Dynamic Events We observe many dynamic events in nature where obvious changes take place - earthquakes volcanoes etc. Question: In all of these events where changes are observed, are there some things (quantities) that do not change? Answer: Yes. Some quantities are conserved even in times of violent change. Furthermore, the quantities that do change, do so in ways predicted by conservation laws. - 2-3 Conservation Laws Conservation Laws What does it mean to conserve something? A conserved quantity: can neither be created or destroyed. But it can be changed from one form to another or transferred from one object to another. Conservation of Mass Electric charge Linear momentum Angular momentum Energy Lepton number Etc. - 4-5 changes in mass are only in physical appearance physical (phase) changes chemical changes chemical reactions addition/depletion w.r.t. surroundings burning a log as an example Before: Log with mass The system must include the atmosphere. Fire After fire: ash water vapor + carbon dioxide & others same total mass Conservation of Mass Mass may change from one form to another, but the total mass after the transformation is always the same as that before. Examples: boiling water forest fire gasoline in car - 6-7
Chemical change scale P1: A container of water is sealed off with a latex glove containing Alka-Seltzer. The container is sitting on a scale. If we drop the Alka-Seltzer into the water, carbon dioxide is released, inflating the glove. The glove is surrounded by air. The reading on the scale will (a) increase, (b) decrease, or (c) remain the same. Is the total mass in the glove and beaker the same? scale - 8 Chemical change 2 P2: We now cut a hole in the glove, releasing the carbon dioxide. The reading on the scale will (a) increase, (b) decrease, or (c) remain the same. CO 2 is heavier than oxygen and nitrogen in air. scale scale - 9 Conservation of TOTAL Electric Charge The difference between the total amount of positive and negative charges does not change. Examples Cat fur and rubber rod Batteries Power plants The Law of Conservation of Electric Charge The total (net) charge (sum of the positive and negative charge) does not change. A clear sunny day net charge = 0 In the middle of a thunderstorm net charge = 0 (when you take system big enough) - 10-11 Conservation of Charge Conservation of Linear Momentum Current is flowing in a circuit from the battery. The circuit has two light bulbs. + - Brightness depends on current through bulb What about relative brightness of the two bulbs? Why? - 12 Momentum vector (p) is (mass) x (velocity) p = m v Conserved if there is no external net force (isolated system). For a particle with constant mass, this is just a restatement of Newton s First Law F = mδv/δt = Δp/Δt Of course, a force on an object will change its velocity (accelerate it) and thus change its momentum. But, with a force it is not isolated. - 13
Conservation of Linear Momentum Examples where law is in effect: Rifle recoils when fired Fireworks Auto collisions Billiard balls Collisions 1 2 Two objects, which are isolated (so no net external forces), total momentum of system is conserved. F 21 F 12-14 Newton s third law says that F 21 and F 12 are equal in magnitude but opposite in direction. Demo: airtrack, equal masses (both moving) - 15 Conservation of momentum The western shootout in outer space. Are he and the gun isolated? P3: The cowboy shoots the gun. Which of the 3 cases is correct? Look to see if momentum is conserved. m cowboy v cowboy m bullet v bullet Demo: balloon, gun glider On earth, friction prevents the cowboy from moving backward. But it does not prevent recoil of the gun. If the gun is not firm against your shoulder you will feel the impulse on your shoulder. - 16 Explosion Is momentum conserved during the short time of the explosion? During this short time we can ignore YES! gravity and thus have only internal forces. P4: What can you say about the velocity of the big mass relative to the little mass? Why? - 17 Conservation of angular momentum for isolated system Angular momentum is mass x speed x radius Examples: Diver, Ice skater, rotating chair Video: Tail wags dog, VE 7-3 - 18-19
Sometimes it is hard to describe all the motion in a system Example: Billiards Motion in a system A more complicated example: Power plant - 20-21 Energy makes it more simple Power plant E in E stack E friction E friction Energy Energy is the capacity to do something Ability to exert a force on an object while moving it through a distance Energy can either be associated with an objects position (potential) or its motion (kinetic) boiler turbine generator E electricity - 22-23 Forms of Energy Conservation of Energy kinetic internal potential nuclear solar chemical gravitational electrical elastic thermal inelastic geothermal wind hydroelectric Energy can be neither created nor destroyed. The total amount of energy in the universe never changes. However, energy can change from one form to another, or be transferred from one object to another. The total energy is conserved in an isolated system. - 24-25
Energy breakdown Mechanical (macroscopic) energy depends on the position or motion of the whole object Mechanical energy can be described in terms of kinetic and/or potential energy Internal (microscopic) energy depends on the position or motion of the atoms or molecules that make up the object - 26 kinetic energy energy arising from motion kinetic energy = (1/2)(mass)(speed 2 ) K.E.=1 50 mph K.E.=17.5 50 mph K.E. = 1.9 75 mph 55 mph K.E. = 1-27 Gravitational Potential Energy is energy arising from the height of an object wrt earth gravitational potential energy = (weight) x (height) Examples Ball rolling down hill (energy transfers from potential to kinetic) Pendulum Ski Jump Bouncing ball work as used in physics Work is a method of transferring energy to a nonisolated system, it is not a form of energy itself. Work = force x distance parallel to force For work to be done in the physics sense, a force must be applied and the object must have some motion parallel to the force. Demo: tracks, pendulum, ball - 28-29 Falling Ball-no work (except gravity) being done on it (isolated) Total energy is conserved (assume no friction) KE + GPE = TE How could this be useful? Video: Pile driver, VE 3-73 Energy = 1/2 mass x speed 2 = weight x height (bottom) (top) Demo: Galileo tracks With friction some of the energy goes into internal energy. - 30 Electrical Potential Energy energy associated with the electrical force Unlike charges attract and behave like gravitational potential (farther apart=more potential) Like charges repel and have more potential when close together Gives rise to chemical potential energy at the microscopic level. - 31
