Work and Energy for an Extended System: Difference between revisions
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==The Main Idea== | ==The Main Idea== | ||
Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves. | |||
When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied. | |||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
Work and Energy for an Extended System: | |||
[[File:Work and Energy for an Extended System.png]] | [[File:Work and Energy for an Extended System.png]] | ||
This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of <math>\vec{F}_{i}•d\vec{r}_{i}</math> must be calculated either analytically or numerically. | |||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 00:37, 4 December 2015
"Work and Energy for an Extended System" in progress by Morgan LaMarca
The Main Idea
Unlike the point particle system where the only energy possible is translational kinetic energy, an extended object can rotate, vibrate, and change shape. Though the point particle system and the extended system both have the same total mass, and are both acted on by the same net force, the point particle system, has no rotational motion, vibrational motion, or internal energy because all of the forces act at the location of the point particle. In contrast, forces act at different locations on the mass in an extended system, thus causing them to rotate, vibrate and stretch. Because of these qualities, not every part of the system always moves in the same direction as the center of mass moves.
When calculating work done on an extended system, the displacement of every point where a force is applied must be considered separately, because it matters where each force is applied.
A Mathematical Model
Work and Energy for an Extended System:
This equation assumes that each force is constant during the displacement. If each force is not constant during the displacement, the work of each force as an integral of [math]\displaystyle{ \vec{F}_{i}•d\vec{r}_{i} }[/math] must be calculated either analytically or numerically.
A Computational Model
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