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CHAPTER 2 Mechanical Energy © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Outline Introduction Work and Energy Forms of Mechanical Energy Kinetic Energy Potential Energy The Law of Conservation of Energy Power The Golden Rule of Mechanics Simple Machines Mechanical Efficiency and Mechanical Advantage Human Body as a Machine Summary © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Introduction Background: Mechanical energy, in the form of muscle power First energy source that humans utilized. (to chase and wrestle animals or escape them) The use of tools for hunting and agriculture The bow and arrow was used in hunting and in warfare, and wind was harnessed to navigate sailboats along rivers and on seas. The great civilizations of China, Egypt, Persia, Greece, and Rome relied on forced labor and animals to plow their farms; at the same time, their soldiers fought for the acquisition of more land and slaves. The work from muscles, the work performed by windmills and watermills, and the work done by simple tools are all examples of mechanical energy. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Work Work = Force x Displacement Work is the change in an object’s state of motion that results from the application of force. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- Work Question: If there is no work done, why is carrying the suitcase not as easy a task as it appears? Answer: Although little or no mechanical work is involved in carrying the suitcase, energy expended in flexing various muscles in the body to simply hold the weight above the ground might not be! © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Torque Torque = Force x Arm of force Torque is a measure of work (energy) required to rotate an object. Torque can be interpreted as “force with a twist”, since it results in rotation of the object upon which the force is applied. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Units (Work & Torque) In SI system… Force is given in newtons (N) and distance in meters (m). The work (also the Torque) is, therefore, expressed as newtons-meters (N.m) or Joules (J). In the U.S., … Work is expressed in Btu or lb-ft. 1 Btu = 778 lb-ft = 1055 J © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- Work Question: Which of the following represents the performance of work? a. An apple falls off an apple tree b. A horse pulls a carriage c. A balloon ruptures and air rushes out d. A woman carries a basket of fruit over her head e. A boy pushes against a wall until exhausted Answer: In each of the first three instances, a force has caused a movement in the direction of the force. In case (a), the force of gravity causes the apple to fall. In case (b), the horse applies a force in the direction of motion. In case (c), the higher pressure in the balloon forces air out. Instances (d) and (e), however, do not constitute work. In case (d), the force that the woman applies to the basket is upward and perpendicular to the direction of her motion. Similarly, in case (e), when the boy pushes on a wall, there is no displacement and he performs no work. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- Work Question: A boy is moving a heavy box along a hallway. If the boy wants to move the box with the smallest amount of effort (putting in the least amount of work), which approach should he choose? a. Pull the box with a rope parallel to the floor. b. Push the box parallel to the floor. c. Pull the box with a rope at an angle. d. All of the above require the same amount of effort. Answer: The answer is (d). Although the boy might be a bit more comfortable in one situation over another, the work done is exactly the same in all cases. Work is needed because of friction between the two surfaces; the amount of work is equal to the magnitude of the friction force, multiplied by the distance traveled. The component of force perpendicular to the ground is not doing any work. The smart thing to do, probably, is to put the box on a wheeled cart or a dolly to reduce the friction. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Forms of Mechanical Energy Kinetic Energy (K.E.) Energy of motion. “The K.E. of an object can be interpreted as the work required for accelerating that object from rest.” K.E. = ½ mV2 Potential Energy (P.E.) Energy at rest. “The P.E. of an object is equal to the work needed to lift or deform the object.” P.E. = mgh © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Sub-classifications Kinetic Energy (K.E.) Linear K.E.: The energy of motion from one location to another. Rotational K.E.: The energy due to rotational motion about the center of mass. Potential Energy (P.E.) P.E. of form: It is the result of twisting, compressing, stretching, and bending matter out of object’s natural shape. P.E. of position (gravitational energy): It is the energy of mass caused by its higher elevation relative to its © Verve Publishers surroundings. - Energy and Environment by Toossi (All Rights Reserved) FAQ Question: You inflate a balloon by blowing into it. Do you perform work? By how much? Answer: Yes, you do work. because you are applying a force (moving your diaphragm to push the air out) through a distance (expanding the balloon outward). The amount of work is equal to the stored elastic potential energy; that is, the amount of energy needed to stretch (deform) the balloon. Question: Which one requires more work in carrying a weight to the second floor -- using a ramp, stairs, or an elevator? Answer: As long as frictional forces are neglected, all three require the same amount of work, equal to the change in potential energies of the weight between the first and second floors. When riding an elevator, the work is being done by the electric motor, but when walking upstairs, the same work must be provided by our muscles. