Energy
Transformation for a Dart
A GIF Animation
Consider an ordinary dart projection from a toy dart gun and
moving through the air. How could work and energy be utilized to
analyze the motion of the dart? Would the total mechanical energy of
the dart/gun system be altered when launched or while mvong through
the air? Or would the total mechanical energy of the dart/gun merely
be conserved?
Of course the answers to these questions begin by determining
whether or not there are any external forces doing work upon the
dart/gun system. According to the work-energy theorem, if external
forces do work upon the dart/gun system, the total mechanical energy
of the dart is not conserved; the initial amount of mechanical energy
is not the same as the final amount of mechanical energy. On
the other hand, if external forces do not do work upon the
dart/gun system, then the total mechanical energy is conserved; that
is, mechanical energy is merely transformed from one form to another
(say from potential to kinetic and/or vice versa) while the total
amount of the two forms remains unchanged.
In this case of the dart being launched from the spring gun, the
only forces doing work upon the dart are internal forces. Initially,
the dart is being acted upon by a spring force in order to be
projected from the dart gun. The coils of the springs are initially
compressed and upon pulling the trigger, the springs return to their
equilibrium position while pushing the dart out of the dart gun. The
dart then becomes a projectile (assuming their is negligible air
resistance); the only force doing work upon during its flight
through the air is gravity. Since both the spring force and the
force of gravity are internal forces, the total mechanical energy of
the dart is conserved. The animation below depicts the motion of the
dart. The animation is accompanied by work-energy bar charts which
further illustrate the tranformation of energy from one form to
another and the conservation of the total amount of mechanical
energy.
The animation above shows that the energy of the dart/gun system
is initially present in the form of the elastic potential energy
(PEs) and gravitational potential energy (PEg).
The springs of the dart gun are compressed which accounts for the
elastic potential energy. Furthermore, the dart is initially
elevated at a height of 1-meter above the ground which accounts for
the gravitational potential energy. The presence of these two
initial forms of energy are shown by the PEg and
PEs bars of the bar chart. Once projected, the dart no
longer has elastic potential energy since the springs of the dart are
no longer compressed. However, the dart does have a large amount of
kinetic energy (energy of motion) since it is now moving at a high
speed as it leaves the dart. The dart also has gravitational
potential energy since it is still elevated to some height above the
ground. As the dart ascends towards its peak, it is continuously
slowing down under the influence of the downward force of gravity.
During this ascent, there is a transformation of the mechanical
energy from the form of kinetic energy (energy of motion) to
gravitational potential energy (the stored energy of vertical
position). At the peak, there is only a small amount of kinetic
energy (the dart still has a horizontal motion) and a large amount of
gravitational potential energy (the dart is at its highest vertical
position). Finally, as the dart descends to the ground, the force of
gravity speeds it up. As it falls, there is an increase in kinetic
energy (due to the gain in speed) and a decrease in gravitational
potential energy (due to a loss in vertical position).
The above animation provides a simple demonstration of how
mechanical energy merely changes form when the only forces acting
upon an object are internal forces. While the form of mechanical
energy changes, the total amount of mechanical energy (TME) is
conserved.
For more information on physical descriptions of motion,
visit
The
Physics Classroom. Specific information is available there on the
following topics:
This page was created by
Tom
Henderson of
Glenbrook South
High School.
Comments and suggestions can be sent by e-mail to
Tom
Henderson.
A hearty thanks is due to lab assistant Carl Bobis for his
assistance with the graphics and GIF animation.
This page last updated on 4/2/98.