Section 3 Conservation of Energy Chapter 5 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.

Chapter 5 Conserved Quantities Section 3 Conservation of Energy Chapter 5 Conserved Quantities When we say that something is conserved, we mean that it remains constant.

Chapter 5 Mechanical Energy Section 3 Conservation of Energy Chapter 5 Mechanical Energy Mechanical energy is the sum of kinetic energy and all forms of potential energy associated with an object or group of objects. ME = KE + PE Mechanical energy is often conserved. MEi = MEf initial mechanical energy = final mechanical energy (in the absence of friction)

Chapter 5 Mechanical Energy Section 3 Conservation of Energy Chapter 5 Mechanical Energy Mechanical Energy is not conserved in the presence of friction.

Conservation of Mechanical Energy Section 3 Conservation of Energy Chapter 5 Conservation of Mechanical Energy

Chapter 5 Sample Problem Conservation of Mechanical Energy Section 3 Conservation of Energy Chapter 5 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, continued Section 3 Conservation of Energy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 1. Define Given: h = hi = 3.00 m m = 25.0 kg vi = 0.0 m/s hf = 0 m Unknown: vf = ?

Sample Problem, continued Section 3 Conservation of Energy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 2. Plan Choose an equation or situation: The slide is frictionless, so mechanical energy is conserved. Kinetic energy and gravitational potential energy are the only forms of energy present.

Sample Problem, continued Section 3 Conservation of Energy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 2. Plan, continued The zero level chosen for gravitational potential energy is the bottom of the slide. Because the child ends at the zero level, the final gravitational potential energy is zero. PEg,f = 0

Sample Problem, continued Section 3 Conservation of Energy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 2. Plan, continued The initial gravitational potential energy at the top of the slide is PEg,i = mghi = mgh Because the child starts at rest, the initial kinetic energy at the top is zero. KEi = 0 Therefore, the final kinetic energy is as follows:

Sample Problem, continued Section 3 Conservation of Energy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 3. Calculate Substitute values into the equations: PEg,i = (25.0 kg)(9.81 m/s2)(3.00 m) = 736 J KEf = (1/2)(25.0 kg)vf2 Now use the calculated quantities to evaluate the final velocity. MEi = MEf PEi + KEi = PEf + KEf 736 J + 0 J = 0 J + (0.500)(25.0 kg)vf2 vf = 7.67 m/s

Sample Problem, continued Section 3 Conservation of Energy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 4. Evaluate The expression for the square of the final speed can be written as follows: Notice that the masses cancel, so the final speed does not depend on the mass of the child. This result makes sense because the acceleration of an object due to gravity does not depend on the mass of the object.

Mechanical Energy, continued Section 3 Conservation of Energy Chapter 5 Mechanical Energy, continued Mechanical Energy is not conserved in the presence of friction. As a sanding block slides on a piece of wood, energy (in the form of heat) is dissipated into the block and surface.