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183_notes:work [2014/10/09 11:53] – [Graphing the Work Done] caballero | 183_notes:work [2015/10/05 18:43] – [The Formal Definition of Work] 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 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 ==== | ||
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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). | 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). | ||
- | {{url> | + | {{url> |
==== Work by the Local Gravitational Force ==== | ==== Work by the Local Gravitational Force ==== | ||