Point Particle Systems: Difference between revisions
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Revision as of 22:17, 30 November 2015
This topic has been claimed akerrison3.
The Main Idea
The point particle method of measuring changes in energy simplifies the system of interest down to a single point, or focuses on its center of mass. Therefore, the only energy changing in the system is translational kinetic energy. Translational kinetic energy is the energy that comes from an object moving from one location to another. This can then be used in the extended system of the object, which includes all energy transfers.
Center of Mass of a Cow as a Point
A Mathematical Model
Translational kinetic energy is equal to 
, where M is mass and v is the velocity of the center of mass.
The change in translational kinetic energy is equal to 
, where F is the net force acting on the object and delta r is the change in position of the object center of mass.
In the point particle system, total change in energy is equal to the total change in kinetic energy. Because of the energy principle, 
, where delta E is change in total energy and W is work, the change in translational kinetic energy is equal to work. Remember, work is equal to as well.
Examples
Jumper Model
A person jumps straight up in the air from a crouching position. Their center of mass moves h, or 2 meters. Their total mass, m is equal to 60 kg. Find the velocity of the center of mass of the jumper. When the jumper jumps, the normal force of the ground is equal to 2x the force of gravity.
Imagine the jumper's center of mass as a point, and it moves up 2 meters.
Remember, 
and 
. Therefore, we need to find Fnet.
The only forces acting on the jumper are the gravitational force of the Earth and the normal force. Therefore, Fnet = Fn-Fg.
Fg = Mg, therefore Fn = 2Mg.
Steps:
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