Part C: Mathematical Model for Conservation of Energy Learning Objectives: 1. Build , explain, and justify (with the sim) equations for total energy, and conservation of energy. 2. Draw scaled graphical models of energy for an object at a specific position using your energy equations. 3. Write equations for the energy of a system at a specific position using scaled graphical models. Activity: 1. Based on your observations of total energy at different times and positions, write an equation to show the relationship between the total energy at A and at C. Use the diagram in #7, page 4. Equation: 2. Use your observations about the relationship between total energy and the different forms of energy (KE, PE, The) to build a general equation for the total energy (Etot) in the system. Etot = Briefly explain your reasoning. 3. Write out the expanded total energy equations for the skater at positions A and C (in terms of KE, PE, and The). Then, combine your two equations to write one equation that shows the relationship between these forms of energy at two different positions (A & C). Position Expanded (KE, PE, The) equation for total energy at each position Expanded mathematical equation showing relationship between total energies at two positions. 5. Compare your new equation with your neighbors', come to consensus on the best equation, then have your teacher sign off on your equation. 6. Follow the example below to write an equation and sketch a graphical model of the energy in each situation