resistance to a change in its (translational) velocity, the moment of inertia
I
of an object is a measure of that object's resistance to a change in its angular velocity. The moment of inertia
of a solid sphere (of uniform density) is given by
( 7 )
I
=
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5
MR
2
where
M
and
R
are the mass and radius of the sphere, respectively. The
total kinetic energy
K
total
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This note was uploaded on 08/21/2011 for the course PY 211 taught by Professor Owen during the Spring '07 term at N.C. State.
 Spring '07
 OWEN

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