Work and Energy for an Extended System - Revision history

Athenawu66: /* Connectedness */

2023-04-25T04:29:38Z

Connectedness

← Older revision		Revision as of 00:29, 25 April 2023
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	This topic is also interesting because one can be able to see how all the various energies come together within the entire system. Unlike the point-particle system where one only considers translational kinetic energy, extended systems go beyond that and consider changes in internal energy. This is very interesting, especially because changes in internal energy sometimes cannot be seen		This topic is also interesting because one can be able to see how all the various energies come together within the entire system. Unlike the point-particle system where one only considers translational kinetic energy, extended systems go beyond that and consider changes in internal energy. This is very interesting, especially because changes in internal energy sometimes cannot be seen
	but can be calculated within an extended system.		but can be calculated within an extended system.


	2. How is it connected to your major?		2. How is it connected to your major?

Athenawu66: /* Connectedness */

2023-04-25T04:28:25Z

Connectedness

← Older revision		Revision as of 00:28, 25 April 2023
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	This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real-world situations is always so exciting for me.		This topic interests me because it involves calculating work in real systems present in the real world, unlike the point particle system which focuses more on calculating work on single atoms or idealized versions of objects modeled as a point particle. Being able to apply physics to real-world situations is always so exciting for me.

			This topic is also interesting because one can be able to see how all the various energies come together within the entire system. Unlike the point-particle system where one only considers translational kinetic energy, extended systems go beyond that and consider changes in internal energy. This is very interesting, especially because changes in internal energy sometimes cannot be seen
			but can be calculated within an extended system.

	2. How is it connected to your major?		2. How is it connected to your major?

Athenawu66: /* Hard */

2023-04-25T04:03:50Z

Hard

← Older revision		Revision as of 00:03, 25 April 2023
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	A system consists of a uniform sphere of mass M and radius R. It is attached to the middle of a massless rod of length L, and two small point masses of 2m are at the end of the rod. This apparatus lies on a frictionless surface.		A system consists of a uniform sphere of mass M and radius R. It is attached to the middle of a massless rod of length L, and two small point masses of 2m are at the end of the rod. This apparatus lies on a frictionless surface.

	A string is wound up around the sphere, and you start pulling on the string with a constant force of magnitude F, causing the apparatus to slide along the frictionless surface. The entire apparatus also moves a total distance of D. The string that is pulled at force F moves/comes off a total of distance D. The sphere+rod is spinning at an angular speed of ω.		A string is wound up around the sphere, and you start pulling on the string with a constant force of magnitude F, causing the apparatus to slide along the frictionless surface. The entire apparatus also moves a total distance of C. The string that is pulled at force F moves/comes off a total of distance D. The sphere+rod is spinning at an angular speed of ω.

	Use the extended system to find what the angular speed ω is in the final state.		Use the extended system to find what the angular speed ω is in the final state.

Athenawu66: /* Solution */

2023-04-25T04:01:37Z

Solution

← Older revision		Revision as of 00:01, 25 April 2023
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	First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.		First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.

	We also know that the change in energy of our real system is equal to the sum of the change in translational kinetic energy and the change in rotational kinetic energy. This should also be equal to the work of the hand on the basketball. However, a place that is tricky is that the work of the hand is FB. After all, the force that the hand exerts on the basketball is F and the hand moves a total distance of B. When we are dealing with real systems, even though the center of mass moved a distance of D, we want to take into account the distance that the force moved, which is B in our case.		We also know that the change in energy of our real system is equal to the sum of the change in translational kinetic energy and the change in rotational kinetic energy. This should also be equal to the work of the hand on the basketball. However, a place that is tricky is that the work of the hand is FB. After all, the force that the hand exerts on the basketball is F and the hand moves a total distance of B. When we are dealing with real and extended systems, even though the center of mass moved a distance of D, we want to take into account the distance that the force moved, which is B in our case.

	[[File:Formula1work1.jpg]]		[[File:Formula1work1.jpg]]

	However, what is velocity v? Well, we know that v = ωR as the basketball is rolling without slipping on a frictionless surface. Hence, we can substitute ωR in the equation of translational kinetic energy into the value of v.		However, what is velocity v? Well, we know that v = ωR, as the basketball is rolling without slipping on a frictionless surface. Hence, we can substitute ωR in the equation of translational kinetic energy into the value of v.

	[[File:Middlingworkanswer.jpg]]		[[File:Middlingworkanswer.jpg]]

Athenawu66: /* Middling */

2023-04-25T04:00:33Z

Middling

← Older revision		Revision as of 00:00, 25 April 2023
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	[[File:Amiddling1final.png]]		[[File:Amiddling1final.png]]

			===Solution===
	First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.		First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.

Athenawu66: /* Middling */

2023-04-25T03:59:50Z

Middling

← Older revision		Revision as of 23:59, 24 April 2023
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	[[File:Amiddling1final.png]]		[[File:Amiddling1final.png]]

Athenawu66: /* Middling */

2023-04-25T03:57:26Z

Middling

← Older revision		Revision as of 23:57, 24 April 2023
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	[[File:Amiddling1final.png]]		[[File:Amiddling1final.png]]




	First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.		First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.

Athenawu66: /* Middling */

2023-04-25T03:56:59Z

Middling

← Older revision		Revision as of 23:56, 24 April 2023
Line 59:		Line 59:

	[[File:Amiddling1final.png]]		[[File:Amiddling1final.png]]



	First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.		First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.

Athenawu66: /* Middling */

2023-04-25T03:54:13Z

Middling

← Older revision		Revision as of 23:54, 24 April 2023
Line 59:		Line 59:

	[[File:Amiddling1final.png]]		[[File:Amiddling1final.png]]



	First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.		First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.

Athenawu66: /* Middling */

2023-04-25T03:54:01Z

Middling

← Older revision		Revision as of 23:54, 24 April 2023
Line 59:		Line 59:

	[[File:Amiddling1final.png]]		[[File:Amiddling1final.png]]

	First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.		First off, we know that the real system we are dealing with is the basketball, with our surroundings being the hand that is exerting force F and the frictionless surface.