183_notes:grav_and_spring_pe

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183_notes:grav_and_spring_pe [2014/10/10 18:15] – caballero183_notes:grav_and_spring_pe [2021/03/12 02:45] (current) – [Types of Potential Energy] stumptyl
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 +Section 6.8 and 7.2 in Matter and Interactions (4th edition) 
 +
 ===== Types of Potential Energy ===== ===== Types of Potential Energy =====
  
-[[183_notes:potential_energy|Potential energy]] is the energy associated with interactions between pairs of objects. In these notes, you will read about two particular types of potential energy: the energy associated with the gravitational interaction and the energy associated with a spring-mass system.+[[183_notes:potential_energy|Potential energy]] is the energy associated with interactions between pairs of objects. **In these notes, you will read about two particular types of potential energy: the energy associated with the gravitational interaction and the energy associated with a spring-mass system.**
  
 ==== (Near Earth) Gravitational Potential Energy ==== ==== (Near Earth) Gravitational Potential Energy ====
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 [{{ 183_notes:potential_energy.006.png?400|A spring-mass system (spring constant, $k_s$) is stretched through a distance ($\Delta s$).}}] [{{ 183_notes:potential_energy.006.png?400|A spring-mass system (spring constant, $k_s$) is stretched through a distance ($\Delta s$).}}]
  
-To determine the potential energy associated with a spring-mass system, consider the work done by a spring on an object (mass, $m$) attached to its end. The spring is stretched through a displacement ($\Delta \vec{s}$). The displacement and the gravitational force are in opposite directions.+To determine the potential energy associated with a spring-mass system, consider the work done by a spring on an object (mass, $m$) attached to its end. The spring is stretched through a displacement ($\Delta \vec{s}$). The displacement and the spring force are in opposite directions.
  
 To calculate the work that the spring does, consider the object as the system. Remember that the [[183_notes:springmotion|spring force changes with displacement]], and thus we must use the [[183_notes:work_by_nc_forces|integral formulation to calculate the work]]. To calculate the work that the spring does, consider the object as the system. Remember that the [[183_notes:springmotion|spring force changes with displacement]], and thus we must use the [[183_notes:work_by_nc_forces|integral formulation to calculate the work]].
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 $$W_{s} = -\dfrac{1}{2}k_s\left(s_f^2-s_i^2\right)$$ $$W_{s} = -\dfrac{1}{2}k_s\left(s_f^2-s_i^2\right)$$
  
-If you include the spring in your system, so that the system is now the spring and the object, then potential energy shared spring-object system is given by,+If you include the spring in your system, so that the system is now the spring and the object, then the potential energy shared between the spring-object system is given by,
  
   - System: object+spring; Surroundings: Nothing   - System: object+spring; Surroundings: Nothing
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 Dissipative forces such as friction and air drag are non-conservative forces. The path that an object takes matters very much when non-conservative forces are present. Moreover, these dissipative forces cannot be associated with any construct like potential energy. Dissipative forces such as friction and air drag are non-conservative forces. The path that an object takes matters very much when non-conservative forces are present. Moreover, these dissipative forces cannot be associated with any construct like potential energy.
 +
 +==== Examples ====
 +
 +  * [[183_notes:examples:sledding|Sledding down a hill]]
 +  * [[183_notes:examples:the_jumper|The Jumper]]
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