8.5 - Energy. Energy The property of an object or system that enables it to do work. Energy is measured in Joules (J).
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1 Work Work The process of moving an object by applying a force. Work = Force x displacement. Work is measured in Joules (J) or Newton-meters (Nm). W = Fd Example: To prove his strength, a weightlifter pushes a refrigerator 2 meters across the floor by applying a force of 200 N. How much work was done by the weightlifter? Answer: W = Fd = (200 N) (2 m) = 400 J Note: To do work on an object, the object must move some distance as a result of the force. The object also must move in the same direction as the object s force. If the object does not move a distance or if that distance is in a different direction than the direction of the force, then 0 J of work is done. Energy The property of an object or system that enables it to do work. Energy is measured in Joules (J). Forms of Mechanical Energy Mechanical Energy The energy due to the positon or movement of an object. The two forms of mechanical energy are potential energy (PE) and kinetic energy (KE). ME = PE + KE Potential Energy Stored energy by virtue of its position. Elastic Potential Energy A spring or rubber band exhibits elastic potential energy when it is stretched or compressed because of its ability to do work. Chemical Potential Energy Any chemical reaction possesses the ability to do work through the altering of atoms and molecules. Examples of this would be the potential energy found in fossil fuels, electric batteries, and food. Gravitational Potential Energy The stored energy in an object that is at some height above the ground. PE = mass x gravity x height PE g = mgh Example: What is the gravitational potential energy of a 10 kg object 4 meters above the ground? Answer: PE = mgh = (10 kg) (10 m/s 2 ) (4 m) = 400 J Kinetic Energy The energy of an object in motion. KE = ½ mass x velocity squared KE = 1 2 mv2 Example: What is the kinetic energy of a 4 kg book tossed across the room at 2 m/s? Answer: KE = ½ mv 2 = ½ (4 kg) (2 m/s) 2 = 8 J Example: If an 8 kg cart has 36 J of total mechanical energy, what will be its maximum possible speed? Answer: KE = 36 J = ½ (8 kg) v 2 72 = 8 v 2 9 = v 2 v = 3 m/s
2 Work-Energy Theorem Work-Energy Theorem Whenever work is done, the energy of an object changes. The net work done is equal to the change in kinetic energy. Work = KE W = KE Example: How much work is required to stop a 4 kg cart going 5 m/s? Example: W = KE = ½ mv 2 = ½ (4 kg) (5 m/s) 2 = 50 J of work Law of Conservation of Energy Law of Conservation of Energy Energy cannot be created or destroyed. It may reside in different forms, but the total amount of energy never changes. Example: The diagram above shows a roller coaster cart of 100 kg at Point A being released from rest 5 meters above the ground. (Assume no frictional forces and so no loss in terms of Thermal Energy). Answer: Utilize an Energy Table to determine the PE, KE, TE (Thermal Energy), and ME at every point. Point A Point B Point C All Points on the Track Height 5 m 0 m 2 m PE mgh = 5000 J mgh = 0 J mgh = 2000 J PE Speed 0 m/s ½ mv 2 = 5000 J ½ mv 2 = 3000 J KE ½ mv 2 = 0 J 5000 J 3000 J KE TE (no friction) 0 J 0 J 0 J TE Total ME 5000 J 5000 J 5000 J ME = PE + KE + TE (A) What is the energy at Point A? ME = KE + PE = ½ mv 2 + mgh = 0 J + (100 kg) (10 m/s 2 ) (5 m) = 5000 J (B) What is the energy at Point B? 5000 J (Energy is conserved) (C) What is the energy at Point C? 5000 J (Energy is conserved) (D) Where is the cart going to have the maximum speed? Point B (There is no PE due to no height, so it will have all 5000 J of KE) (E) What is the gravitational potential energy and kinetic energy at Point C? PE = mgh = (100 kg) (10 m/s 2 ) (2 m) = 2000 J. ME = PE + KE = 5000 J = 2000 J + KE. KE = 3000 J (F) What is the speed of the cart at Point C? KE = ½ mv 2 = 3000 J = ½ (100 kg) v 2 v = 7.75 m/s
