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| 183_notes:examples:finalloccf [2014/07/11 02:58] – [Example: Predicting the location of an object undergoing constant force motion] caballero | 183_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 ===== |
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| 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 0.45N. Determine the how far the has traveled after 2.2s 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 0.45N. Determine the how far the fan cart has traveled after 2.2s if the cart starts from rest. |
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| === Facts ==== | === Facts ==== |
| * 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. |
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| === Lacking === | === Lacking === |
| === Approximations & Assumptions === | === Approximations & Assumptions === |
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| * 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. |
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| * The displacement of the fan cart in the x-direction can be written like this: xf−xi=vxiΔt+12Fnet,xmΔt2 | * The displacement of the fan cart in the x-direction can be written like this: xf−xi=vxiΔt+12Fnet,xmΔt2 |
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| | ==== Solution ==== |
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| | The displacement of the cart is given by, |
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| | Δxcart=xcart,f−xcart,i=vcart,xiΔt+12Fnet,xmcartΔt2 |
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| | We can compute this displacement, |
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| | Δxcart=(0ms)(2.2s)+120.45N0.3kg(2.2s)2=3.6m
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| ==== Solution ==== | |