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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: | + | The fan cart in the video below is observed to [[183_notes: |
=== 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' | + | * Over the interval that we care about it, we will assume the net force doesn' |
* 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' |
{{ : | {{ : | ||
* 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, | |
==== 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, | ||
+ | |||
+ | We can compute this displacement, | ||
+ | |||
+ | $$\Delta x_{cart} = (0 \dfrac{m}{s}) (2.2 s) + \dfrac{1}{2}\dfrac{0.45 N}{0.3kg}(2.2s)^2 = 3.6 m$$ | ||
+ |