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Re: Work-Energy or Work-Kinetic Energy??





On Thu, 6 Nov 1997, Martha Takats wrote:

The following distinction is made in most of the elementary texts I've
used:
Work of ALL forces (the net force) = change in kinetic energy

Not true. Some of this work may result in thermal energy.

Work of all nonconservative forces = change in total energy

I think you have these backwards. Total energy is usually taken to
*include* any potential energy terms due to conservative forces.

because effect of conservative forces is taken into account in the
potential energy terms.

Well, it can be, if you choose to do it that way. It's more instructive to
think of the conservative forces as doing work on the body just as any
force does, but since the forces are conservative it is possible to treat
their effect on the system as potential energy if you wish. Just don't mix
the two methods in one problem. The rigid interpretations you cite above
are generally not emphasized in college courses.

Some texts use W' for the work of
nonconservative forces.
I have always found these two W-E theorems equally useful.
One thing to remember is that the force YOU (or I) exert is
nonconservative.

A test of these concepts is this:

Consider a simple pendulum hung from the ceiling. Discuss the conservation
of energy, momentum, and angular momentum for this system, considering not
only the extreme positions of the bob, but the changes that occur during
the entire swing.

Is the kinetic energy conserved? No. Is the total energy of the bob
conserved? Yes. The total energy is the sum of kinetic and potential
energy. Is the bob a closed system? No. It does work on the earth, and
the earth does work on it. The string does no work on it, for the string
exerts a force always perpendicular to the bob's displacement.

Is any work done on the ceiling? Well, if the string does no work on the
bob, the bob does no work on the string, and therefore the string does no
work on the ceiling. Hmm... There's an assumption here. We implicitly
assume a rigid geometry, allowing no flexing of the components and no
stretch of the string. And a force can't do work unless there's a
displacement with a component in the direction of the force. In fact,
there will be a flexing of the point of attachment of the string and
ceiling, as could be demonstrated by putting a small spring there. Then
what about our assumption that the string is always exactly perpendicular
to the path? Not strictly true. Then can the string be transmitting a bit
of momentum to and from the bob? How about a bit of energy? But these are
small effects relative to others, which I will cheerfully ignore.

Is the momentum of the bob conserved? Obviously not, for its velocity
changes during the swing. The bob is not a closed system, remember. What
accounts for this change? The gravitational force provides an impulse F_g
dt continually, so the earth and the bob are exchanging momentum. Does the
string tension provide an impulse? Yes. To analyze that it's good to
consider the components of momentum separately.

The x-component of bob momentum is not affected by the impulse due to the
gravitational force, only by the impulse due to the x component of tension
of the string.

The y-component of bob momentum is affected by both the gravitational
force and the y component of tension of the string.

The angular momentum of the bob is obviously changing. This is due
entirely to the gravitational force exerting a torque on the bob. The
torque changes sign each half-period. The string provides no torque.

Now sketch graphs of all of the above.

If there are any blunders in the above, I'm sure someone will find them.
My mind is mush today.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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