Chapter 7: Work, Energy and Energy Resources PDF

Chapter 7: Work, Energy and Energy Resources Mrs. Pooja Brahmaiahchari Introduction Energy plays an essential role both in everyday events and in scientific phenomena. You can no doubt name many forms of energy, from that provided by our foods, to the energy we us...

Chapter 7: Work, Energy and Energy Resources Mrs. Pooja Brahmaiahchari Introduction Energy plays an essential role both in everyday events and in scientific phenomena. You can no doubt name many forms of energy, from that provided by our foods, to the energy we use to run our cars, to the sunlight that warms us on the beach. Energy is characterized by its many forms and the fact that it is conserved. We can loosely define energy as the ability to do work, admitting that in some circumstances not all energy is available to do work. WORK The scientific definition of work reveals its relationship to energy— whenever work is done, energy is transferred. For work, in the scientific sense, to be done, a force must be exerted and there must be displacement in the direction of the force. Formally, the work done on a system by a constant force is defined to be the product of the component of the force in the direction of motion times the distance through which the force acts. 𝑊 = 𝐹𝑑 cos 𝜃 where W is work, d is the displacement of the system, and θ is the angle between the force vector F and the displacement vector d.  (a) The work done by the force on this lawn mower is 𝐹𝑑 cos 𝜃. (b) A person holding a briefcase does no work on it, because there is no displacement. No energy is transferred to or from the briefcase. (c) The person moving the briefcase horizontally at a constant speed does no work on it, and transfers no energy to it. (d) Work is done on the briefcase by carrying it up stairs at constant speed, because there is necessarily a component of force in the direction of the motion. Energy is transferred to the briefcase and could in turn be used to do work. (e) When the briefcase is lowered, energy is transferred out of the briefcase and into an electric generator. Here the work done on the briefcase by the generator is negative, removing energy from the briefcase, because and are in opposite directions.  Work and energy have the same units. In SI units, work and energy are measured in newton-meters. A newton-meter is given the special name joule (J). 𝑚2 1𝐽 = 1 𝑁. 𝑚 = 1 𝑘𝑔. 2 𝑠 1. How much work is done on the lawn mower, if he exerts a constant force of 75.0 N at an angle of 35obelow the horizontal and pushes the mower 25.0m on level ground? Kinetic Energy and the Work-Energy Theorem Net Work and Work energy theorem Net work is defined to be the sum of work done by all external forces—that is, net work is the work done by the net external force Fnet 1 The net work on a system equals the change in the quantity 𝑚𝑣 2 2 1 1 𝑊𝑛𝑒𝑡 = 𝑚𝑣 − 𝑚𝑣02 2 2 2 1 The quantity 𝑚𝑣 2 in the work-energy theorem is defined to be the 2 translational kinetic energy (KE) of a mass m moving at a speed v. 2. A 15 kg block, initially at rest, slides down frictionless incline and comes to the bottom with speed of 7m/s. What is the kinetic energy of object at top and bottom of the ramp? 3. How much work is required to stop a 1500kg car moving at speed of 25m/s? Gravitational Potential Energy If the object is lifted straight up at constant speed, then the force needed to lift it is equal to its weight mg. The work done on the mass is then 𝑊 = 𝐹𝑑 = 𝑚𝑔ℎ We define this to be the gravitational potential energy PEg put into (or gained by) the object-Earth system. This energy is associated with the state of separation between two objects that attract each other by the gravitational force.  Potential energy is a property of a system rather than of a single object— due to its physical position. An object’s gravitational potential is due to its position relative to the surroundings within the Earth-object system. The force applied to the object is an external force, from outside the system. When it does positive work, it increases the gravitational potential energy of the system. Because gravitational potential energy depends on relative position, we need a reference level at which to set the potential energy equal to 0.  Gravitational potential energy may be converted to other forms of energy, such as kinetic energy. If we release the mass, gravitational force will do an amount of work equal to mgh on it, thereby increasing its kinetic energy by that same amount. we define the change in gravitational potential energy to be ∆𝑃𝐸𝑔 ∆𝑃𝐸𝑔 = 𝑚𝑔ℎ The units of gravitational potential energy turn out to be joules, the same as for work and other forms of energy. 4. How much work is required to lift 40kg crate 20m high? 5. What is the final speed of the roller coaster shown in Figure if it starts from rest at the top of the 20.0 m hill and work done by frictional forces is negligible?  In which of these scenarios is useful mechanical work being done? A. Dave climbing a ladder B. Dave’s stomach begins to digest his lunch C. Dave reads a manual on how to fix his car D. Dave washes his car  Consider a situation where you lift a book from the ground onto the shelf. Which of the following affects the work you do in lifting the book? A. The path taken by the book B. The time it takes to lift the book C. The height of the shelf D. The mass of the book Conservative Forces and Potential Energy Potential energy is the energy a system has due to position, shape, or configuration. It is stored energy that is completely recoverable. For example, Energy we absorb from the food we eat, when we digest and metabolize it. A conservative force is one for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken. Gravitational force is an example for conservative force. Potential energy of a spring We calculate the work done to stretch or compress a spring that obeys Hooke’s law. The potential energy of a spring, 𝑃𝐸𝑠 , to be 1 𝑃𝐸𝑠 = 𝑘𝑥 2 2 Where k is the spring’s force constant and x is the displacement from its undeformed position. The potential energy represents the work done on the spring and the energy stored in it as a result of stretching or compressing it a distance x. The potential energy of the spring 𝑃𝐸𝑠 does not depend on the path taken; it depends only on the stretch or squeeze in the final configuration. 