SOLVE

Learning Goal: To practice Problem-Solving Strategy 10.1 Conservation of energy problems. An ice cube of mass m can slide without friction up and down a 25.0 slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring x. The spring constant is . When the ice cube is released, how far will it travel up the slope before reversing direction? PROBLEM-SOLVING STRATEGY 10.1 Conservation of energy problems The work-energy equation and the law of conservation of energy relate a system's final energy to its initial energy. We can solve for initial and final heights, speeds, and displacements from these energies. PREPARE Draw a before-and-after visual overview, as was outlined in Tactics Box 9.1. Note the known quantities, and identify what you're trying to find. SOLVE Apply the before-and-after version of the work-energy equation, Equation 10.18: Ki + Ug)t + Us) + AEn = Ki + (Ug) + (Us) + W There are three common situations: If work is done on the system, then use the full version of Equation 10.18. If the system is isolated, no work is done. Use Equation 10.18 with W = 0 (the law of conservation of energy, Equation 10.18a): Ke + (Ug) + (Us) + An = Ki + (Ug)i + Us)i If the system is isolated and there's no friction, the mechanical energy is conserved. Use Equation 10.18 with both W = 0 and AF, = 0 thatis, Equation 10.19: Kr + (Ug)e + (Us)e = Ki + (Ug) + Us)i Depending on the problem, you'll need to calculate the initial and/or final values of these energies. You can then solve for the unknown energies, and from these, you can solve for any unknown speeds (from J), heights and distances (from U, and Us), or displacements or friction forces (from AFin = fx Az). ASSESS Check the signs of your energies. Kinetic energy is always positive, as is the change in thermal energy. Check that your result has the correct units, is reasonable, and answers the question. PREPARE You should choose what to include in your system. Then, identify your known and unknown quantities and draw a visual overview. Lastly, identify which mechanical energies are changing. vy PartA Choose which items to include in your system. All items that do not belong to your system are part of the environment. View Available Hint(s) System Environment