Chapter 11 Lecture physics FOR SCIENTISTS AND ENGINEERS

Chapter 11 Work Chapter Goal: To develop a more complete understanding of energy and

Chapter 11 Preview © 2013 Pearson Education, Inc. Slide 11 -3

Chapter 11 Preview © 2013 Pearson Education, Inc. Slide 11 -5

Chapter 11 Preview © 2013 Pearson Education, Inc. Slide 11 -6

Chapter 11 Preview © 2013 Pearson Education, Inc. Slide 11 -7

Chapter 11 Preview © 2013 Pearson Education, Inc. Slide 11 -8

Chapter 11 Reading Quiz © 2013 Pearson Education, Inc. Slide 11 -9

Reading Question 11. 1 The statement K = W is called the A. Law

Reading Question 11. 2 The transfer of energy to a system by the application

Reading Question 11. 3 A vector has magnitude C. Then the dot product of

Reading Question 11. 4 The work done by a dissipative force like friction, Wdiss,

Reading Question 11. 5 Light bulbs are typically rated in terms of their watts.

Chapter 11 Content, Examples, and Quick. Check Questions © 2013 Pearson Education, Inc. Slide

The Basic Energy Model W > 0: The environment does work on the system

The Basic Energy Model § The energy of a system is a sum of

Quick. Check 11. 1 A skier is gliding down a slope at a constant

Work and Kinetic Energy § The word “work” has a very specific meaning in

Work and Kinetic Energy § Consider a force acting on a particle which moves

The Work-Kinetic Energy Theorem § The net force is the vector sum of all

An Analogy with the Impulse-Momentum Theorem § The impulse-momentum theorem is: § The work-kinetic

Quick. Check 11. 2 A tow rope pulls a skier up the slope at

Work Done by a Constant Force § A force acts with a constant strength

Example 11. 1 Pulling a Suitcase © 2013 Pearson Education, Inc. Slide 11 -32

Example 11. 1 Pulling a Suitcase © 2013 Pearson Education, Inc. Slide 11 -33

Quick. Check 11. 3 A crane lowers a girder into place at constant speed.

Tactics: Calculating the Work Done by a Constant Force © 2013 Pearson Education, Inc.

Quick. Check 11. 4 Robert pushes the box to the left at constant speed.

Quick. Check 11. 5 A constant force pushes a particle through a displacement. In

Example 11. 2 Work During a Rocket Launch © 2013 Pearson Education, Inc. Slide

Quick. Check 11. 6 Which force below does the most work? All three displacements

Quick. Check 11. 7 A light plastic cart and a heavy steel cart are

Force Perpendicular to the Direction of Motion § The figure shows a particle moving

Quick. Check 11. 8 A car on a level road turns a quarter circle

The Dot Product of Two Vectors § The figure shows two vectors, and ,

The Dot Product of Two Vectors § The dot product © 2013 Pearson Education,

Example 11. 3 Calculating a Dot Product © 2013 Pearson Education, Inc. Slide 11

The Dot Product Using Components If and , the dot product is the sum

Example 11. 4 Calculating a Dot Product Using Components © 2013 Pearson Education, Inc.

Example 11. 5 Calculating Work Using the Dot Product © 2013 Pearson Education, Inc.

The Work Done by a Variable Force To calculate the work done on an

Example 11. 6 Using Work to Find the Speed of a Car © 2013

Conservative Forces § The figure shows a particle that can move from A to

Nonconservative Forces § The figure is a bird’s-eye view of two particles sliding across

Mechanical Energy § Consider a system of objects interacting via both conservative forces and

Example 11. 8 Using Work and Potential Energy © 2013 Pearson Education, Inc. Slide

Finding Force from Potential Energy § The figure shows an object moving through a

Finding Force from Potential Energy § In the limit s 0, we find that

Finding Force from Potential Energy § Figure (a) shows the potential-energy diagram for an

Finding Force from Potential Energy § Figure (a) is a more general potential energy

Quick. Check 11. 9 A particle moves along the x -axis with the potential

Thermal Energy § Figure (a) shows a mass M moving with velocity with macroscopic

Dissipative Forces As two objects slide against each other, atomic interactions at the boundary

Dissipative Forces § The figure shows a box being pulled at a constant speed

Example 11. 9 Calculating the Increase in Thermal Energy © 2013 Pearson Education, Inc.

