Real Systems - Revision history

Sanjan Sen: added a new glowscipt simulation and added step by steps for how to do a real sysem

2026-04-29T03:40:02Z

added a new glowscipt simulation and added step by steps for how to do a real sysem

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 This page describes real systems and how they can be used to model certain aspects of a system's motion.
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 The equation above is the basis for answering work/energy questions using real systems. It is important to remember that when modeling a system as a real system, calculating the work done on the system as described above finds <b>all</b> of the work done on the system- both translational kinetic energy and internal types of energy.
 ===A Computational Model===
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 [[File:Pointparticlesystemtwomass.png]]
-[https://www.glowscript.org/#/user/YorickAndeweg/folder/PhysicsBookFolder/program/twomasssystem Here is a simulation of the system to help you visualize it.]
+[https://www.glowscript.org/#/user/YorickAndeweg/folder/MyPrograms/program/twomasssystem Here is a simulation of the system to help you visualize it.]
 By modeling the system as both a real system and a point particle system (which was done on the point particle systems page), we are able to answer the question. Finding more detailed information about the oscillations, such as their frequency, amplitude, and phase, is much more difficult and requires an entirely real model. A difficult-to-solve system of differential equations would have to be devised, describing the accelerations of the masses in terms of their positions.

Rcooper47 1: /* The Main Idea */

2022-04-09T22:37:02Z

The Main Idea

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	A real system is a system in which every part of the system is modeled separately, allowing for the internal behaviors of the system to be analyzed in addition to the system's motion through its environment.		A real system is a system in which every part of the system is modeled separately, allowing for the internal behaviors of the system to be analyzed in addition to the system's motion through its environment.

	In [[Point Particle Systems]], forces are analyzed as though they act directly on the system's center of mass, and only the translational kinetic energy of a system can change. Through week 9, we have ~~been~~ most bodies as point particles, as we have been primarily interested in their translational motion. However, we may now encounter problems where we want to analyze the internal behaviors of systems as well. For example, we may want to calculate a change in a system's [[Translational, Rotational and Vibrational Energy]], [[Potential Energy]], or [[Thermal Energy]]. In a real system, the point of application of each force must be considered. Furthermore, when calculating the work done by a force, the distance over which the force is applied is not the distance traveled by the system's center of mass, but rather the distance traveled by the force's point of contact. These two key differences lead to a mathematical model that can be more complicated than that of a point particle system, but yields insights about the internal behavior of the system.		In [[Point Particle Systems]], forces are analyzed as though they act directly on the system's center of mass, and only the translational kinetic energy of a system can change. Through week 9, we have modelled most bodies as point particles, as we have been primarily interested in their translational motion. However, we may now encounter problems where we want to analyze the internal behaviors of systems as well. For example, we may want to calculate a change in a system's [[Translational, Rotational and Vibrational Energy]], [[Potential Energy]], or [[Thermal Energy]]. In a real system, the point of application of each force must be considered. Furthermore, when calculating the work done by a force, the distance over which the force is applied is not the distance traveled by the system's center of mass, but rather the distance traveled by the force's point of contact. These two key differences lead to a mathematical model that can be more complicated than that of a point particle system, but yields insights about the internal behavior of the system.

	===A Mathematical Model===		===A Mathematical Model===

YorickAndeweg: /* A Mathematical Model */

2019-08-03T19:15:23Z

A Mathematical Model

← Older revision		Revision as of 15:15, 3 August 2019
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	===A Mathematical Model===		===A Mathematical Model===

	The mathematical concepts used to analyze point particle systems depend on the system. Often, the work-energy theorem ~~(see Work/Energy)~~ is used. This section explains how to use the work-energy theorem for a point particle system because this is the concept that varies the most significantly from its application to point particle systems.		The mathematical concepts used to analyze point particle systems depend on the system. Often, the [[Work/Energy\|work-energy theorem]] is used. This section explains how to use the work-energy theorem for a point particle system because this is the concept that varies the most significantly from its application to point particle systems.

