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Material Recycling

Material Recycling. No longer your problem!. Christopher White, Jeffry Jimenez, KwokChing Hui. Objectives. To explore a model that would separate free falling recyclable materials Determine the constants within the model Understand the forces applied to the system

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Material Recycling

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  1. Material Recycling No longer your problem! Christopher White, Jeffry Jimenez, KwokChing Hui

  2. Objectives To explore a model that would separate free falling recyclable materials Determine the constants within the model Understand the forces applied to the system Develop potential improvements

  3. Visualization Materials Distance for materials to reach terminal velocity h1 Wind stream h2 Cardboard Paper

  4. Assumptions Force due to gravity : -9.8m/s^2 Density of Air3: = 1.225 kg/m^3 Mass of Objects4 : Standard A4 Paper = 0 .0045 kg Cardboard = 0.12190295 kg Cross-Sectional Area: Standard A4 Paper = 0.06 m^2 Cardboard = 0.13935456 m^2 Drag Coefficient5: Standard A4 Paper = 1.98 Cardboard = 1.28 Size of containers that the materials are being sorted into

  5. Assumptions continued The distribution between paper and cardboard being dropped is 50-50, uniformly distributed. Our model includes drag force. The displacement of the paper being pushed by the wind speed is 25 m. The wind speed used to separate the materials is constant.

  6. Model Creation 4

  7. Terminal Velocity and Minimum Height In order to find the minimum height that required for the object to have its terminal velocity, we use the following differential equation solution.

  8. Terminal Velocity 5 Terminal Velocity for Paper Terminal Velocity for Cardboard

  9. Finding the Minimum Height including Wind speed The previous equation just helped us determine the height before the material reaches the wind stream, however, our total height has two different components. The missing component can be found by looking at projectiles in motions.

  10. Additional Problem... Since the velocity will be constant by the time the material reaches the stream (h1), a small change of height would not affect our sorting quality as the distribution will continue to be uniform and thus the the sorting will remain pretty similar. If the speed of the wind stream changes, and all our other variables stay the same, our sorting quality would decline since the protected trajectory of the materials would be either too far for the heavier materials (cardboard) or too close for the lighter materials (paper). The container size for the materials being sorted could have also been altered to increase the accuracy of the model.

  11. References Executive Summary: • http://www.softschools.com/formulas/physics/air_resistance_formula/85/ • http://ansuz.sooke.bc.ca/entry/12 Presentation: • https://en.wikipedia.org/wiki/Density_of_air • https://en.wikipedia.org/wiki/Corrugated_fiberboard • https://en.wikipedia.org/wiki/Drag_coefficient • http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node29.html • https://www.maplesoft.com/support/help/maple/view.aspx?path=DEtools/DEplot

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