Chapter 4 - Notes - Work and Energy PDF

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Work and Energy (Ch 4) Mechanical work involves force and motion. The universe is made up of matter and energy. Matter we can touch. Energy is not tangible. We are aware of energy only when it is being transformed, when it is used to do work. Main source of energy is the sun. Energy can be classified as Kinetic or Potential Energy 4.1 Work Work involves F and M (motion). If there is no motion, then there is technically no work. The work done by a constant force F acting on an obj is the product of the magnitude of the force (or parallel component of the force) and the parallel distance d through which the obj moves while the force is applied Work = Force x Parallel distance or W=Fd If d=0 then the obj has not moved and no work is done. Ex1: No mechanical work done: man pushing against the wall. A force is applied but no work is done bc the wall doesn’t move. Man become tired, but no mechanical work is done. Ex2: When a lawn mower (cortar grama) is pushed at an angle to the horizontal, only the component of the force that is parallel to the level lawn (horizontal component fh ) moves through a parallel distance and does work. The vertical component fv does not work, it does not act through distance, it acts pushing the machine against the ground. Work is a scalar, has only magnitude, no directions, but force and parallel distance (displacement) are vector. The unit of work are N.M (force x length) = newton/meter this unit is called Joule or J. One J is the amount of work done by 1 N through a distance of 1M. When doing work you applied force and feel the other part *newton 3 law force pair acting against you. Therefore, the work is done against something such as gravity or friction. When smth is lifted a force must be applied to overcome gravity’s force (w=Mass x gravity), so work is done against gravity. This work is given by W= Fd= wh (height) = m.g.h (height which the obj was lifted) Similarly work is done against friction. Friction opposes motion. To move smth on a surface you must apply a force. In doing so, you do work against the friction. The work done by the applied force against friction is W = Fd. The frictional force acts through the distance therefore it works. The frictional force and displacement are in different direction so the work done by the frictional force will be –fd = -W.

When walking there must be friction btw feet and floor. In this case though no work is done against friction, bc frictional force prevent us from slipping. No motion of the foot, no work. Of course muscles do work bc in walking there is motion. Is work vector? W is scalar, But f and d are vector, bc they have direction associated with them. What are the units of work? Newton Meter N.m = Joule (J)

4.2 Kinetic and Potential Energy When work is done against the gravity an obj height is changed, and when work is done against friction, heat is produced. When work is done there is a change in energy and the amount of work done is = to the change in energy. Energy is the ability to do work, that is an obj or system that possesses energy has the ability or capability to do work. When work is done by a system, the amount of energy of the system decreases. Vice versa, when work is done on a system, the system gains energy. (remember however that not all the energy possessed by a system may be available to do work) So, work is the process by which energy is transferred from 1 obj or system to another. Work and energy have the same units of measurement. In the SI, energy is measured in Joules as is work. Both work and energy are scalar, so no direction. Kinetic Energy When a constant net force acts and work is done on an obj, the obj velocity changes. (We use: d= ½ at2.. Then we have W= F (mass x ace) x d =

F= m (mass) x a (ace) x =

½ m (at)2

d (½ at2

= ½ mv2.

This amount of work is now energy of motion and is defined as kinetic energy Kinetic Energy is the energy an obj possesses bc of its motion, or simply stated it is the energy of motion. Kinetic Energy= ½. Mass.V2 Ek = ½ mv2

Suppose work is done on a moving obj. Because the obj is moving, it already has some kinetic energy, and the work done goes into changing the kinetic energy. Work = change in kinetic energy W= change Ek = EK2- Ek1 = ½ mv22 – ½ mv21 IF an obj is initially at rest v1 = 0, then the change in kinetic energy is equal to the kinetic energy of the ob. To find the change in kinetic energy, you must find the kinetic energy for each velocity and then subtract, not find the change or difference in velocities and then compute to find the change in kinetic energy Ex 4.1 done Suppose now that you wanted to stop a moving obj such as an automobile. Work must change in kinetic energy. The work is generally supplied by brake fiction. Now we are concerned about the braking distance, which is the distance the car travels after the brakes are applied. The work done to stop a moving car is equal to the braking force (F) x d the braking distance. (W= F.d) F.d = ½ m.v2. Assuming that the braking force is constant, the braking distance is directly proportional to the square of the velocity d = v2. Squaring the V makes a big difference in the braking distances. If the speed is doubled, then the braking distance is increased by a factor of 4. The braking distance of a car traveling at 32 km/hr is about 8m . For a car traveling 64 ( twice velocity) the braking distance is 4 times 8 m (32 m). Potential Energy Potential Energy is the energy an obj has because of its position or location, or more simply, it is the energy of position. Work is done in changing the position of an obj, so there is a change in energy. Ex: When an obj is lifted at a slow constant velocity, there is no net force on it, bc its not accelerating. The weight m.g of the obj acts downward, and there is an equal and opposite upward force. The distance parallel to the applied upward force is the height h, which the object is lifted. Thus, the work done against gravity is Work = weight x height or W= m.g.h With work being done, the energy of the book changes from 1 to 8kg, and the book on the table has the ability to do work bc of its height or position. It could crush something if fall from a table.

