PHYSICS. Chapter 9 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 9 Lecture RANDALL D. KNIGHT

Chapter 9 Work and Kinetic Energy IN THIS CHAPTER, you will begin your study of how energy is transferred and transformed. Slide 9-2

Chapter 9 Preview Slide 9-3

Chapter 9 Preview Slide 9-4

Chapter 9 Preview Slide 9-5

Chapter 9 Preview Slide 9-6

Chapter 9 Preview Slide 9-7

Chapter 9 Preview Slide 9-8

Chapter 9 Reading Questions Slide 9-9

Reading Question 9.1 The statement ΔK sys = W ext is called the A. Law of conservation of energy. B. Energy principle. C. Kinetic energy equation. D. Weight kinetic energy principle. Slide 9-10

Reading Question 9.1 The statement ΔK sys = W ext is called the A. Law of conservation of energy. B. Energy principle. C. Kinetic energy equation. D. Weight kinetic energy principle. Slide 9-11

Reading Question 9.2 Kinetic energy is A. Mass times velocity. B. ½ mass times speed-squared. C. The area under the force curve in a forceversus-time graph. D. Velocity per unit mass. Slide 9-12

Reading Question 9.2 Kinetic energy is A. Mass times velocity. B. ½ Mass times speed-squared. C. The area under the force curve in a forceversus-time graph. D. Velocity per unit mass. Slide 9-13

Reading Question 9.3 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. Slide 9-14

Reading Question 9.3 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. Slide 9-15

Reading Question 9.4 A vector has magnitude C. Then the dot product of the vector with itself, is A. 0 B. C/2 C. C D. 2C E. C 2 Slide 9-16

Reading Question 9.4 A vector has magnitude C. Then the dot product of the vector with itself, is A. 0 B. C/2 C. C D. 2C E. C 2 Slide 9-17

Reading Question 9.5 Hooke s law describes the force of A. Gravity. B. A spring. C. Collisions. D. Tension. E. None of the above. Slide 9-18

Reading Question 9.5 Hooke s law describes the force of A. Gravity. B. A spring. C. Collisions. D. Tension. E. None of the above. Slide 9-19

Reading Question 9.6 The work done by a dissipative force like friction is A. Always zero. B. Always positive. C. Always negative. Slide 9-20

Reading Question 9.6 The work done by a dissipative force like friction is A. Always zero. B. Always positive. C. Always negative. Slide 9-21

Reading Question 9.7 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. Slide 9-22

Chapter 9 Content, Examples, and QuickCheck Questions Slide 9-24

Energy Overview Everyone has some sense of what energy means. Moving objects have energy. Energy is the ability to make things happen. Energy is associated with heat and with electricity. We re constantly told to conserve energy. Living organisms need energy. Engineers harness energy to do useful things. Some scientists consider the law of conservation of energy to be the most important of all the laws of nature. Slide 9-25

Kinetic Energy K Kinetic energy is the energy of motion. All moving objects have kinetic energy. The more massive an object or the faster it moves, the larger its kinetic energy. Slide 9-26

Potential Energy U Potential energy is stored energy associated with an object s position. The roller coaster s gravitational potential energy depends on its height above the ground. Slide 9-27

Thermal Energy E th Thermal energy is the sum of the microscopic kinetic and potential energies of all the atoms and bonds that make up the object. An object has more thermal energy when hot than when cold. Slide 9-28

The System and the Environment Within a system, energy can be transformed from one type to another. As long as the system is not interacting with the environment, the total energy of the system is unchanged. A process that transfers energy to or from a system by mechanical means is called work, with the symbol W. A process that transfers energy to or from a system by thermal means is called heat. Slide 9-29

Energy Transfer Example Putting a shot System:The shot Transfer: W K The athlete (the environment) does work pushing the shot to give it kinetic energy. Slide 9-30

Energy Transfer Example Pulling a slingshot System:The slingshot Transfer: W U The boy (the environment) does work by stretching the rubber band to give it potential energy. Slide 9-31

Energy Transformation Example A falling diver System:The diver and the earth Transfer: U K The diver is speeding up as gravitational potential energy is transformed into kinetic energy. Slide 9-32

Energy Transformation Example A speeding meteor System:The meteor and the air Transfer: K E th The meteor and the air get hot enough to glow as the meteor s kinetic energy is transformed into thermal energy. Slide 9-33

The Energy Principle Transformations of energy within a system move the energy around but don t change the total energy of the system. Change occurs only when there s a transfer of energy between the system and the environment. If we treat incoming energy as a positive transfer and outgoing energy as a negative transfer, and with work being the only energy-transfer process that we consider for now, we can write where the subscript on W refers to external work done by the environment. This is called the energy principle. Slide 9-34

