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 PE g, 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). –ME i = ME f –½ mv i 2 + mgh i = ½ mv f 2 + mgh f

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 = h i = 3.00 m –m = 25.0 kg –v i = 0.0 m/s –h f = 0 m –v f = ?

Sample Problem Solution 2. Choose the correct equation. –Since the slide is considered frictionless, mechanical energy is conserved. KE and PE g are the only forms of energy present. –KE = ½ mv 2 –PE g = mgh –The zero level chosen for our situation is the bottom of the slide. Because the child ends at the zero level, the final PE g = 0.

Sample Problem Solution 2. Choose the correct equation –The initial PE g 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 ½ mv i 2 + mgh i = ½ mv f 2 + mgh f OR mgh i = ½ mv f 2 gh i = ½ v f 2

Sample Problem Solution 3. Calculate –gh i = ½ v f 2 –(9.81 m/s 2 )(3.00 m) = ½ v f 2 –v f 2 = (2)(9.81 m/s 2 )(3.00 m) –v f = √58.86 m 2 /s 2 –v f =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