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183_notes:work [2014/10/09 11:42] – [Work can be positive, negative, or zero] caballero | 183_notes:work [2018/05/29 21:16] – hallstein | ||
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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 ===== | ||
- | As you read earlier, 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, |
+ | ==== Lecture Video ==== | ||
+ | |||
+ | {{youtube> | ||
==== The Formal Definition of Work ==== | ==== The Formal Definition of Work ==== | ||
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$$W = \vec{F}\cdot\Delta\vec{r} = F_x dx + F_y dy + F_z dz$$ | $$W = \vec{F}\cdot\Delta\vec{r} = F_x dx + F_y dy + F_z dz$$ | ||
- | The dot product is one way that two vectors are " | + | The dot product is one way that two vectors are " |
[{{183_projects: | [{{183_projects: | ||
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$$Work = (Force)*(distance) = (Newtons)*(meters) = Nm = Joule$$ | $$Work = (Force)*(distance) = (Newtons)*(meters) = Nm = Joule$$ | ||
- | The units of work is a Joule named after [[http:// | + | The units of work is a Joule named after [[http:// |
==== Work can be positive, negative, or zero ==== | ==== Work can be positive, negative, or zero ==== | ||
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When the force has a component opposite the direction of motion, the work done by the force is negative; it decreases the kinetic energy of the system. | When the force has a component opposite the direction of motion, the work done by the force is negative; it decreases the kinetic energy of the system. | ||
- | In case 3, the force is perpendicular to the direction of motion, hence the cart will neither slow down or speed up. It will experience an increased vertical force due to the track (by additional compression of the bonds in the track). This doesn' | + | In case 3, the force is perpendicular to the direction of motion, hence the cart will neither slow down or speed up. It will experience an increased vertical force due to the track (by [[183_notes: |
$$W_3 = \vec{F}_3\cdot\Delta \vec{r}_3 = \Delta K_3 = 0$$ | $$W_3 = \vec{F}_3\cdot\Delta \vec{r}_3 = \Delta K_3 = 0$$ | ||
When using work, it is critical to pay attention to the relative direction of the force and the displacement to determine how the kinetic energy will change (if at all). | When using work, it is critical to pay attention to the relative direction of the force and the displacement to determine how the kinetic energy will change (if at all). | ||
+ | ==== Lecture Video ==== | ||
- | ==== Graphing the Work Done ==== | + | {{youtube> |
- | {{url> | + | ==== Graphing the Work Done: Force vs Displacement Graphs ==== |
+ | |||
+ | The work that is done by a single force (or the net force) can be represented graphically in a force vs displacement graph. This is similar to the [[183_notes: | ||
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+ | In force vs displacement graphs, the limitations are more strict. Because the work done (green area under the curve below) is a result of a dot product between two vectors, we lose information about the direction of the forces and displacement when we compute it. So, these graphs are useful to think about the force in a particular direction and a displacement in that or opposite that direction. | ||
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+ | For example, in the figure below, this might represent the net force acting on a cart in the x-direction. Sometimes, that force is in the direction of the displacement (positive work represented by the green shaded area above the y=0 line). At other times that force is opposite the direction of the displacement (negative work represented by the green shaded area below the y=0 line). | ||
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+ | {{url> | ||
==== Work by the Local Gravitational Force ==== | ==== Work by the Local Gravitational Force ==== | ||
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What's very interesting about the work done by the local gravitational force is that it is // | What's very interesting about the work done by the local gravitational force is that it is // | ||
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+ | ==== Examples ==== | ||
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+ | * [[: |