The Basic Energy Model Slide 9-35

QuickCheck 9.1 A skier is gliding down a slope at a constant speed. What energy transformation is taking place? A. K U B. U K C. E th K D. U E th E. K E th Slide 9-36

QuickCheck 9.1 A skier is gliding down a slope at a constant speed. What energy transformation is taking place? A. K U B. U K C. E th K D. U E th E. K E th Slide 9-37

Work and Kinetic Energy for a Single Particle Consider one particle acted on by one constant force that acts parallel to the direction of motion, pushing or pulling on the particle as it undergoes a displacement s. We define the particle to be the system while the agent of the force is in the environment. The figure shows both an interaction diagram and a before-and-after representation. Slide 9-38

Work and Kinetic Energy for a Single Particle We can define a new quantity called the kinetic energy of the particle: K depends on the particle s mass and speed but not on its position. For the case in which a single constant force acts on a single particle, K changes in direct proportion to the distance traveled. The SI unit of K is given its own name, the joule: 1 joule = 1 J = 1 kg m 2 /s 2 Slide 9-39

QuickCheck 9.2 Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio v A /v B? A. 16 B. 4 C. 2 D. 1/4 E. 1/16 Slide 9-40

QuickCheck 9.2 Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio v A /v B? A. 16 B. 4 C. 2 D. 1/4 E. 1/16 Slide 9-41

Work and Kinetic Energy for a Single Particle The work done on a one-particle system causes the system s kinetic energy to change: For the case of a constant force parallel to the direction of motion (the s-axis), the work is an integral: The SI unit of W is the same as for K: the joule. Slide 9-42

Signs of Work Work can be either positive or negative. If the force causes the particle to speed up, then the work done by that force is positive. Negative work means that the force is causing the object to slow and lose energy. The sign of W is determined by the force direction and the displacement direction. Slide 9-43

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 θ is the angle makes relative to Slide 9-44

Example 9.2 Pulling a Suitcase Slide 9-45

Example 9.2 Pulling a Suitcase Slide 9-46

QuickCheck 9.3 A crane lowers a girder into place at constant speed. Consider the work W G done by gravity and the work W T done by the tension in the cable. Which is true? A. W G > 0 and W T > 0 B. W G > 0 and W T < 0 C. W G < 0 and W T > 0 D. W G < 0 and W T < 0 E. W G = 0 and W T = 0 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 9-48

Tactics: Calculating the Work Done by a Constant Force Slide 9-49

Tactics: Calculating the Work Done by a Constant Force Slide 9-50

Tactics: Calculating the Work Done by a Constant Force Slide 9-51

QuickCheck 9.4 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 Slide 9-52

QuickCheck 9.4 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 Slide 9-53

QuickCheck 9.5 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 Slide 9-54

QuickCheck 9.5 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 Slide 9-55

Example 9.3 Launching a Rocket Slide 9-56

Example 9.3 Launching a Rocket Slide 9-57

Example 9.3 Launching a Rocket Slide 9-58

Example 9.3 Launching a Rocket Slide 9-59

QuickCheck 9.6 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. sin60º = 0.87 cos60º = 0.50 Slide 9-60

QuickCheck 9.7 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. greater than B. equal to C. less than D. Can t say. It depends on how big the force is. Slide 9-62

QuickCheck 9.7 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. greater than Same force, same distance same work done B. equal to Same work change of kinetic energy C. less than D. Can t say. It depends on how big the force is. Slide 9-63

The Dot Product of Two Vectors The figure shows two vectors, and, with angle α between them. The dot product of and is defined as The dot product is also called the scalar product because the value is a scalar. Slide 9-64

The Dot Product of Two Vectors The dot product as α ranges from 0º to 180º. Slide 9-65

Example 9.4 Calculating a Dot Product Slide 9-66

The Dot Product Using Components If and, the dot product is the sum of the products of the components: Slide 9-67

Example 9.5 Calculating a Dot Product Using Components Slide 9-68

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 Slide 9-69

Example 9.6 Calculating Work Using the Dot Product Slide 9-70

Example 9.6 Calculating Work Using the Dot Product Slide 9-71

Example 9.6 Calculating Work Using the Dot Product Slide 9-72

Example 9.6 Calculating Work Using the Dot Product Slide 9-73

Zero-Work Situations The figure shows a particle moving in uniform circular motion. At every point in the motion, F s, 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 = ΔK = 0. A force everywhere perpendicular to the motion does no work. Slide 9-74

