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| 184_notes:energy_review [2023/08/18 19:42] – [Forms of Energy] tdeyoung | 184_notes:energy_review [2023/08/22 14:51] (current) – [What is Energy?] tdeyoung |
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| It's actually not easy to give a precise definition of energy that covers all of the situations in which it occurs. For our course, a reasonable way to think about it is that **energy is either motion, or the ability to produce motion**. (However, some forms of this motion, like random molecular motion associated with thermal energy produced by friction, may be difficult to see.) | It's actually not easy to give a precise definition of energy that covers all of the situations in which it occurs. For our course, a reasonable way to think about it is that **energy is either motion, or the ability to produce motion**. (However, some forms of this motion, like random molecular motion associated with thermal energy produced by friction, may be difficult to see.) |
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| There are two important types of energy we talk about: //**kinetic energy**//, which is the energy associated with objects currently moving in a particular direction, and //**potential energy**//, which is energy stored somehow in a system that could cause things to move in the future (like a compressed spring that could push a block and make it move). | There are two important types of energy we talk about: //**kinetic energy**//, which is the energy associated with objects currently moving in a particular direction, and //**potential energy**//, which is energy stored somehow in a system that could cause things to move in the future (like a compressed spring that could push a block and make it move). A third form of energy is //thermal energy//, which is associated with the random motion of atoms and molecules. Kinetic or potential energy can be turned into thermal energy, but thermal energy cannot easily be turned back into kinetic or potential energy. |
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| A really nice feature of energy is that **energy is a scalar**, not a vector. Energy is just a number without any direction associated with it, which means there are no //x// and //y// components and no trigonometry to worry about. | A really nice feature of energy is that **energy is a scalar**, not a vector. Energy is just a number without any direction associated with it, which means there are no //x// and //y// components and no trigonometry to worry about. |
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| Although thermal energy is difficult to utilize, it can be measured through an object's temperature. Every object has a parameter called its //heat capacity,// $C$, which relates the heat flowing into or out of the object to the change in its temperature: $$\Delta E_{th} = C \, \Delta T.$$ The heat capacity can be related to the object's properties, such as its mass and the specific heat of the material it's made of. | Although thermal energy is difficult to utilize, it can be measured through an object's temperature. Every object has a parameter called its //heat capacity,// $C$, which relates the heat flowing into or out of the object to the change in its temperature: $$\Delta E_{th} = C \, \Delta T.$$ The heat capacity can be related to the object's properties, such as its mass and the specific heat of the material it's made of. |
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| | ==== Common Mistakes ==== |
| | * **Setting one type of energy equal to another, such as $K = U$**. Energy conservation relates the total energy at one time to the total energy at some other time. If the initial energy and the final energy are each entirely one type you may get something like $K=U$, but that is a special case, not a universal principle. It's a good idea to always start by writing down $E_f = E_i + \Delta E$ to remind yourself of the correct structure. |
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| | * **Sign errors.** If energy is transferred, it's flowing into one object but out of another. The magnitude of $\Delta E$ is the same for both objects, but one has a positive sign (gains energy) while the other is negative (loses energy), so it's easy to make a sign error. Always be sure the sign of a change in energy makes physical sense for the object you're looking at, don't assume equations will always be written with the right sign for your problem. |
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| | * **Forgetting that $U$ can be negative.** There's no absolute scale for potential energy; only changes in potential energy matter, so you can set the zero of $U$ to be whatever reference point you want. (There are situations where a particular choice may be useful, though.) You may have a problem where an object has $E_{tot} = 0$ but has positive $K$ and negative $U$ at some point in time. This is perfectly valid but a but counter-intuitive, so it's easy to make sign errors or make bad assumptions, like "if $E = 0$, then $K$ must be zero too." |