ENERGY Chapter 3 1 When you have completed

ENERGY Chapter 3 1

When you have completed this chapter you should be able to: n n n n Explain what is meant by work. Explain what is meant by power. Distinguish between kinetic energy and potential energy. Give several examples of potential energy. State the law of conservation of energy and give several examples of energy transformations. Use the principle of conservation of energy to analyze events in which work and different forms of energy are transformed into one another. Discuss why heat is today regarded as a form of energy rather than as an actual substance. Define linear momentum and discuss its significance. Use the principle of conservation of linear momentum to analyze the motion of objects that collide with each other or push each other apart, for instance, when a rocket is fired. State what is meant by angular momentum. Explain how conservation of angular momentum is used by skaters to spin faster and by footballs to travel farther. Describe several relativistic effects and indicate why they are not conspicuous in the everyday world. Explain what is meant by rest energy and be able to calculate the rest energy of an object of given mass. Describe how gravity is interpreted in Einstein's general theory of relativity. 2 Discuss the various factors that are part of the energy problems of the future.

Main Concepts in Ch 3 n Work n Power n Energy n Momentum n Relativity 3

Energy n In general, energy refers to an ability to accomplish change n “Change” is not a very precise notion n We will start with the simpler concept of “Work” and use it to relate change and energy in the orderly way of science 4

Work n Changes that take place in the physical world are the result of forces n However, not all forces act to produce changes n It is the distinction between forces that accomplish change and forces that do not that is central to the idea of work 5

Work n Work done by a force acting on an object is equal to the magnitude of the force multiplied by the distance through which the force acts n. W=Fxd W = work F = applied force d = distance through which the force acts 6

Was Change Accomplished? Figure 3 -1 tam 3 s 6_1 7

Work n The SI unit of work is the joule (J) n 1 joule is the amount of work done by a force of one Newton when it acts through a distance of one meter n 1 joule (J) = 1 newton-meter (N. m) n Joule is named after the English scientist James Joule 8

Work n The direction of the force F is assumed to be the same as the direction of displacement d n If not, we use the magnitude Fd of the projection of the applied force that act in the direction of motion n A force that is perpendicular to the direction of motion of an object can do NO WORK on the object n n Gravity does no work on objects moving horizontally along the Earth’s surface However, when we drop an object, work is done on it as it falls to the ground 9

Force and distance are parallel Force and distance are not parallel Tam 3 s 6_2 Figure 3 -3 10

Work Done Against Gravity n Work done in lifting an object against gravity can be calculated using: n W = mgh where n n mg = force of gravity on the object is its weight h = height raised above its original position 11

Example 3. 1 n Calculate work done when (a) horizontal force of 100 N is used to push a 20 -kg box across a level floor for 10 m and (b) when raising the same box over your head by 10 m n. W=Fxd= n (100 N) x (10 m) = 1000 J n W = mgh = n (20 kg)(9. 8 m/s 2)(10 m) = 1960 J 12

Power n The rate at which work is being done n The more powerful, the faster something can do work n P = W/t P = power n W = Work n t = time n The SI unit of power is the watt (W) n 1 watt (W) = 1 joule/second (J/s) n 1 k. W = 1000 W n 1 hp = 746 W (hp = horsepower) n 13

Example 3. 2 n A 15 -k. W electric motor provides power for the elevator of a building. What is the minimum time needed for the elevator to rise 30 m to the sixth floor when its total mass loaded is 900 kg? 14

Energy n Is the property something has that enables it to do work n When we say that something has energy, it means that it is able, directly or indirectly, to exert a force on something else and perform work n When work is done on something, energy is added to it n The SI unit of energy is also the joule (J) 15

Kinetic Energy · The energy of a moving object. · Kinetic energy of moving things depend upon its mass and speed, such that n KE = ½ mv 2 n The v 2 factor means the KE increases very rapidly with increasing speed 16