	The work done on a real system should be calculated separately for each force acting on it because each force might be exerted over a different distance due to the geometry of the system. The work done on a real system by each force is defined as		The work done on a real system should be calculated separately for each force acting on it because each force might be exerted over a different distance due to the geometry of the system. The work done on a real system by each force is defined as

YorickAndeweg: /* A Computational Model */

2019-07-12T20:19:18Z

A Computational Model

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	Most computer simulations treat systems as real systems, modeling each part of a system separately. This is because [[Iterative Prediction]] makes keeping track of each part of the system separately easy even when it might be difficult to do so analytically. The last example on the [[Point Particle Systems]] page describes a system in which two masses are connected by a spring and one of them is pulled by a force. Consider the following simulation of the system:		Most computer simulations treat systems as real systems, modeling each part of a system separately. This is because [[Iterative Prediction]] makes keeping track of each part of the system separately easy even when it might be difficult to do so analytically. The last example on the [[Point Particle Systems]] page describes a system in which two masses are connected by a spring and one of them is pulled by a force. Consider the following simulation of the system:

	[https://www.glowscript.org/#/user/YorickAndeweg/folder/PhysicsBookFolder/program/~~twomasssystem~~ Two mass system simulation]		[https://www.glowscript.org/#/user/YorickAndeweg/folder/PhysicsBookFolder/program/TwoMassSystem Two mass system simulation]

	If you click "view source" on the top left corner, you will see that the process of iterative prediction is performed separately for each of the two masses- they each have their own position vectors, and the forces acting on each are calculated. There is no need to treat them as a single particle and thereby lose information about their internal behavior- in this case, their oscillations.		If you click "view source" on the top left corner, you will see that the process of iterative prediction is performed separately for each of the two masses- they each have their own position vectors, and the forces acting on each are calculated. There is no need to treat them as a single particle and thereby lose information about their internal behavior- in this case, their oscillations.

YorickAndeweg: /* Examples */

2019-07-07T18:32:53Z

Examples

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	==Examples==		==Examples==

	Some of the examples on the [[Point Particle Systems]] page can also be analyzed as real systems. Modeling each system as a real system makes the math more complicated but allows us to calculate the internal energies of the systems. Let us look at each example from the point particle systems page. (If you haven't already looked at them on the point particle ~~system's~~ page, do that first.)		Some of the examples on the [[Point Particle Systems]] page can also be analyzed as real systems. Modeling each system as a real system makes the math more complicated but allows us to calculate the internal energies of the systems. Let us look at each example from the point particle systems page. (If you haven't already looked at them on the point particle systems page, do that first.)

	===1.===		===1.===

YorickAndeweg: /* 4. */

2019-07-04T19:08:24Z

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	===4.===		===4.===

	A uniform disk of mass <math>M</math> starts at rest and rolls without slipping down a ramp. The plane of the ramp makes an angle of <Math>\Theta</Math> with the horizontal. The force of [[Static Friction]] acting on the bottom of ~~the~~ disk an causing it to ~~roll~~ always has a magnitude of 1/3 the force acting to move the disk down the ramp. What is the translational speed of the disk after it has traveled a distance of <math>d</math> diagonally down the ramp?		A uniform disk of mass <math>M</math> starts at rest and rolls without slipping down a ramp. The plane of the ramp makes an angle of <Math>\Theta</Math> with the horizontal. The force of [[Static Friction]] acting on the bottom of such a disk, causing it to rotate, always has a magnitude of 1/3 the force acting to move the disk down the ramp. What is the translational speed of the disk after it has traveled a distance of <math>d</math> diagonally down the ramp?