Conservation of Energy For a system with both internal interaction forces and external forces,

Conservation of Energy © 2013 Pearson Education, Inc. Slide 11 -84

The Basic Energy Model For a system with both internal interaction forces and external

The Basic Energy Model When a system is isolated, Esys, the total energy of

Energy Bar Charts We may express the conservation of energy concept as an energy

Quick. Check 11. 10 How much work is done by the environment in the

Problem-Solving Strategy: Solving Energy Problems © 2013 Pearson Education, Inc. Slide 11 -90

Problem-Solving Strategy: Solving Energy Problems © 2013 Pearson Education, Inc. Slide 11 -91

Example 11. 10 Energy Bar Chart I © 2013 Pearson Education, Inc. Slide 11

Example 11. 11 Energy Bar Chart Il © 2013 Pearson Education, Inc. Slide 11

Example 11. 12 Energy Bar Chart Ill © 2013 Pearson Education, Inc. Slide 11

Power § The rate at which energy is transferred or transformed is called the

Example 11. 13 Choosing a Motor © 2013 Pearson Education, Inc. Slide 11 -99

Example 11. 13 Choosing a Motor © 2013 Pearson Education, Inc. Slide 11 -100

Examples of Power © 2013 Pearson Education, Inc. Slide 11 -101

Power § When energy is transferred by a force doing work, power is the

Quick. Check 11. 11 Four students run up the stairs in the time shown.

Example 11. 14 Power Output of a Motor © 2013 Pearson Education, Inc. Slide

Chapter 11 Summary Slides © 2013 Pearson Education, Inc. Slide 11 -107

General Principles © 2013 Pearson Education, Inc. Slide 11 -108

General Principles © 2013 Pearson Education, Inc. Slide 11 -109

General Principles © 2013 Pearson Education, Inc. Slide 11 -110

Important Concepts © 2013 Pearson Education, Inc. Slide 11 -111

Important Concepts © 2013 Pearson Education, Inc. Slide 11 -112

Important Concepts © 2013 Pearson Education, Inc. Slide 11 -113

Important Concepts © 2013 Pearson Education, Inc. Slide 11 -114

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Reading Question 11. 1 The statement K = W is called the A. Law of conservation of energy. B. Work-kinetic energy theorem. C. Kinetic energy equation. D. Weight-kinetic energy theorem. © 2013 Pearson Education, Inc. Slide 11 -10

Reading Question 11. 2 The transfer of energy to a system by the application of a force is called A. Dot product. B. Power. C. Work. D. Watt. E. Energy transformations. © 2013 Pearson Education, Inc. Slide 11 -12

Reading Question 11. 5 Light bulbs are typically rated in terms of their watts. The watt W is a measure of A. The change in the bulb’s potential energy. B. The energy consumed. C. The force exerted on the bulb holder. D. The power dissipated. © 2013 Pearson Education, Inc. Slide 11 -18

The Basic Energy Model W > 0: The environment does work on the system and the system’s energy increases. W < 0: The system does work on the environment and the system’s energy decreases. © 2013 Pearson Education, Inc. Slide 11 -21

The Basic Energy Model § The energy of a system is a sum of its kinetic energy K, its potential energy U, and its thermal energy Eth. § The change in system energy is: 1. Energy can be transferred to or from a system by doing work W on the system. This process changes the energy of the system: � Esys = W. 2. Energy can be transformed within the system among K, U, and Eth. These processes don’t change the energy of the system: � Esys = 0. © 2013 Pearson Education, Inc. Slide 11 -22

Quick. Check 11. 1 A skier is gliding down a slope at a constant speed. What energy transformation is taking place? A. K Ug B. Ug K C. Eth K D. Ug Eth E. K Eth © 2013 Pearson Education, Inc. Slide 11 -23

Work and Kinetic Energy § The word “work” has a very specific meaning in physics. § Work is energy transferred to or from a body or system by the application of force. § This pitcher is increasing the ball’s kinetic energy by doing work on it. © 2013 Pearson Education, Inc. Slide 11 -25

Work and Kinetic Energy § Consider a force acting on a particle which moves along the s-axis. § The force component Fs causes the particle to speed up or slow down, transferring energy to or from the particle. § The force does work on the particle: § The units of work are N m, where 1 N m = 1 kg m 2/s 2 = 1 J. © 2013 Pearson Education, Inc. Slide 11 -26

The Work-Kinetic Energy Theorem § The net force is the vector sum of all the forces acting on a particle. § The net work is the sum Wnet = Wi, where Wi is the work done by each force. § The net work done on a particle causes the particle’s kinetic energy to change. © 2013 Pearson Education, Inc. Slide 11 -27

An Analogy with the Impulse-Momentum Theorem § The impulse-momentum theorem is: § The work-kinetic energy theorem is: § Impulse and work are both the area under a force graph, but it’s very important to know what the horizontal axis is! © 2013 Pearson Education, Inc. Slide 11 -28

