Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 1 Work Chapter 5 Definition of Work Work is done on an object when a force causes a displacement of the object. Work is done only when components of a force are parallel to a displacement.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 5 Definition of Work Section 1 Work

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 5 Sign Conventions for Work Section 1 Work

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Kinetic Energy The energy of an object that is due to the object’s motion is called kinetic energy. Kinetic energy depends on speed and mass.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 5 Kinetic Energy Section 2 Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Kinetic Energy, continued Work-Kinetic Energy Theorem –The net work done by all the forces acting on an object is equal to the change in the object’s kinetic energy. The net work done on a body equals its change in kinetic energy. W net = ∆KE net work = change in kinetic energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 5 Work-Kinetic Energy Theorem Section 2 Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Sample Problem Work-Kinetic Energy Theorem On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Sample Problem, continued Work-Kinetic Energy Theorem 1. Define Given: m = 10.0 kg v i = 2.2 m/s v f = 0 m/s µ k = 0.10 Unknown: d = ?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Sample Problem, continued Work-Kinetic Energy Theorem 2. Plan Choose an equation or situation: This problem can be solved using the definition of work and the work-kinetic energy theorem. W net = F net dcos  The net work done on the sled is provided by the force of kinetic friction. W net = F k dcos  = µ k mgdcos 

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Sample Problem, continued Work-Kinetic Energy Theorem 2. Plan, continued The force of kinetic friction is in the direction opposite d,  = 180°. Because the sled comes to rest, the final kinetic energy is zero. W net = ∆KE = KE f - KE i = –(1/2)mv i 2 Use the work-kinetic energy theorem, and solve for d.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Sample Problem, continued Work-Kinetic Energy Theorem 3. Calculate Substitute values into the equation:

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Sample Problem, continued Work-Kinetic Energy Theorem 4. Evaluate According to Newton’s second law, the acceleration of the sled is about -1 m/s 2 and the time it takes the sled to stop is about 2 s. Thus, the distance the sled traveled in the given amount of time should be less than the distance it would have traveled in the absence of friction. 2.5 m < (2.2 m/s)(2 s) = 4.4 m

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Energy Chapter 5 Potential Energy Potential Energy is the energy associated with an object because of the position, shape, or condition of the object. Gravitational potential energy is the potential energy stored in the gravitational fields of interacting bodies. Gravitational potential energy depends on height from a zero level. PE g = mgh gravitational PE = mass  free-fall acceleration  height

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 5 Potential Energy Section 2 Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 3 Conservation of Energy Chapter 5 Conserved Quantities When we say that something is conserved, we mean that it remains constant.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu 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. ME i = ME f initial mechanical energy = final mechanical energy (in the absence of friction)

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 5 Conservation of Mechanical Energy Section 3 Conservation of Energy

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu 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.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 3 Conservation of Energy Chapter 5 Sample Problem, continued Conservation of Mechanical Energy 1. Define Given: h = h i = 3.00 m m = 25.0 kg v i = 0.0 m/s h f = 0 m Unknown: v f = ?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu 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.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu 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. PE g,f = 0

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu 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 PE g,i = mgh i = mgh Because the child starts at rest, the initial kinetic energy at the top is zero. KE i = 0 Therefore, the final kinetic energy is as follows:

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 3 Conservation of Energy Chapter 5 Conservation of Mechanical Energy 3. Calculate Substitute values into the equations: PE g,i = (25.0 kg)(9.81 m/s 2 )(3.00 m) = 736 J KE f = (1/2)(25.0 kg)v f 2 Now use the calculated quantities to evaluate the final velocity. ME i = ME f PE i + KE i = PE f + KE f 736 J + 0 J = 0 J + (0.500)(25.0 kg)v f 2 v f = 7.67 m/s Sample Problem, continued

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu 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.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu 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.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 4 Power Chapter 5 Rate of Energy Transfer Power is a quantity that measures the rate at which work is done or energy is transformed. P = W/∆t power = work ÷ time interval An alternate equation for power in terms of force and speed is P = Fv power = force  speed