183_notes:torquediagram

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183_notes:torquediagram [2021/05/31 16:39] – [A balanced situation] stumptyl183_notes:torquediagram [2021/11/15 17:25] (current) – [Lecture Video] pwirving
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 **In these notes, you will read through an example where we will apply the ideas that the net force and net torque are zero and make use of the torque diagram to construct a mathematical representation of the problem.** **In these notes, you will read through an example where we will apply the ideas that the net force and net torque are zero and make use of the torque diagram to construct a mathematical representation of the problem.**
  
-==== Lecture Video ==== 
  
-{{youtube>rQUWKAKlc2U?large}} 
  
 ===== A Balanced Situation ===== ===== A Balanced Situation =====
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 Consider the situation in the figure below. A uniform plank of mass $m_p$ and length $3d$ is placed on a pivot as shown below. A mass $m_2$ is placed on the far left edge of the plank. To balance the whole setup, you want to place a mass $m_1$ on the far right edge. You need to figure out how large $m_1$ should be compared to the other masses in the setup to determine what mass to place on the far left edge (As shown). Consider the situation in the figure below. A uniform plank of mass $m_p$ and length $3d$ is placed on a pivot as shown below. A mass $m_2$ is placed on the far left edge of the plank. To balance the whole setup, you want to place a mass $m_1$ on the far right edge. You need to figure out how large $m_1$ should be compared to the other masses in the setup to determine what mass to place on the far left edge (As shown).
  
-{{ 183_notes:balance.png?400 }}+{{ 183_notes:week12_torquediagrams1.png?400 }}
  
 //Because you are designing for no motion, you want the entire system to be in static equilibrium.// We can do a typical force analysis to see if this yields anything helpful, but first, let's draw the extended free-body diagram -- the torque diagram. Below, you will see a diagram that labels the four forces acting on the system: the gravitational force on each of the three objects, which points downward, and the force due to the pivot, which points upward. In addition, a torque diagram labels all the lever arm distances (given a specific choice of the pivot point, red dot in this case). //Because you are designing for no motion, you want the entire system to be in static equilibrium.// We can do a typical force analysis to see if this yields anything helpful, but first, let's draw the extended free-body diagram -- the torque diagram. Below, you will see a diagram that labels the four forces acting on the system: the gravitational force on each of the three objects, which points downward, and the force due to the pivot, which points upward. In addition, a torque diagram labels all the lever arm distances (given a specific choice of the pivot point, red dot in this case).
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 Notice the forces are positioned at the location where they act. For each of the three objects, we treat the gravitational force as acting at the center of masses (in this case at their centers because they are of uniform density). For objects of non-uniform density, [[https://en.wikipedia.org/wiki/Center_of_mass|the situation would be a bit different]]. The pivot force acts at the point of contact (i.e., where the pivot touches the plank). This diagram will help us determine how the torques will play out. Notice the forces are positioned at the location where they act. For each of the three objects, we treat the gravitational force as acting at the center of masses (in this case at their centers because they are of uniform density). For objects of non-uniform density, [[https://en.wikipedia.org/wiki/Center_of_mass|the situation would be a bit different]]. The pivot force acts at the point of contact (i.e., where the pivot touches the plank). This diagram will help us determine how the torques will play out.
  
-{{ 183_notes:torquediagram.png?400 }}+{{ 183_notes:week12_torquediagrams2.png?400 }}
  
 ==== An Analysis of the Forces ==== ==== An Analysis of the Forces ====
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