Quick. Check 11. 2 A tow rope pulls a skier up the slope at constant speed. What energy transfer (or transfers) is taking place? A. W Ug B. W K C. W Eth D. Both A and B. E. Both A and C. © 2013 Pearson Education, Inc. Slide 11 -29

Work Done by a Constant Force § A force acts with a constant strength and in a constant direction as a particle moves along a straight line through a displacement. § The work done by this force is: § Here is the angle © 2013 Pearson Education, Inc. makes relative to . Slide 11 -31

Quick. Check 11. 3 A crane lowers a girder into place at constant speed. Consider the work Wg done by gravity and the work WT done by the tension in the cable. Which is true? A. B. Wg > 0 and WT > 0 Wg > 0 and WT < 0 C. Wg < 0 and WT > 0 D. Wg < 0 and WT < 0 E. Wg = 0 and WT = 0 © 2013 Pearson Education, Inc. Slide 11 -34

Quick. Check 11. 3 A crane lowers a girder into place at constant speed. Consider the work Wg done by gravity and the work WT done by the tension in the cable. Which is true? A. Wg > 0 and WT > 0 B. Wg > 0 and WT < 0 C. Wg < 0 and WT > 0 D. Wg < 0 and WT < 0 E. Wg = 0 and WT = 0 © 2013 Pearson Education, Inc. The downward force of gravity is in the direction of motion positive work. The upward tension is in the direction opposite the motion negative work. Slide 11 -35

Quick. Check 11. 4 Robert pushes the box to the left at constant speed. In doing so, Robert does ______ work on the box. A. positive B. negative C. zero Force is in the direction of displacement positive work © 2013 Pearson Education, Inc. Slide 11 -40

Quick. Check 11. 5 A constant force pushes a particle through a displacement. In which of these three cases does the force do negative work? D. Both A and B. E. Both A and C. © 2013 Pearson Education, Inc. Slide 11 -41

Quick. Check 11. 6 Which force below does the most work? All three displacements are the same. A. B. C. D. The 10 N force. The 8 N force The 6 N force. They all do the same work. © 2013 Pearson Education, Inc. sin 60 = 0. 87 cos 60 = 0. 50 Slide 11 -47

Quick. Check 11. 6 Which force below does the most work? All three displacements are the same. A. The 10 N force. B. The 8 N force C. The 6 N force. D. They all do the same work. © 2013 Pearson Education, Inc. sin 60 = 0. 87 cos 60 = 0. 50 Slide 11 -48

Quick. Check 11. 7 A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1. 0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ____ that of the heavy steel cart. A. B. C. D. greater than equal to less than Can’t say. It depends on how big the force is. © 2013 Pearson Education, Inc. Slide 11 -49

Quick. Check 11. 7 A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1. 0 m, starting from rest. After the force is removed, the kinetic energy of the light plastic cart is ____ that of the heavy steel cart. A. B. C. D. greater than Same force, same distance same work done equal to Same work change of kinetic energy less than Can’t say. It depends on how big the force is. © 2013 Pearson Education, Inc. Slide 11 -50

Force Perpendicular to the Direction of Motion § The figure shows a particle moving in uniform circular motion. § At every point in the motion, Fs, the component of the force parallel to the instantaneous displacement, is zero. § The particle’s speed, and hence its kinetic energy, doesn’t change, so W = K = 0. § A force everywhere perpendicular to the motion does no work. © 2013 Pearson Education, Inc. Slide 11 -51

Quick. Check 11. 8 A car on a level road turns a quarter circle ccw. You learned in Chapter 8 that static friction causes the centripetal acceleration. The work done by static friction is _____. A. positive B. negative C. zero © 2013 Pearson Education, Inc. Slide 11 -52

The Dot Product of Two Vectors § The figure shows two vectors, and , with angle between them. § The dot product of is defined as: and § The dot product is also called the scalar product, because the value is a scalar. © 2013 Pearson Education, Inc. Slide 11 -54

The Work Done by a Variable Force To calculate the work done on an object by a force that either changes in magnitude or direction as the object moves, we use the following: We must evaluate the integral either geometrically, by finding the area under the curve, or by actually doing the integration. © 2013 Pearson Education, Inc. Slide 11 -62

Conservative Forces § The figure shows a particle that can move from A to B along either path 1 or path 2 while a force is exerted on it. § If there is a potential energy associated with the force, this is a conservative force. § The work done by as the particle moves from A to B is independent of the path followed. © 2013 Pearson Education, Inc. Slide 11 -67

