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183_notes:work [2014/10/09 11:59] – [Graphing the Work Done: Force vs Displacement Graphs] caballero | 183_notes:work [2015/10/06 10:50] – [Work can be positive, negative, or zero] caballero | ||
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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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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 ==== | ||
+ | |||
+ | {{youtube> | ||
==== Graphing the Work Done: Force vs Displacement Graphs ==== | ==== Graphing the Work Done: Force vs Displacement Graphs ==== |