Material Recycling No longer your problem Christopher White

Material Recycling No longer your problem! Christopher White, Jeffry Jimenez, Kwok. Ching 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 Develop potential improvements

Visualization Materials h 1 Distance for materials to reach terminal velocity Wind stream h 2 Cardboard Paper

Assumptions Force due to gravity : -9. 8 m/s^2 Density of Air 3: = 1. 225 kg/m^3 Mass of Objects 4 : Standard A 4 Paper = 0. 0045 kg Cardboard = 0. 12190295 kg Cross-Sectional Area: Standard A 4 Paper = 0. 06 m^2 Cardboard = 0. 13935456 m^2 Drag Coefficient 5: Standard A 4 Paper = 1. 98 Cardboard = 1. 28

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.

Model Creation 4

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.

Terminal Velocity 5 Terminal Velocity for Paper Terminal Velocity for Cardboard

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.

Additional Problem. . . Since the velocity will be constant by the time the material reaches the stream (h 1), a small change of height would not affect our sorting quality as the distribution will continue to be uniform and thus 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.

References Executive Summary: 1. http: //www. softschools. com/formulas/physics/air_resistance_formula/85/ 2. http: //ansuz. sooke. bc. ca/entry/12 Presentation: 1. https: //en. wikipedia. org/wiki/Density_of_air 2. https: //en. wikipedia. org/wiki/Corrugated_fiberboard 3. https: //en. wikipedia. org/wiki/Drag_coefficient 4. http: //farside. ph. utexas. edu/teaching/336 k/Newtonhtml/node 29. html 5. https: //www. maplesoft. com/support/help/maple/view. aspx? path=DEtools/DEplot