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| 183_notes:point_particle [2015/10/05 14:43] – [Work: Mechanical Energy Transfer] caballero | 183_notes:point_particle [2021/05/06 20:42] (current) – [The Total Energy of a Single Particle] stumptyl |
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| | Section 6.2 in Matter and Interactions (4th edition) |
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| ===== The Simplest System: A Single Particle ===== | ===== The Simplest System: A Single Particle ===== |
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| The [[183_notes:define_energy#the_first_law_of_thermodynamics_the_energy_principle|energy principle]] is widely applicable and helps to explain or to predict the motion of systems by considering how the system exchanges energy with its surroundings. For now, you will read about the simplest of systems, that of a single particle. Here, you will read about the total energy of a particle, the energy due to its motion, and how those energies are connected in situations where we can neglect the [[183_notes:heat|heat exchanges]]. | The [[183_notes:define_energy#the_first_law_of_thermodynamics_the_energy_principle|energy principle]] is widely applicable and helps to explain or to predict the motion of systems by considering how the system exchanges energy with its surroundings. For now, you will read about the simplest of systems, that of a single particle. **In these notes, you will read about the total energy of a particle, the energy due to its motion, and how those energies are connected in situations where we can neglect the [[183_notes:heat|heat exchanges]]**. |
| ==== Lecture Video ==== | ==== Lecture Video ==== |
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| ==== The Total Energy of a Single Particle ==== | ==== The Total Energy of a Single Particle ==== |
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| [{{183_notes:real_to_pp.001.png?500|A real car crushed down to a point particle for the purpose of modeling the translation of the car. }}] | [{{ 183_notes:week7_cartopoint.png?500|A real car crushed down to a point particle for the purpose of modeling the translation of the car. }}] |
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| The systems that you will consider will be approximated by a single object, the //point particle//. The point particle is an object that has no size of its own, but carries the mass of the object it is meant to represent. This point particle experiences the same force that the real object experiences, and thus models the motion of that real physical system to the extent that you only care about how the object translates (moves without rotation). Point particles do not spin or change their shape. Later, [[183_notes:energy_sep|we will relax these conditions]]. | The systems that you will consider will be approximated by a single object, **__the point particle__**. The point particle is an object that has no size of its own, but carries the mass of the object it is meant to represent. This point particle experiences the same force that the real object experiences, and thus models the motion of that real physical system to the extent that you only care about how the object translates (moves without rotation). Point particles do not spin or change their shape. Later, [[183_notes:energy_sep|we will relax these conditions]]. |
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| Thanks to Einstein, we know the total energy of a single particle system is given by, | Thanks to Einstein, we know the total energy of a single particle system is given by, |
| $$E_{rest} = mc^2$$ | $$E_{rest} = mc^2$$ |
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| It appears that the rest of the energy is associated with the motion of the particle. As such, it is refereed to as the //kinetic energy// of the particle. | It appears that the rest of the energy is associated with the motion of the particle. As such, it is refereed to as the __**kinetic energy (J)**__ of the particle. |
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| $$K = E_{tot} - E_{rest} = \gamma m c^2 - mc^2 = (\gamma - 1)mc^2$$ | $$K = E_{tot} - E_{rest} = \gamma m c^2 - mc^2 = (\gamma - 1)mc^2$$ |