3 Thermal Energy Temperature The measure of the average kinetic energy of the individual particles in matter. Objects that have a high temperature have a high average kinetic energy. Temperature is measured in degrees Celsius ( C) or on an absolute scale of Kelvin (K). Thermal Energy or Internal Energy The total energy of all of the particles in an object. This depends on the number of particles, the temperature of the object, and the arrangement of the particles. An object can have the same temperature, but different energies. An example would be liquid water at 100 C and water vapor at 100 C. The water vapor has more internal energy than the liquid water. Heat - The transfer of thermal energy from matter at a high temperature to matter at a lower temperature. Note: Heat always transfers from the warmer object to the cooler object or from the high temperature matter to the low temperature matter. Calorimetry The experimentation of measuring thermal energy changes. Heat (Q) = mass(m)x specific heat (C)x change in temperature ( T) Q = mc T Specific Heat (C) The amount of energy to raise 1 gram of matter 1 degree Celsius. Example: 5 grams of liquid water is raised from 40 C to 50 C. How much heat was absorbed by the water? Liquid water has a specific heat of 4.18 J/g C. Answer: Q = mcδt = (5 grams) (4.18 J/g C) (50 C-40 C) = 209 J Example: A 10 gram piece of unknown metal (specific heat is unknown) is at 100 C. It is placed in 10 grams of liquid water (specific heat 4.18 J/g C) at 20 C. The liquid water and the unknown metal both come to a temperature of 24 C. What is the specific heat of the metal? Answer: Q of water = mcδt = (10 grams) (4.18 J/g C) (24 C-20 C) = J Q absorbed by the water = Q released by the metal = J Q of metal = mcδt = (10 grams) (? J/g C) (24 C-100 C) = J C of metal = 0.22 J/g C
4 Transfer of Heat Exothermic Releasing Heat (-) Endothermic Absorbing Heat (+) Heat is always transferred from the warmer object to the cooler object. Conductor Transfers thermal energy well. An example would be metals. Insulators Does not transfer thermal energy well. An example would be rubber, wool, and wood. Three Forms of Heat Transfer Conduction Heat is transferred from one particle of matter to another without the movement of matter. An example would be a warm hand melting a piece of ice. Convection Heat is transferred by the movement of currents within a fluid. An example would be the thermal energy from an oven. Radiation Heat is transferred by electromagnetic waves. Example would be the thermal energy from the sun. Example: Match the following description of a process with either: A. Conduction B. Convection C. Radiation Answer: Process of energy exchange where cold air displaces warmer air B Process of energy exchange of light rays passing through space C Process of energy exchange where molecules within a substance are colliding A
5 Electromagnetic Radiation and the Energy of a Wave Energy is also emitted in the form of electromagnetic radiation. There are many types of radiation found in the universe ranging from radio waves, microwaves, infrared radiation, through our visible spectrum, ultraviolet, x-rays, and gamma rays. These types of radiation are found on the electromagnetic spectrum. These forms of radiation found on the electromagnetic spectrum travel in waves. Each wave has a specific wavelength, frequency, and energy and travels at the speed of light in a vacuum. The larger the wavelength (radio waves, microwaves, infrared), the lower the frequency, and lower the energy. The smaller the wavelength (ultraviolet, x-rays, and gamma rays), the higher the frequency, and higher the energy. c = λf where c is the speed of light, λ is the wavelength, and f is the frequency E = hf where E is the energy of the wave, h is a constant, and f is the frequency
6 Example: Which has a greater amount of energy red light or blue light? Answer: Blue light is closer to the ultraviolet region of the electromagnetic spectrum so it would have a smaller wavelength, larger frequency, and larger energy. Therefore, red light would have a lesser amount of energy (most inexpensive laser pointers contain red light).
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