Nonconservative Forces § The figure is a bird’s-eye view of two particles sliding across a surface. § The friction does negative work: Wfric = kmg s. § The work done by friction depends on s, the distance traveled. § This is not independent of the path followed. § A force for which the work is not independent of the path is called a nonconservative force. © 2013 Pearson Education, Inc. Slide 11 -68

Mechanical Energy § Consider a system of objects interacting via both conservative forces and nonconservative forces. § The change in mechanical energy of the system is equal to the work done by the nonconservative forces: § Mechanical energy isn’t always conserved. § As the space shuttle lands, mechanical energy is being transformed into thermal energy. © 2013 Pearson Education, Inc. Slide 11 -69

Finding Force from Potential Energy § The figure shows an object moving through a small displacement s while being acted on by a conservative force. § The work done over this displacement is: § Because is a conservative force, the object’s potential energy changes by U = −W = −FsΔs over this displacement, so that: © 2013 Pearson Education, Inc. Slide 11 -73

Finding Force from Potential Energy § In the limit s 0, we find that the force at position s is: § The force on the object is the negative of the derivative of the potential energy with respect to position. © 2013 Pearson Education, Inc. Slide 11 -74

Finding Force from Potential Energy § Figure (a) shows the potential-energy diagram for an object at height y. § The force on the object is (FG)y = mg. § Figure (b) shows the corresponding F-versus-y graph. § At each point, the value of F is equal to the negative of the slope of the U-versus-y graph. © 2013 Pearson Education, Inc. Slide 11 -75

Finding Force from Potential Energy § Figure (a) is a more general potential energy diagram. § Figure (b) is the corresponding F-versus-x graph. § Where the slope of U is negative, the force is positive. § Where the slope of U is positive, the force is negative. § At the equilibrium points, the force is zero. © 2013 Pearson Education, Inc. Slide 11 -76

Quick. Check 11. 9 A particle moves along the x -axis with the potential energy shown. At x = 4 m, the x-component of the force on the particle is A. – 4 N. B. – 2 N. C. 0 N. D. 2 N. E. 4 N © 2013 Pearson Education, Inc. Slide 11 -77

Quick. Check 11. 9 A particle moves along the x -axis with the potential energy shown. At x = 4 m, the x-component of the force on the particle is A. – 4 N. B. – 2 N. C. 0 N. D. 2 N. E. 4 N. © 2013 Pearson Education, Inc. Slide 11 -78

Thermal Energy § Figure (a) shows a mass M moving with velocity with macroscopic kinetic energy Kmacro = ½ Mvobj 2. § Figure (b) is a microphysics view of the same object. § The total kinetic energy of all the atoms is Kmicro. § The total potential energy of all the atoms is Umicro. § The thermal energy of the system is: © 2013 Pearson Education, Inc. Slide 11 -79

Dissipative Forces As two objects slide against each other, atomic interactions at the boundary transform the kinetic energy Kmacro into thermal energy in both objects. K Eth Kinetic friction is a dissipative force. © 2013 Pearson Education, Inc. Slide 11 -80

Dissipative Forces § The figure shows a box being pulled at a constant speed across a horizontal surface with friction. § Both the surface and the box are getting warmer as it slides. § Dissipative forces always increase thermal energy; they never decrease it. © 2013 Pearson Education, Inc. Slide 11 -81

The Basic Energy Model For a system with both internal interaction forces and external forces, Esys, the total energy of the system, changes only if external forces transfer energy in or out of the system. © 2013 Pearson Education, Inc. Slide 11 -85

Energy Bar Charts We may express the conservation of energy concept as an energy equation. We may also represent this equation graphically with an energy bar chart. © 2013 Pearson Education, Inc. Slide 11 -87

Quick. Check 11. 10 How much work is done by the environment in the process represented by the energy bar chart? A. – 2 J B. – 1 J C. 0 J D. 1 J E. 2 J © 2013 Pearson Education, Inc. The system started with 5 J but ends with 4 J. 1 J must have been transferred from the system to the environment as work. Slide 11 -89

Power § The rate at which energy is transferred or transformed is called the power P. § The SI unit of power is the watt, which is defined as: Highly trained athletes have a tremendous power output. 1 watt = 1 W = 1 J/s § The English unit of power is the horsepower, hp. 1 hp = 746 W © 2013 Pearson Education, Inc. Slide 11 -98

Power § When energy is transferred by a force doing work, power is the rate of doing work: P = d. W/dt. § If the particle moves at velocity while acted on by force , the power delivered to the particle is: © 2013 Pearson Education, Inc. Slide 11 -102