Kinetic Energy Example 3. 3 The kinetic energy of a 1000 -kg car when its speed is 10 m/s is what? The kinetic energy of a 1000 -kg car when its speed is 30 m/s is what? Figure 3 -7 Tam 3 s 6_3 17

Potential Energy · The energy of position · The amount of work something could do A raised stone has PE because it can do work on the ground when dropped. Figure 3 -9 18

Kinetic and Potential Energy 19

Potential Energy Examples tam 3 s 6_6 Figure 3 -10 20

Gravitational Potential Energy · When an object with mass m is raised a certain height h above its original position, its gravitational PE is equal to the work that was done against gravity to bring it to that height n PE = mgh § m = mass § h = height § g = gravity 21

The increase in PE of a raised object is equal to the work used to lift it Tam 3 s 6_7 Figure 3 -11 22

Energy Transformations n Nearly all familiar mechanical processes involve interchanges among KE, PE, and work n Kinetic energy can be changed to potential energy and vice versa 23

Energy Transformations KE is low PE is high KE is high PE is low Figure 3 -13 Tam 3 s 6_8 24

Total Energy is constant; Angular momentum is constant Angular Momentum is constant for all points along orbit Velocity at Aphelion VA Minimum KE Maximum PE RA Total Energy KE + PE Is also Constant At Aphelion Angular Momentum Is VA x RA Which is also equal to Sun RP Maximum KE Minimum PE VP x RP Velocity at Perihelion VP 25

Energy Transformations in Pendulum Motion Figure 3 -15 Tam 3 s 6_10 26

Other Forms of Energy n Chemical energy n gasoline is used to propel a car and the chemical energy of food enables us to perform work n Heat energy n burning coal or oil is used to form the steam that drives the turbines of power stations n Radiant energy n the sun performs work in causing water from the earth’s surface to rise and form clouds 27

The Law of the Conservation of Energy n Energy cannot be created or destroyed, although it can be changed from one form to another n Kinetic, potential, chemical, heat, and radiant energy can all be changed between one another 28

The Nature of Heat n What is Heat? n Heat is a form of energy n The heat content of a body of matter consists of the KE of random motion of the atoms and molecules of which the body consists Vibrating molecules in a solid 29

The Nature of Heat n Less than 2 centuries ago, heat was thought of as a substance called caloric n Count Rumford (a. k. a. Benjamin Thompson) regarded heat as energy, not as a substance n Heat as a substance could not account for the unlimited heat generated by friction 30

The Nature of Heat n James Prescott Joule (1818 -1889) performed a classic experiment that proved heat was energy and not a substance n The SI unit of energy, the Joule, was subsequently named after James Prescott Joule 31

Joule’s experimental demonstration that heat is a form of energy. Tam 3 s 6_11 Figure 3 -20 32

Momentum n Momenta can give us further insights into the behavior of moving objects n Linear and angular momenta are vector quantities and will be described subsequently 33

Linear Momentum n Linear momentum (p) – Moving objects tend to continue to move at constant speed along a straight path n The linear momentum (or momentum) of such an object is a measure of this tendency n p = mv where m = mass n v = velocity n n The greater m and v are, the harder it is to change the object’s speed or direction 34

Linear Momentum of a Moving Object Observe what happens to various variables (p, m, v) when one is changed What happens to p when m is changed? What happens to p when v is changed? Tam 3 s 6_12 Figure 3 -21 35

Law of Conservation of Momentum n In the absence of outside forces, the total momentum of a set of objects remains the same no matter how the objects interact with one another n Momentum considerations are useful when explosions and collisions are involved n Rocket propulsion 36

Law of Conservation of Momentum tam 3 s 6_13 Figure 3 -22 37

Angular Momentum n The rotational quantity that corresponds to linear momentum is called angular momentum n The conservation of angular momentum is the formal way to describe the tendency of a spinning body to continue to spin n Spinning earth n Precise definition is complicated because it depends not only on: n mass and velocity but n how the mass is arranged in the body 38