QuickCheck 9.8 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 Slide 9-75

Zero-Work Situations Consider the roller skater shown who straightens her arms and pushes off from a wall. By Newton s third law, the wall applies a force on her. Although the skater s center of mass is displaced, the palms of her hands where the force is exerted are not. The force acts, but the force doesn t push any physical thing through a displacement. Hence no work is done! Slide 9-77

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. Slide 9-78

Example 9.7 Using Work to Find the Speed of a Car Slide 9-79

Example 9.7 Using Work to Find the Speed of a Car Slide 9-80

Example 9.7 Using Work to Find the Speed of a Car Slide 9-81

Restoring Forces and Hooke s Law If you stretch a rubber band, a force tries to pull the rubber band back to its equilibrium, or unstretched, length. A force that restores a system to an equilibrium position is called a restoring force. If you stretch (or compress) an elastic object such as a spring, measurements show that The force provided by the spring is opposite the displacement. If you don t stretch or compress the spring too much, the force provided by the spring is proportional to the displacement from equilibrium. The relationship between the force and displacement of a spring was discovered by Robert Hooke, a contemporary of Newton. Slide 9-82

Hooke s Law One end of a spring is attached to a fixed wall. (F Sp ) s is the force produced by the free end of the spring. Δs = s s eq is the displacement from equilibrium. The minus sign is the mathematical indication of a restoring force. The constant k is called the spring constant of the spring. Slide 9-83

QuickCheck 9.9 The restoring force of three springs is measured as they are stretched. Which spring has the largest spring constant? Slide 9-84

QuickCheck 9.9 The restoring force of three springs is measured as they are stretched. Which spring has the largest spring constant? Steepest slope. Takes lots of force for a small displacement. Slide 9-85

Example 9.8 Pull Until It Slips Slide 9-86

Example 9.8 Pull Until It Slips Slide 9-87

Example 9.8 Pull Until It Slips Slide 9-88

Example 9.8 Pull Until It Slips Slide 9-89

Example 9.8 Pull Until It Slips Slide 9-90

Stick-Slip Motion Earthquakes are an example of stick-slip motion. Tectonic plates are attempting to slide past each other, but friction causes the edges of the plates to stick together. Large masses of rock are somewhat elastic and can be stretched. Eventually the elastic force of the deformed rocks exceeds the friction force between the plates. An earthquake occurs as the plates slip and lurch forward. The slip can range from a few centimeters in a relatively small earthquake to several meters in a very large earthquake. Slide 9-91

Work Done by Springs Shown is a spring acting on an object as it moves from s i to s f. The spring s work can be computed by integrating: The solution to this integral is Slide 9-92

Thermal Energy Figure (a) shows a mass M moving with velocity with macroscopic kinetic energy K macro = ½ Mv obj2. Figure (b) is a microphysics view of the same object. The total kinetic energy of all the atoms is K micro. The total potential energy of all the atoms is U micro. The thermal energy of the system is Slide 9-93

QuickCheck 9.10 A tow rope pulls a skier up the slope at constant speed. What energy transfer (or transfers) is taking place? A. W U B. W K C. W E th D. Both A and B E. Both A and C Slide 9-94

QuickCheck 9.10 A tow rope pulls a skier up the slope at constant speed. What energy transfer (or transfers) is taking place? A. W U B. W K C. W E th D. Both A and B E. Both A and C Slide 9-95

Dissipative Forces As two objects slide against each other, atomic interactions at the boundary transform the kinetic energy K macro into thermal energy in both objects: K E th Kinetic friction is a dissipative force. Slide 9-96

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 the thermal energy; they never decrease it. Slide 9-97

Example 9.10 Increasing Kinetic and Thermal Energy Slide 9-98

Example 9.10 Increasing Kinetic and Thermal Energy Slide 9-99

Example 9.10 Increasing Kinetic and Thermal Energy Slide 9-100

Power Work is a transfer of energy between the environment and a system. In many situations we would like to know how quickly the energy is transferred. 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 1 watt = 1 W = 1 J/s The English unit of power is the horsepower, hp: 1 hp = 746 W Slide 9-101

Examples of Power Slide 9-102

Power When energy is transferred by a force doing work, power is the rate of doing work: P = dw/dt. If the particle moves at velocity while acted on by force, the power delivered to the particle is Slide 9-103

QuickCheck 9.11 Four students run up the stairs in the time shown. Which student has the largest power output? A. B. C. D. Slide 9-104

QuickCheck 9.11 Four students run up the stairs in the time shown. Which student has the largest power output? A. B. C. D. Slide 9-105