183_notes:work

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183_notes:work [2015/10/05 14:44] – [Work: Mechanical Energy Transfer] caballero183_notes:work [2015/10/06 10:50] – [Work can be positive, negative, or zero] caballero
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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 "multiplied". It is the sum of the product of each pair of components. This dot product is related to the angle that the force makes with the displacement. Essentially, the dot product will "pick out" the component of one vector that is parallel to another vector.+The dot product is one way that two vectors are "multiplied." It is the sum of the product of each pair of components. This dot product is related to the angle that the force makes with the displacement. Essentially, the dot product will "pick out" the component of one vector that is parallel to another vector.
  
 [{{183_projects:work.001.png?350|A point particle moves through a distance $d$ while a force $F$ is applied at an angle $\theta$ relative to the displacement.}}] [{{183_projects:work.001.png?350|A point particle moves through a distance $d$ while a force $F$ is applied at an angle $\theta$ relative to the displacement.}}]
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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't change the kinetic energy of the cart.+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:friction|additional compression of the bonds in the track]]). This doesn't change the kinetic energy of the cart.
  
 $$W_3 = \vec{F}_3\cdot\Delta \vec{r}_3 = \Delta K_3 = 0$$ $$W_3 = \vec{F}_3\cdot\Delta \vec{r}_3 = \Delta K_3 = 0$$
  
 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).
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 ==== Lecture Video ==== ==== Lecture Video ====
  
  • 183_notes/work.txt
  • Last modified: 2021/03/12 02:32
  • by stumptyl