Angular Momentum The farther away from the axis of rotation the mass is distributed, the more angular momentum Also demonstrates conservation of angular momentum. Tam 3 s 6_17 Figure 3 -17 39

Another Example of Angular Momentum n Kepler’s second law of planetary motion is similar to the changing spin rate of a skater in the previous slide n A planet moving around the sun has angular momentum, which must be the same everywhere in its orbit n As a result, the planet’s speed is greatest when it is close to the sun, least when it is far away n http: //hyperphysics. phy-astr. gsu. edu/HBASE/mechanics/indexv. html 40

Table 3 -1 Energy, Power, and Momentum 41

Einstein 42

Einstein’s Relativity n Albert Einstein (1879 -1955) published three papers in 1905. n Proposed light has a dual character (chapter 8) n Brownian motion n Theory of Special Relativity (1905) revolutionized science. n Relativity links not only time and space but also energy and matter n From this paper came many remarkable predictions, all of which have been confirmed by experiment 43

Einstein’s Relativity n Eleven years later, Einstein took relativity a step further by interpreting gravity as a distortion in the structure of space and time known as the Theory of General Relativity 44

Special Relativity n Einstein’s 1905 theory, which led to the two postulates is called special relativity because it is restricted to constant velocities 45

Special Relativity n First Postulate states the laws of physics are the same in all frames of reference moving at constant velocity with respect to one another n Two observers in motion relative to each other n Each will disagree on what they observe n Each viewpoint is equally valid 46

Windowless Airplane n This introduces the first postulate. There is no experiment you can perform to determine if you are standing still or moving in a straight line at a constant speed. 47

Bottom Line n All uniform motion is relative. That is, you can not determine if you are standing “still” or moving in a straight line at a constant speed, and the speed of light in a vacuum is the same for all observers undergoing uniform motion. 48

Special Relativity n Second Postulate which comes from the results of numerous experiments says n The speed of light in free space has the same value for all observers no matter their motion n And that value is c = 3 x 108 m/s or about 186, 000 mi/s n Nothing can travel faster than the speed of light-it’s the ultimate speed limit n http: //www. davidcolarusso. com/blog/? p=39#more-39 49

Key Outcomes of Special Relativity n Time is not the same as seen by two observers having relative constant velocity (know this) n Events seen as simultaneous by one observer not seen as simultaneous by another if there is relative constant velocity n Time Dilation is seen by stationary observer relative to a moving “clock” n The twin Paradox 50

Key Outcomes of Special Relativity n Length is contracted in the direction of motion as seen by a stationary observer measuring a moving object. (know this) n The can be seen as an outcome of time dilation n All of this is predicated on speeds approaching a significant % of the speed of light 51

Key Outcomes of Special Relativity n Mass of an object increases with velocity and would become infinite as speed approaches the speed of light ( know this) n Matter cannot move at the speed of light meaning that the speed of light is a speed limit for everything but light n As V approaches the speed of light the kinetic energy can exceed ½ m c 2 where m is “rest mass” 52

The Lorenz Factor Gamma n The Lorenz factor ɣ is a measure of how much special relativity is kicking in n ɣ = 1/ [ 1 - v 2 / c 2 ] v/c ɣ 10% 1. 005 80% 1. 67 90% 2. 29 99. 99% 70. 7 v/c = 10% is 18, 600 miles / sec equivalent to 75% around the world/ second 53

Velocity Impact on time, length and mass n Time contracts, length contracts, mass increases T observer = T of mover x ɣ n Length stationary = length moving x ɣ n Rest Mass = Moving Mass / ɣ n 54

Time Dilation and Length Contraction n http: //www. pbs. org/wgbh/nova/einstein/hotsciencetwin/ n The Time Traveler n http: //www. glenbrook. k 12. il. us/gbssci/phys/mmedia/specrel/lc. html n Length Contraction n http: //www. phys. unsw. edu. au/einsteinlight/ n Univ New S. Whales – Good Stuff on Einstein 55