Internal Energy Internal energy is microscopic energy inside materials. It is associated with the temperature of the materials (thermal energy) and the chemical potential energy of materials (shape or Physical state) Shape Examples Mass on a spring Garage Door Thermal Energy Internal energy associated with temperature. Related to average KE of atoms and molecules A warm object has more internal energy than when it is cold Two objects at the same temperature may have different amounts of thermal energy water 1 cal/g o C gold.03 cal/g o C - 32-33 Elastic Potential Energy Energy stored in a material by deforming it in such a way that its molecules are displaced from their equilibrium positions. Examples: Rubber band Trampoline Chemical Potential Energy Electrical potential energy of atoms in a material Examples deformation (springs, balls) ball demo, weight/spring change of state (rearrangement of atoms) chemical bonds burning gasoline, rust, exploding firecracker - 34-35 Energy Transfer and Transformation Conduction (Heat Flow ): a process in which internal energy is transferred because of a difference in temperature. (electric stove, soldering iron) Radiation: energy is transmitted by visible light, infrared radiation, ultraviolet radiation, X-rays, or radio waves. (sun, space heater) Convection: internal energy is transferred because matter moves from one place to another. (hot air furnace, gulf stream) Work: energy is transferred or transformed by forces acting on an object. (friction, muscles, electric motor) Combustion: chemical potential energy is transformed into another form (gasoline engine, dynamite, light stick) Popcorn P5: Three methods for popping popcorn Microwave -- Hot air -- Stove top -- Identify the method of heat transfer for each. - 36-37
Question (pendulum demo) P6: A pendulum is made when a ball on the end of a string is hooked to a peg and set in motion. It is a real pendulum with friction. Which of the following is true? a. The total energy (including internal) is not conserved because of the friction. b. The sum of the gravitational potential energy and the kinetic energy is conserved. c. The kinetic energy has its maximum value when the ball is at its highest point -- just as it begins its downward swing. d. The internal energy always decreases because of friction. e. None of the above. - 38 Energy Conservation in the Pendulum Problem When you add up the total energy, energy in all its forms, there is as much after the event as there was before. Example: Pendulum swinging Total energy = KE + GPE + IE If there were no friction, then IE unchanged, just need to consider Total energy = KE + GPE - 39 Analysis of the Pendulum Suppose a real pendulum were set in motion, and gradually came to rest: a. Describe what would be observed. The pendulum would swing back and forth. The ball would speed up until it reached the lowest point. It would then slow down until it had zero speed at its highest point. In each succeeding swing the ball would reach a lower point at the top of the swing. Finally, the pendulum would stop. b. Name and state the fundamental principle that will explain this observation: The Conservation of energy: : In an isolated system, the total amount of energy remains constant. - 40 Pendulum continued c. Use the principle to explain what would be observed. The total, KE + GPE + IE = constant --During each swing, the KE and the GPE vary inversely. As the ball speeds up, KE increases and GPE decreases. As the ball slows down, KE decreases and GPE increases. --Due to friction, the IE always increases. Therefore, the sum of KE and GPE decreases. --Finally, all of the energy is IE. KE and GPE are both zero. - 41 K.E. - Elastic vs. Inelastic Is momentum conserved when the cars stick together? Which hits harder? The board falls in one case. Inelastic Elastic mv-mv=0 Yes! Is kinetic energy? No-This is called a perfectly inelastic collision (when they stick together). The kinetic energy is lost into heat and sound. Demo: Newton with duckpins Most collisions are somewhere between perfectly elastic and perfectly inelastic, called inelastic. Demo: Newton s s Cradle - 42 m ball v ball After P7: In which case will the board fall. Demo: pendulum collision m ball v ball - 43
Conversion of Energy between Kinetic and Potential You ve already seen this with the pendulum Here is another example Oscillating weight on a spring There is an elastic potential energy from work done by the spring force. Mechanical energy is now PE PE + KE grav. + spring Kinetic energy at very high speeds The engine is running, doing work on the car. Energy is going in, but speed can t increase past the speed of light. Energy depends on Mass and Speed --Mass must increase. Pole vault - 44-45 Conservation of Mass-Energy E=mc 2 Mass and energy are two manifestations of the same quantity The total amount of mass-energy in an isolated system is constant Mass and energy can be converted from one form to the other Nuclear Potential Energy By studying the masses of nuclear decay products, we find that the products are significantly lessmassive than the original nucleus. - 46-47