183_notes:newton_grav_pe

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183_notes:newton_grav_pe [2021/04/01 12:53] – [Gravitational Potential Energy] stumptyl183_notes:newton_grav_pe [2021/04/01 12:54] (current) – [Newtonian Gravitational Potential Energy] stumptyl
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 ==== (Near Earth) Gravitational Potential Energy ==== ==== (Near Earth) Gravitational Potential Energy ====
  
-Earlier, you read how the gravitational potential energy for a system consisting of two objects (the Earth and something on the surface of the Earth) is given by,+Earlier, you read how the gravitational potential energy (J) for a system consisting of two objects (the Earth and something on the surface of the Earth) is given by,
  
 $$\Delta U_{grav} = +mg\Delta y$$ $$\Delta U_{grav} = +mg\Delta y$$
  
-where the separation distance ($\Delta y$) is measured from the surface of the Earth. In this previous calculation, you assumed that the gravitational force was a constant ($\vec{F}_{grav} = \langle 0,-mg,0\rangle$) over the distances that you were considering. This is an approximation, but it's not a bad one for the most part.+where the separation distance ($\Delta y$) is measured from the surface of the Earth. __In this previous calculation, you assumed that the gravitational force was a constant ($\vec{F}_{grav} = \langle 0,-mg,0\rangle$) over the distances that you were considering.__ This is an approximation, but it's not a bad one for the most part.
  
 However, you will relax this condition now, because as you have read, that [[183_notes:gravitation|the gravitational force between two objects with mass is not a constant vector]]. However, you will relax this condition now, because as you have read, that [[183_notes:gravitation|the gravitational force between two objects with mass is not a constant vector]].
  
  
-==== Newtonian Gravitational Potential Energy ====+===== Newtonian Gravitational Potential Energy =====
  
 In general, the gravitational force exerted on a object of mass $m_1$ due to an object of mass $m_2$ is non-constant, In general, the gravitational force exerted on a object of mass $m_1$ due to an object of mass $m_2$ is non-constant,
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 So for this force, what is the gravitational potential energy? So for this force, what is the gravitational potential energy?
  
-=== Solve the 1-dimensional problem first ===+==== Solve the One-Dimensional Problem First ====
  
 Remember that the potential energy change is the negative change in the internal work ($\Delta U = -W_{int}$). So, you can calculate what the work done by the gravitational force would be and use that to determine that change in potential energy in going from location 1 to location 2, Remember that the potential energy change is the negative change in the internal work ($\Delta U = -W_{int}$). So, you can calculate what the work done by the gravitational force would be and use that to determine that change in potential energy in going from location 1 to location 2,
  • 183_notes/newton_grav_pe.txt
  • Last modified: 2021/04/01 12:54
  • by stumptyl