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SMU PHYSICS 1303: Introduction to Mechanics

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SMU PHYSICS 1303: Introduction to Mechanics SMU PHYSICS 1303: Introduction to Mechanics Stephen Sekula1 1Southern Methodist University Dallas, TX, USA SPRING, 2019 S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 1 Outline Conservation of Energy S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 2 Conservation of Energy Conservation of Energy NASA, “Hipnos” by Molinos de Viento and available under Creative Commons from Flickr S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 3 Conservation of Energy Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will come to understand that energy can change forms, but is neither created from nothing nor entirely destroyed. I We will understand the mathematical description of energy conservation. I We will explore the implications of the conservation of energy. Jacques-Louis David. “Portrait of Monsieur de Lavoisier and his Wife, chemist Marie-Anne Pierrette Paulze”. Available under Creative Commons from Flickr. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Conservation of Energy Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will come to understand that energy can change forms, but is neither created from nothing nor entirely destroyed. I We will understand the mathematical description of energy conservation. I We will explore the implications of the conservation of energy. Jacques-Louis David. “Portrait of Monsieur de Lavoisier and his Wife, chemist Marie-Anne Pierrette Paulze”. Available under Creative Commons from Flickr. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Conservation of Energy Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will come to understand that energy can change forms, but is neither created from nothing nor entirely destroyed. I We will understand the mathematical description of energy conservation. I We will explore the implications of the conservation of energy. Jacques-Louis David. “Portrait of Monsieur de Lavoisier and his Wife, chemist Marie-Anne Pierrette Paulze”. Available under Creative Commons from Flickr. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Conservation of Energy Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will come to understand that energy can change forms, but is neither created from nothing nor entirely destroyed. I We will understand the mathematical description of energy conservation. I We will explore the implications of the conservation of energy. Jacques-Louis David. “Portrait of Monsieur de Lavoisier and his Wife, chemist Marie-Anne Pierrette Paulze”. Available under Creative Commons from Flickr. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Conservation of Energy A Principle of Nature: Energy is Conserved It is a remarkable fact of the universe: that this quantity which we call “energy” is, in a system where nothing can leave and nothing can enter the system, conserved. I That is to say, if we wall off a system of matter such that nothing can get in and nothing can get out, and if we can account for all the ways in which energy can be distributed inside the system, we observe that energy changes form but is neither created nor destroyed. I Figuring this out for the first time took immense effort. Consider the experiments of the French chemists (and husband and wife) Lavoisier and Paulze, whose careful and quantitative experiments with chemical transformations showed that the mass of matter before and after chemical reactions was the same — that something was conserved. I Ultimately it would be realized that not mass, but in fact energy, is what nature conserves. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Conservation of Energy A Principle of Nature: Energy is Conserved It is a remarkable fact of the universe: that this quantity which we call “energy” is, in a system where nothing can leave and nothing can enter the system, conserved. I That is to say, if we wall off a system of matter such that nothing can get in and nothing can get out, and if we can account for all the ways in which energy can be distributed inside the system, we observe that energy changes form but is neither created nor destroyed. I Figuring this out for the first time took immense effort. Consider the experiments of the French chemists (and husband and wife) Lavoisier and Paulze, whose careful and quantitative experiments with chemical transformations showed that the mass of matter before and after chemical reactions was the same — that something was conserved. I Ultimately it would be realized that not mass, but in fact energy, is what nature conserves. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Conservation of Energy A Principle of Nature: Energy is Conserved It is a remarkable fact of the universe: that this quantity which we call “energy” is, in a system where nothing can leave and nothing can enter the system, conserved. I That is to say, if we wall off a system of matter such that nothing can get in and nothing can get out, and if we can account for all the ways in which energy can be distributed inside the system, we observe that energy changes form but is neither created nor destroyed. I Figuring this out for the first time took immense effort. Consider the experiments of the French chemists (and husband and wife) Lavoisier and Paulze, whose careful and quantitative experiments with chemical transformations showed that the mass of matter before and after chemical reactions was the same — that something was conserved. I Ultimately it would be realized that not mass, but in fact energy, is what nature conserves. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Conservation of Energy A Principle of Nature: Energy is Conserved It is a remarkable fact of the universe: that this quantity which we call “energy” is, in a system where nothing can leave and nothing can enter the system, conserved. I That is to say, if we wall off a system of matter such that nothing can get in and nothing can get out, and if we can account for all the ways in which energy can be distributed inside the system, we observe that energy changes form but is neither created nor destroyed. I Figuring this out for the first time took immense effort. Consider the experiments of the French chemists (and husband and wife) Lavoisier and Paulze, whose careful and quantitative experiments with chemical transformations showed that the mass of matter before and after chemical reactions was the same — that something was conserved. I Ultimately it would be realized that not mass, but in fact energy, is what nature conserves. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Conservation of Energy The Conservation of Mechanical Energy Mechanical Energy is defined explicitly as the sum of kinetic energy and potential energy. Note that mechanical energy excludes situations where a non-conservative force acts. Considering only conservative forces, it is observed that mechanical energy is conserved. Let us define the total mechanical energy in a given moment of time as: Emec = K + U The conservation of mechanical energy then requires that the following be true at some initial time, ti , and some final time, tf > ti : Emec;f = Emec;i −! Kf + Uf = Ki + Ui S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6 Conservation of Energy The Conservation of Mechanical Energy Mechanical Energy is defined explicitly as the sum of kinetic energy and potential energy. Note that mechanical energy excludes situations where a non-conservative force acts. Considering only conservative forces, it is observed that mechanical energy is conserved. Let us define the total mechanical energy in a given moment of time as: Emec = K + U The conservation of mechanical energy then requires that the following be true at some initial time, ti , and some final time, tf > ti : Emec;f = Emec;i −! Kf + Uf = Ki + Ui S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6 Conservation of Energy The Conservation of Mechanical Energy Mechanical Energy is defined explicitly as the sum of kinetic energy and potential energy. Note that mechanical energy excludes situations where a non-conservative force acts. Considering only conservative forces, it is observed that mechanical energy is conserved. Let us define the total mechanical energy in a given moment of time as: Emec = K + U The conservation of mechanical energy then requires that the following be true at some initial time, ti , and some final time, tf > ti : Emec;f = Emec;i −! Kf + Uf = Ki + Ui S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6 Conservation of Energy The Conservation of Mechanical Energy Mechanical Energy is defined explicitly as the sum of kinetic energy and potential energy. Note that mechanical energy excludes situations where a non-conservative force acts. Considering only conservative forces, it is observed that mechanical energy is conserved. Let us define the total mechanical energy in a given moment of time as: Emec = K + U The conservation of mechanical energy then requires that the following be true at some initial time, ti , and some final time, tf > ti : Emec;f = Emec;i −! Kf + Uf = Ki + Ui S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6 Conservation of Energy Conservative Forces and the Conservation of Mechanical Energy We almost derived this conservation earlier, when considering changes in kinetic energy and work done by a conservative force. We know from our earlier exploration of, for instance, gravity that ∆K = Kf − Ki = W where W is the work done by a conservative force. We also saw that: ∆U = −W It’s a small leap from those observations to the conservation of mechanical energy, once we define Emec = K + U: ∆K = W = −∆U −! Kf − Ki = −(Uf − Ui ) −! Kf + Uf = Ki + Ui S.
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