183_notes:examples:finalloccf

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183_notes:examples:finalloccf [2014/07/11 02:56] – created caballero183_notes:examples:finalloccf [2014/07/14 17:08] (current) – caballero
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 ===== Example: Predicting the location of an object undergoing constant force motion ===== ===== Example: Predicting the location of an object undergoing constant force motion =====
  
-The fan cart in the video below is observed to [[183_notes:acceleration|accelerate]] uniformly to the right. The air exerts a [[183_notes:constantf|constant force]] on the blades that is around $0.45 N$. Determine the how far the has traveled after $2.2 s$ if the cart starts from rest.+The fan cart in the video below is observed to [[183_notes:acceleration|accelerate]] uniformly to the right. The air exerts a [[183_notes:constantf|constant force]] on the blades that is around $0.45 N$. Determine the how far the fan cart has traveled after $2.2 s$ if the cart starts from rest.
  
 === Facts ==== === Facts ====
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     * the force applied by the track (directly upward)     * the force applied by the track (directly upward)
     * a frictional forces and air resistance that resist the motion     * a frictional forces and air resistance that resist the motion
-  * The acceleration due to gravity is 9.8 $\dfrac{m}{s^2} and is directed downward.+  * The acceleration due to gravity is 9.8 $\dfrac{m}{s^2}$ and is directed downward.
  
 === Lacking === === Lacking ===
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 === Approximations & Assumptions === === Approximations & Assumptions ===
  
-  * Over the interval that we care about it, we will assume the net force is doesn't change. That is, the cart experiences [[183_notes:constantf|constant force motion]].+  * Over the interval that we care about it, we will assume the net force doesn't change. That is, the cart experiences [[183_notes:constantf|constant force motion]].
   * As a result, the motion occurs only in the horizontal direction.   * As a result, the motion occurs only in the horizontal direction.
  
 === Representations === === Representations ===
-    + 
-   * The forces acting on the fan cart (the system's interactions with its surroundings) are represented in this free-body diagram.+  * The forces acting on the fan cart (the system's interactions with its surroundings) are represented in this free-body diagram.
 {{ :183_notes:mi3e_02-011.jpg?200 }} {{ :183_notes:mi3e_02-011.jpg?200 }}
   * The net force acting on the fan cart is the sum of all the forces, $\vec{F}_{net} = \sum \vec{F}_i = \langle 0.45, 0, 0 \rangle N$.   * The net force acting on the fan cart is the sum of all the forces, $\vec{F}_{net} = \sum \vec{F}_i = \langle 0.45, 0, 0 \rangle N$.
- +  * The displacement of the fan cart in the $x$-direction can be written like this: $x_{f} - x_{i} = v_{xi} \Delta t + \dfrac{1}{2}\dfrac{F_{net,x}}{m} \Delta t^2$
  
 ==== Solution ==== ==== Solution ====
 +
 +The displacement of the cart is given by,
 +
 +$\Delta x_{cart} = x_{cart,f} - x_{cart,i} = v_{cart,xi} \Delta t + \dfrac{1}{2}\dfrac{F_{net,x}}{m_{cart}} \Delta t^2$
 +
 +We can compute this displacement,
 +
 +$$\Delta x_{cart} = (0 \dfrac{m}{s}) (2.2 s) + \dfrac{1}{2}\dfrac{0.45 N}{0.3kg}(2.2s)^2 = 3.6 m$$
 +
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  • Last modified: 2014/07/11 02:56
  • by caballero