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Section 5–3: Conservation of Energy Physics Coach Kelsoe Pages 173–178 Objectives • Identify situations in which conservation of mechanical energy is valid. • Recognize the forms that conserved energy can take. • Solve problems using conservation of mechanical energy. Conserved Quantities • When we say that something is conserved, we mean that is remains constant. • Mass is an entity that is conserved. If a light bulb is dropped on the floor, no matter how it shatters, the total mass of the debris is the same as the intact bulb. • Energy is also an entity that is conserved. Mechanical Energy • The description of the motion of many objects involves a combination of kinetic and potential energy as well as different forms of potential energy. • The pendulum of a clock is a great example of kinetic and potential energy. At the top of its swing, the pendulum has only PEg, but at the very bottom has only KE. Mechanical Energy • Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects. • Don’t let the term “mechanical energy” confuse you. It is simply energy that is not nuclear, chemical, internal, or electrical. • Nuclear, chemical, internal, and electrical energy is called nonmechanical energy. Mechanical Energy • The total amount of mechanical energy can be found from – ME = KE + ΣPE • Mechanical energy is often conserved (in the absence of friction). – MEi = MEf – ½mvi2 + mghi = ½mvf2 + mghf Sample Problem • Conservation of Mechanical Energy Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg. Sample Problem Solution • 1. Identify givens and unknowns: – h = hi = 3.00 m – m = 25.0 kg – vi = 0.0 m/s – hf = 0 m – vf = ? Sample Problem Solution • 2. Choose the correct equation. – Since the slide is considered frictionless, mechanical energy is conserved. KE and PEg are the only forms of energy present. – KE = ½mv2 – PEg = mgh – The zero level chosen for our situation is the bottom of the slide. Because the child ends at the zero level, the final PEg = 0. Sample Problem Solution • 2. Choose the correct equation – The initial PEg at the top of the slide = mgh. – Because the child starts at rest, the initial KE at the top is zero. – Therefore the final kinetic energy is • ½mvi2 + mghi = ½mvf2 + mghf OR • mghi = ½mvf2 • ghi = ½vf2 Sample Problem Solution • 3. Calculate – ghi = ½vf2 – (9.81 m/s2)(3.00 m) = ½vf2 – vf2 = (2)(9.81 m/s2)(3.00 m) – vf = √58.86 m2/s2 – vf =7.67 m/s In the Presence of Friction • Mechanical energy is not conserved in the presence of friction. • For example, as a sanding block slides across a piece of wood, energy (in the form of heat) is dissipated into the block and surface. • Energy is ALWAYS conserved, but it isn’t always conserved in its current form. Vocabulary • Mechanical energy