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) The Law of Conservation of Energy The principle of conservation of energy implies that the amount of energy in a system does not change; only its form does. Conservation of Mechanical Energy P.E. + K.E. = Constant (Ideal Condition) P.E. + K.E. + Heat losses= Constant © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ Question: As you walk, it is the static frictional force between your shoes and the ground that propels you. How much work is done by this force on your shoes? Answer: None. At the point of contact, your shoes do not move. The ground does work on you as a whole, and you do work on your shoes. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Power Power = Work / Time Power = Force x Velocity Power is a measure of rate of change of work; or the rate of energy consumption. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Units (Power) In SI system… The power is expressed in Joules per second (J/s), commonly called a watt (W) in honor of James Watt, the inventor of the steam engine. However, as a watt (W) is relatively small unit of power, a kilowatt (1 kW = 1000 W) is often used. In the U.S., … Power is customarily expressed in horsepower. 1 hp = 746 W = 0.746 kW © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Power Outputs of Few Basic Machines Laptop Computer Man Horse Automobiles Water/Gas Turbines Power Plants Space Shuttle Main Engine 10 W 100 W 746 W (1 horsepower) 100 kW 1 MW 1 GW 30 GW © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- Power Question: Two identical cars are leaving Los Angeles at the same time. The first car arrives in San Francisco in five hours, while it takes ten hours for the second car to reach the same destination. Which car consumes more energy? Which car puts out more power? Answer: Assuming that the cars’ efficiencies are equal at all speeds [in reality, cars are designed to give better gas mileage at about 80-100 km/h (50-60 mph)], both cars use the same amount of fuel (energy), i.e., work the same amount. The first car, however, uses up fuel twice as fast, therefore putting out twice the power of the second car. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- Power Question: Suppose a small passenger sedan with a power rating of 80 hp can accelerate from 0-60 mph in twelve seconds. How long would it take a sports car with a power rating of 240 hp to accelerate by the same amount? Which car performs more work? Answer: Both cars accelerate to the same speed (and gain the same amount of kinetic energy), therefore they perform the same amount of work. The second car uses three times the power—which means it does the same work in one third of the time, or four seconds. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ - Power Question: A cart filled with bricks is to be loaded onto a truck. Three ramps of different lengths are available (see figure on the right). 1. Which situation requires the least amount of force? 2. Which situation requires the least amount of work? 3. Which situation requires the least amount of power? Answer: Situation (a) requires the least amount of force, but the force must be applied over the longest distance. The product of force times distance, or work, is the same in all cases. The power expenditure depends on how long it takes to perform this work. If you pull faster, the time is shorter and more power is needed. Assuming speeds are the same in all cases, it takes longest for the cart to move up the longest ramp (a), and the least power is consumed. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) The “Golden Rule” of Mechanics “Whatever you lose in power you gain in displacement.” Although the output work is less than the input work, output force does not have to be small than input force. This is exactly what a machine is supposed to do – transform a part of the energy (work) into a form most convenient – that which requires less force. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ Question: Consider a bottle opener. In lifting the handle, you do work on the opener which, in turn, does work on the cap it is lifting. Which one is greater, your work or the work of the bottle opener? Answer: Because the opener cannot be a source of energy, the output work (work of opener) can never exceed the input work (your work). The opener simply aids in the transfer of energy from you to the bottle cap. In fact, nearly all of your work will go into deforming, rather than into lifting, the bottle cap. Of course, energy was not really lost; it was just not used in the way you intended. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ Question: A transmission gearbox transmits power from the engine to the axle through a number of interlocking gears. To get more power, we need to put the transmission into a lower gear. Speed, at the same time, decreases. Can we design transmissions that increase the power without reducing the speed? Answer: No. A machine can increase the magnitude of the effort (input) force, or increase the velocity of the object to be moved, but not both. If a machine increased the power without a corresponding decrease in velocity, the output work would exceed the input work, which is impossible. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Simple Machines They are designed to perform one simple task. Types: A. B. C. D. E. F. Inclined Plane (ramp) Wedge Screw Lever Wheel and Axle Pulley © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) A. Inclined Plane – Ramp Inclined plane: any slanted surface used to raise a load from a lower level to a higher level. Work is carried out using less effort by moving a smaller force over greater distances. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) B. Wedge Two back-to-back ramps turned on their sides. