The theme for this week is closely related to last week's
theme of Work and Energy. The work-energy principle relates the net work
done on some system to its change in one type of energy that the system
can possess - kinetic energy. Another broad category of energy that
can be possessed by a system is potential energy. Together, the kinetic
and potential energies possessed by a system is labeled the system's mechanical
energy, i.e. the sum of a system's kinetic and potential energies equals
the system's total mechanical energy. The work-energy principle
is a general statement. If, however, only conservative forces
act (i.e. do work) on a system, the net work done also equals minus the
change in the system's potential energy. This leads quickly to the
conclusion that in such cases the total mechanical energy of the system
in question remains constant. Such situations represent
an example of a very important class of physical principles: CONSERVATION
PRINIPLES. In the present case, mechanical energy remains
constant, i.e. is conserved. The activities today not only
illustrate the relationship between work and energy and the conversion
of energy from one form to another, in each case the primary forces that
accomplish work on the system are conservative forces. By the
way, CONservation of Energy = CONE & keep in mind we are restricting
our attention to mechanical energy only.
1. LOOP-THE-LOOP
Our ancient version of a popular child's toy has
the force of gravity being the primary force that acts on a ball.
A small amount of energy is lost to friction, but we'll ignore it.
Note carefully the interchange between kinetic and (gravitational) potential
energies in this case. Try to find the minimum height from which
the ball may be released for it to make it around the loop and onto the
"finish" platform. Compare that minimum height to the height of the
"finish" platform. What does that height difference represent?
2. JUMPING DISK - it's baaaack.The "Physics is Fun at Miami" jumping disk has become
world famous through its annual appearance in the Edmund Scientific Catalog.
It is a bimetalic disk that operates on the principle of differential expansion.
Warm the disk in your hand and fingers and press on the convex non-Miami
side until it clicks. Put the disk on a hard, smooth, relatively cool surface
and wait until it returns to its original shape. As the disk snaps back
to its original shape, it exerts a force on the table top. According to
Newton's Third Law, the surface pushes back on the disk performing work
on the disk. The work done on the disk is transformed, according to the
work-energy principle, into kinetic energy, which in turn is transformed
into gravitational potential energy (as gravity does negative work
on the disk as it travels upward, eventually slowing the disk to a stop).
On the way down, gravity does positve work on the disk and increases the
disk's kinetic energy. Analyze the motion of the disk for yourself, step-by-step,
and relate it to the work-energy principle. During the disk's
flight only gravity acts - is it's mechanical energy conserved?
3. HORIZONTAL SPRING-MASS.Elastic forces exerted by (ideal) springs are another
example of conservative forces. Displace the mass from equilibrium and
watch the interchange between kinetic and elastic potential energies. But
it runs down - why? Molecules vibrate too, but they never run down.
4. BOWLING BALL PENDULUM - another view
- CONE.Release the ball from your nose and remain motionless
as the ball swings out and returns to its starting position. If you believe
that transformation of energy does not increase the amount of energy, you
will not move. Caution, release the ball and do not push on it,
because the work done on the ball will result in an additional initial
kinetic energy for the ball and possible damage to your nose. After
you release the ball, only gravity acts. You don't worry about smashing
your face because as the ball trades gravitational and kinetic energy back
and forth, their sum remains constant. Why does the wire supporting
the ball do no work? But the pendulum eventually "runs down."
Why?
5. COUPLED PENDULUA - other issues are involved,
but CONE applies too.
6. CONE IN ATOMS - lab tour.
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