	[[File:Pointparticlesystemsramp.png]]		[[File:Pointparticlesystemsramp.png]]

YorickAndeweg: /* 4. */

2019-06-14T21:06:08Z

← Older revision		Revision as of 17:06, 14 June 2019
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	since the gravitational force force acts on the center of the disk's mass, which travels a distance of d.		since the gravitational force force acts on the center of the disk's mass, which travels a distance of d.

	The work done by the friction force, however, is actually 0. This is because the friction force is applied to the point on the edge of the disk: the point that is in contact with the ramp. Since the disk rolls instead of slides and is affected by ~~static friction~~ with the ramp, this point is not moving relative to the ramp, and so the friction force is exerted over a distance of 0.		The work done by the friction force, however, is actually 0. This is because the friction force is applied to the point on the edge of the disk: the point that is in contact with the ramp. Since the disk rolls instead of slides and is affected by [[Static Friction]] with the ramp, this point is not moving relative to the ramp, and so the friction force is exerted over a distance of 0.

	When modeling the disk as a real system, therefore, the final energy of the disk is		When modeling the disk as a real system, therefore, the final energy of the disk is

YorickAndeweg: /* 5. */

2019-06-13T16:17:51Z

← Older revision		Revision as of 12:17, 13 June 2019
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	[https://www.glowscript.org/#/user/YorickAndeweg/folder/PhysicsBookFolder/program/twomasssystem Here is a simulation of the system to help you visualize it.]		[https://www.glowscript.org/#/user/YorickAndeweg/folder/PhysicsBookFolder/program/twomasssystem Here is a simulation of the system to help you visualize it.]

	By modeling the system as both a real system and a point particle system (which was done on the point particle systems page), we are able to answer the question. Finding more detailed information about the oscillations, such as their frequency ~~and particularly their~~ amplitude and phase, is much more difficult and requires an entirely ~~realmodel~~. A difficult-to-solve system of differential equations would have to be devised, describing the accelerations of the masses in terms of their positions.		By modeling the system as both a real system and a point particle system (which was done on the point particle systems page), we are able to answer the question. Finding more detailed information about the oscillations, such as their frequency, amplitude, and phase, is much more difficult and requires an entirely real model. A difficult-to-solve system of differential equations would have to be devised, describing the accelerations of the masses in terms of their positions.

	==See also==		==See also==

YorickAndeweg: /* See also */

2019-06-13T16:16:48Z

YorickAndeweg: /* 5. */

2019-06-12T22:27:01Z

← Older revision		Revision as of 18:27, 12 June 2019
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	===5.===		===5.===

	A pair of 10kg masses are connected by a spring of unknown spring constant. They begin at rest at the spring's equilibrium length. A 30N rightward force is applied to the mass on the right for 4s. At the end of the 4 second period, the force ceases to act and the mass on the right has traveled 20m. The system continues to travel to the right, and the distance between the two masses oscillates sinusoidally. How much vibrational kinetic energy does the system have? (Vibrational kinetic energy is the energy of the mass' oscillatory movement, as opposed to their translational kinetic energy, which is the energy of the rightward movement of their center of mass.)		A pair of 10kg masses are connected by a massless spring of unknown spring constant. They begin at rest at the spring's equilibrium length. A 30N rightward force is applied to the mass on the right for 4s. At the end of the 4 second period, the force ceases to act and the mass on the right has traveled 20m. The system continues to travel to the right, and the distance between the two masses oscillates sinusoidally. How much vibrational kinetic energy does the system have? (Vibrational kinetic energy is the energy of the mass' oscillatory movement, as opposed to their translational kinetic energy, which is the energy of the rightward movement of their center of mass.)

	[[File:Pointparticlesystemtwomass.png]]		[[File:Pointparticlesystemtwomass.png]]

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	==See also==		==See also==

	*[[~~Real~~ Systems]]		*[[Point Particle Systems]]
	*[[Work/Energy]]		*[[Work/Energy]]
	*[[Translational, Rotational and Vibrational Energy]]		*[[Translational, Rotational and Vibrational Energy]]