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) C. Screw The circular version of the inclined plane. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) D. Lever A bar or a rigid object that rests and rotates about a point called fulcrum. Depending upon the position where force and weight apply relatively to the pivot, there are three kind of levers: First class lever Second class lever Third class lever © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) D1. First Class Levers Fulcrum is between the force and weight. • Pliers • Seesaw • Scissors © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) D2. Second Class Levers Weight is between the fulcrum and the force. • Nutcracker • Wheelbarrow © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) D3. Third Class Levers Force is between the fulcrum and weight. • Baseball bat • Shovel • Tongs © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) E. Wheel and Axle A wheel or spoke attached to an axle or a lever. A smaller force applied to the longer motion at the wheel results in a shorter, more powerful motion at the axle. Examples: Windmills, Gears, Doorknobs, Steering wheels etc. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) F. Pulley A chain, belt, or rope wrapped around a wheel. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ – Simple Machines Question: Which of the six simple machines reduce the amount of work needed to raise a load? Answer: None of them. Machines do not change the amount of work required. They merely make the work easier. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Mechanical Efficiency (M.E.) M.E. is a measure of losses that may be included while performing a certain work. It is given by a fraction of the input work that is available for carrying out the desired output work. M.E. = Desired Work Output / Necessary Work Input © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- M.E. Question: Suppose you hook two machines together, one with an efficiency of 40% and the other with an efficiency of 60%. What is the efficiency of the two machines operating together? Answer: If you are tempted to say 100%, try to resist. The first machine will feed only 40% of the original input energy into the second machine, which then puts out 60% of the 40%. In other words, each machine loses some energy and the net efficiency is 0.40 X 0.60= 0.24 (or 24%). © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Mechanical Advantage (M.A.) M.E. is the factor by which the machine multiplies the force. It is given by a ration of the force exerted by a machine to the force exerted up on the machines. M.E. = Resistance force (load) / Effort Force = Force exerted by machine / Applied Force © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- M.A. Question: What is the mechanical advantage of a hammer driving a nail through a block of wood? Answer: The energy used to carry the hammer through its flight (from the time of raising your hand until the time that the hammer hits the nail) is used to push the nail only a few millimeters into the wood. For example, if we lower our hand by 50 cm, but the nail is pushed down only by 0.5 cm, then we have reduced the displacement by 100 times and, at the same time, multiplied the force by a factor of 100. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- M.A. Question: What is the mechanical advantage of the system of pulleys shown here? Answer: The mechanical advantage of a pulley system is approximately equal to the number of supporting ropes or strands. A single, fixed pulley can only change the direction of the pull to lift a load; it does not multiply the force. Therefore, the pulley shown in (a) has a mechanical advantage of one (MA = 1). The pulley system in (b) has two ropes that are supporting the moving pulleys and, therefore, has a mechanical advantage of two (MA = 2). © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ -- M.A. Question: How does a car jack allow you to raise a 2,000-lb car, when you can only lift a weight of 50 pounds? Answer: The jack is a lever allowing a much smaller force applied over a longer distance. In this particular case, you must lower the jack handle 40 cm just to raise the car by 1 cm. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Human Body as a Machine Human Body = A machine that consumes food and converts it to mechanical work and heat. Power Transmission through the action of forces on the muscles, bones and joints. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) A Human Elbow (Third class Lever during Weight Lifting) © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) FAQ Question: A man is lifting a heavy weight by contracting the biceps muscle and, at the same time, relaxing his triceps muscle. The elbow acts as the fulcrum. What is the force needed to lift a 10-pound weight? Answer: The force needed is higher by ratio of the arms (40 to 4); we need ten times the weight of the object to support the weight when assumed that there are no losses involved. When losses are present, mechanical advantage will be reduced by a factor equal to the mechanical efficiency. Question: Our muscles are much stronger than they seem. For instance, the biceps is attached to the forearm about eight times closer to the fulcrum (the elbow) than one’s hand is, when lifting a weight. What is the advantage of this seemingly inefficient arrangement? Answer: The advantage is speed (also a factor of eight), which is frequently more important in the animal world. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) Summary Add the summary notes as per your convenient. © Verve Publishers - Energy and Environment by Toossi (All Rights Reserved) To receive your free examination copy of the 2011 Edition, please visit http://www.vervepublishers.com/toossii/ee2011