6. How much work is required to stretch a spring from 25cm beyond its natural length to 85cm beyond its natural length given spring constant of 500N/m? Conservation of mechanical energy The total kinetic and potential energy is constant for any process involving only conservative forces. That is, 𝐾𝐸 + 𝑃𝐸 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 or (Conservative forces 𝐾𝐸𝑖 + 𝑃𝐸𝑖 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓 only) where i and f denote initial and final values. This equation is a form of the work- energy theorem for conservative forces; It is known as the conservation of mechanical energy principle. The total kinetic plus potential energy of a system is defined to be its Mechanical Energy. Nonconservative Forces and Friction A nonconservative force is one for which work depends on the path taken. Friction is a good example of a nonconservative force. Because of this dependence on path, there is no potential energy associated with nonconservative forces. An important characteristic is that the work done by a nonconservative force adds or removes mechanical energy from a system. Friction, for example, creates thermal energy that dissipates, removing energy from the system. How Nonconservative Forces Affect Mechanical Energy Mechanical energy may not be conserved when nonconservative forces act. For example, when a car is brought to a stop by friction on level ground, it loses kinetic energy, which is dissipated as thermal energy, reducing its mechanical energy.  (a) A system with only conservative forces. When a rock is dropped onto a spring, its mechanical energy remains constant (neglecting air resistance) because the force in the spring is conservative. The spring can propel the rock back to its original height, where it once again has only potential energy due to gravity. (b) A system with nonconservative forces. When the same rock is dropped onto the ground, it is stopped by nonconservative forces that dissipate its mechanical energy as thermal energy, sound, and surface distortion. The rock has lost mechanical energy.  The amount of work done by nonconservative forces adds to the mechanical energy of a system. 𝐾𝐸𝑖 + 𝑃𝐸𝑖 + 𝑊𝑛𝑐 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓 If 𝑾𝒏𝒄 is positive, then mechanical energy is increased, such as when the person pushes the crate up the ramp. If 𝑾𝒏𝒄 is negative, then mechanical energy is decreased, such as when the rock hits the ground. If 𝑾𝒏𝒄 is zero, then mechanical energy is conserved, and nonconservative forces are balanced. For example, when you push a lawn mower at constant speed on level ground, your work done is removed by the work of friction, and the mower has a constant energy. Conservation of Energy The law of conservation of energy can be stated as follows: Total energy is constant in any process. It may change in form or be transferred from one system to another, but the total remains the same. Let us include all other energies as OE thus, 𝐾𝐸𝑖 + 𝑃𝐸𝑖 + 𝑊𝑛𝑐 + 𝑂𝐸𝑖 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓 + 𝑂𝐸𝑓  Some of the other forms of energies are: 1. Electrical energy is a common form that is converted to many other forms and does work in a wide range of practical situations. 2. Fuels, such as gasoline and food, carry chemical energy that can be transferred to a system through oxidation. Chemical fuel can also produce electrical energy, such as in batteries. 3. Most energy sources on Earth are in fact stored energy from the energy we receive from the Sun. We sometimes refer to this as radiant energy, or electromagnetic radiation, which includes visible light, infrared, and ultraviolet radiation. 4. Nuclear energy is transformed into the energy of sunlight, into electrical energy in power plants, and into the energy of the heat transfer and blast in weapons. 5. Thermal energy, Because of random motions of atoms and molecules. Transformation of Energy The chemical energy in food is converted into thermal energy through metabolism; light energy is converted into chemical energy through photosynthesis. Another example of energy conversion occurs in a solar cell. Sunlight impinging on a solar cell produces electricity, which in turn can be used to run an electric motor. Energy is converted from the primary source of solar energy into electrical energy and then into mechanical energy. Efficiency Even though energy is conserved in an energy conversion process, the output of useful energy or work will be less than the energy input. The efficiency Eff of an energy conversion process is defined as, 𝑢𝑠𝑒𝑓𝑢𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑟 𝑤𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 𝑊𝑜𝑢𝑡 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝐸𝑓𝑓 = = 𝑡𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛𝑝𝑢𝑡 𝐸𝑖𝑛 Power Power is defined as the rate at which work is done. 𝑊 𝑃= 𝑡 The SI unit for power is the watt (W ), where 1 watt equals 1 joule/second ( 1W = 1 J/s) Because work is energy transfer, power is also the rate at which energy is expended. Great power means a large amount of work or energy developed in a short time. For example, when a powerful car accelerates rapidly, it does a large amount of work and consumes a large amount of fuel in a short time. Power and Energy Consumption We usually have to pay for the energy we use. It is interesting and easy to estimate the cost of energy for an electrical appliance if its power consumption rate and time used are known. The higher the power consumption rate and the longer the appliance is used, the greater the cost of that appliance. So, the energy consumed over a time is 𝐸 = 𝑃𝑡; Electricity bills state the energy used in units of kilowatt-hours(kW.h) 7. What is the power output for a 60.0-kg woman who runs up a 3.00 m high flight of stairs in 3.50 s, starting from rest but having a final speed of 2.00 m/s? 8. A 20kg crate is lifted 200m above ground in 5 minutes. a) How much work is required to lift it 200m into air? b) What is average power exerted on crate? 9. How long will it take a 2.5kW motor to lift a 80kg block 30m high? 10. What is the cost of running a 0.200-kW computer 6.00 h per day for 30.0 d if the cost of electricity is $0.120 per kWh? THANK YOU