Special Relativity n The most far-reaching conclusion of special relativity is that mass and energy are related to each other so closely that matter can be converted into energy and energy into matter. n The rest energy of a body is the energy equivalent of its mass. n If a body has the mass m 0 when it is as rest, its rest energy is: E 0 = m 0 c 2 n Rest energy = (rest mass)(speed of light)2 n n n http: //www. pbs. org/wgbh/nova/einstein/experts. html Neil Tyson, Tim Halpin-Healy, Sheldon Glashow 56

The Tree of Relativity 57

Special Relativity n Calculate the rest energy and potential energy of a 1. 5 kg book on top of Mt. Everest (8850 m high) n Eo = mc 2 = (1. 5 kg)(3 x 108 m/s)2=1. 35 x 1017 J n PE = mgh = (1. 5 kg)(9. 8 m/s 2)(8850 m)=1. 3 x 105 J 58

Special Relativity n Can you think of examples of matter converting into energy? n All energy producing reactions in chemistry and physics from the n n Lighting of a match Nuclear fusion of sun Sun consumes 28 billion Tons of its mass per second Fortunately the sun contains 2 x 1030 Kg So good for 5 B more years 59

Special Relativity n Can you think of examples of energy converting into matter? n Particle accelerators convert energy into subatomic particles, for example by colliding electrons and positrons. Some of the kinetic energy in the collision goes into creating new particles. n Pair production – when a particle and its anti-particle materialize when a high-energy gamma ray passes near an atomic nucleus. 60

General Relativity n Einstein’s later theory of general relativity dealt with gravity, including accelerations n Einstein’s General Theory of Relativity related gravitation to the structure of space and time n The force of gravity arises from a warping of spacetime around a body of matter so that a nearby mass tends to move toward the body n General Relativity does not interpret gravity as a force n http: //www. pbs. org/wgbh/nova/einstein/relativity/ n http: //archive. ncsa. uiuc. edu/Cyberia/Num. Rel/Grav. Waves. html 61

The Elevator Thought Experiment n There is no experiment that can allow a determination of the difference between an elevator at rest on the ground and one that accelerates at the rate of gravity n This is the principle of EQUIVALENCE n This led to conclusion that gravity can deflect light reinforcing the warped space hypothesis 62

General Relativity n http: //www. pbs. org/wgbh/nova/einstein/relativi ty/ n General relativity may be the biggest leap of the scientific imagination in history. Unlike many previous scientific breakthroughs, such as the principle of natural selection, or the discovery of the physical existence of atoms, general relativity had little foundation upon theories or experiments of the time. No one except Einstein was thinking of gravity as equivalent to acceleration, as a geometrical phenomenon, as a bending of time and space. 63

Gravity Tam 3 s 6_21 Figure 3 -35 64

Mass Warps space 65

Light is affected by Gravity n Possibly the most spectacular of Einstein’s results was that light should be subject to gravity n To check this prediction, photos were taken of stars that appeared in the sky near the sun during an eclipse in 1919 (stars could be seen during an eclipse because the moon obscured the sun’s disk) n Photos were compared with other photos taken of the same area when the sun was far away 1. 75 arc-seconds, versus a Newtonian prediction of 0. 87 66

Another verification of General Relativiy n The planet Mercury has very high orbital eccentricity n The major axis of its orbit is rotating faster than would be accounted by Newtonion mechanics n It was found that Einstein’s equations of General Relativity accounted for the discrepancy n Rotation rate is 42 seconds of Arc per century 67

Time and relativity n Special relativity n General Relativity n Time is affected by the relative speeds n Time is modified by the factor ɣ Mass warping the space time dimensionality n Clocks above the Earth run faster The GPS system would not function without correcting for both of these effects 68