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183_notes:work [2015/10/06 10:50] – [Work can be positive, negative, or zero] caballero | 183_notes:work [2021/03/12 02:32] (current) – [The Formal Definition of Work] stumptyl |
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| Section 6.3 and 6.4 in Matter and Interactions (4th edition) |
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===== Work: Mechanical Energy Transfer ===== | ===== Work: Mechanical Energy Transfer ===== |
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As you read earlier, [[183_notes:point_particle|the change in the total energy of a system is equal to the work done on that system by its surroundings]]. In these notes, you will read about the formal definition of work, which is the transfer of mechanical energy, and a mathematical idea that underpins work - the dot product. | As you read earlier, [[183_notes:point_particle|the change in the total energy of a system is equal to the work done on that system by its surroundings]]. **In these notes, you will read about the formal definition of work, which is the transfer of mechanical energy, and a mathematical idea that underpins work - the dot product.** |
==== Lecture Video ==== | ==== Lecture Video ==== |
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==== The Formal Definition of Work ==== | ==== The Formal Definition of Work ==== |
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The work that is done by a force is the //scalar// product (or dot product) of that force and the displacement. | The work that is done by a force is the **__scalar product__** (or dot product) of that force and the displacement. |
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$$W = \vec{F}\cdot\Delta\vec{r} = F_x dx + F_y dy + F_z dz$$ | $$W = \vec{F}\cdot\Delta\vec{r} = F_x dx + F_y dy + F_z dz$$ |
$$Work = (Force)*(distance) = (Newtons)*(meters) = Nm = Joule$$ | $$Work = (Force)*(distance) = (Newtons)*(meters) = Nm = Joule$$ |
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The units of work is a Joule named after [[http://en.wikipedia.org/wiki/James_Prescott_Joule|James Joule]], an English physicist and beer brewer. One Joule is equal to 1 $Nm$ or 1 $kgm/s^2$. | The units of work is a Joule named after [[http://en.wikipedia.org/wiki/James_Prescott_Joule|James Joule]], an English physicist and beer brewer. One Joule is equal to 1 $Nm$ or 1 $kgm^2/s^2$. |
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==== Work can be positive, negative, or zero ==== | ==== Work can be positive, negative, or zero ==== |
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What's very interesting about the work done by the local gravitational force is that it is //[[http://en.wikipedia.org/wiki/Conservative_force|conservative]]//. The work done by the gravitational force does not depend on the path the object takes, only on the initial and final location of the object, which is how conservative forces are defined. In particular, it only depends on the change in the vertical position of the particle. That's all that matters for conservative forces -- the end points. | What's very interesting about the work done by the local gravitational force is that it is //[[http://en.wikipedia.org/wiki/Conservative_force|conservative]]//. The work done by the gravitational force does not depend on the path the object takes, only on the initial and final location of the object, which is how conservative forces are defined. In particular, it only depends on the change in the vertical position of the particle. That's all that matters for conservative forces -- the end points. |
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| ==== Examples ==== |
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| * [[:183_notes:examples:videoswk7|Video Example: Work and Friction + Ramp]] |