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183_notes:work [2017/10/17 02:44] – [The Formal Definition of Work] pawlakal183_notes:work [2026/01/04 20:24] (current) – hallstein
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 +Section 6.3 and 6.4 in Matter and Interactions (4th edition) 
 +
 ===== Work: Mechanical Energy Transfer ===== ===== Work: Mechanical Energy Transfer =====
  
-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 ====
  
-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.
  
 $$W = \vec{F}\cdot\Delta\vec{r} = F_x dx + F_y dy + F_z dz$$ $$W = \vec{F}\cdot\Delta\vec{r} = F_x dx + F_y dy + F_z dz$$
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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.  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. 
  
-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 blue shaded area above the y=0 line). At other times that force is opposite the direction of the displacement (negative work represented by the red shaded area below the y=0 line).
  
-{{url>https://plot.ly/~PERLatMSU/18/640/480 640px,480px|Force vs Displacement}}+{{url>https://msuperl.org/interactive/mechanics/net_force_vs_position_discrete.html 640px,480px|Force vs Displacement}}
 ==== Work by the Local Gravitational Force ==== ==== Work by the Local Gravitational Force ====
  
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