This energy is called Gravitational potential energy. Another example, the water stored behind a dam has potential energy is used to generate electrical energy. The gravitational potential energy Ep is equal to the work done, and this is equal to the weight of the object x by the height. Gravitational potential energy = weight x height or Ep = (m.g).h When work is done by or against gravity, the potential energy changes and Work = change in potential energy Ep2 – Ep1 =

m.g.h2 – mgh1

so = mg (h2-h1)

= mg change in h (height) An obj has a potential energy for each particular height or position. The value of the gravitational potential energy at a particular position depends on the reference point or zero point from which the height is measured. Using an arbitrary zero point is like using a point other than the zero mark on a meterstick to measure length. This practice may give rise to negative positions, such as the minus positions on a cartersian graph. Ex paper Heights may be positive or negative relative to the zero reference point. A negative (–h) gives a negative potential energy. A negative potential energy is analogous to a position. There are other types of potential energy besides gravitational. For example, when a spring is compressed or stretched, work is done (against the spring force) and the spring has potential energy as a result of the change in length (position). By what process is energy transferred from one object to another? Energy is the ability to do work, and work is the process by which energy is transferred from one obj to another To find the difference in gravitational potential energies, the difference in heights is taken. What is taken to find the difference in kinetic energies? To find the difference in kinetic energies, the difference in the squares of the velocity is taken change in Ek= ½.m.v22 – v21. Not the difference in velocities squared (v2- v1)

4.3 Conservation of Energy Energy may change from one form to another and does so without a net gain or a net lost. Energy is then conserved and the total amount remains constant. For example, energy can be neither created nor destroyed. And in changing from one form to another, energy is always conserved. The law of conversation of total energy may be stated as follows. The total energy of an isolated system remains constant A system is something enclosed, and isolated means that nothing from the outside affects the system (and vice versa) For example, the students in a classroom might be considered a system. They may move around in the room, but if no one leaves or enters, then the number of students is conserved (the law of conservation of students). It is sometimes said that the total energy of the universe is conserved, which is true. The universe is the largest system of which we can think, and all the energy that has ever been in the universe is still there somewhere in some form or other. To simplify the understanding of the conservation of energy, we often consider ideal systems in which the energy is in only two forms, kinetic, and potential. In this case, there is conversation of mechanical energy, it can be written as initial energy

=

final energy

(Ek + Ep)1

=

(Ek + Ep)2

(1/2 m.v2 + mgh)1

= (1/2m.v2 + mgh)2

Here no energy is lost in the form of heat bc of frictional effects (or any other cause) Ex 4.2 done Overall, can energy be created or destroyed? In changing energy from one form to another, the total energy is always conserved What is the difference btw total and mechanical energy? Total energy is all the energy of an isolated system, which may be of any form. Mechanical energy is that of an ideal system having only kinetic and potential energies.

4.4 Power To express how fast work is done, the concept of power is used. Power is the time rate of doing work. Power is calculated by dividing the work done by the time required to do the work Power= work/ time

p= W/t

Or the same as Power = Force x distance/ time =

p= F x d /t

Power has the units of joules per second J/s. This unit has the special name of WATT. It because James Watt, who improved steam system. 1 W = 1 J/s A larger unit, the horsepower (hp) is used to rate the power of motors and engines 1 horsepower = 550 ft. lb/s = 746 W The greater the power of an engine or motor, the faster it can do work, that is, 2 hp motor can o twice as much work as a 1 hp motor in the same amount of time. Or one 2hp motor can do the same amount of work as a 1 hp in half the time Ex 4.3 done pg 89 As we have seen, work produces a change in energy. Thus, power may be thought of as energy produced or consumed divided by the time taken to do so. Power = energy produced or consumed / time taken or

p= E/t

E = p.t The equation above is useful in computing the amount of electrical energy consumed in the home. Bc Energy is power x times (W.s). Using the larger units of kilowat (kW) and hour (h) gives the larger unit of kilowat-hour = (kWh) Ex 4.4 pag 90 What is the difference in the operations of a 2hp motor and 1 hp motor? 2 hp motor can do twice as much work as a 1 hp in the same amount of time, or the same amount of work in half the time Electric bills from power companies charge for so many kilowatts hours. What are we paying for? The kilowatt hour is a unit of energy E= pt

4.5 Forms of Energy and Consumption We commonly talk about various forms of energy such as chemical energy and electrical energy. Many forms of energy exist, but the main unifying concept is the conservation of energy. Energy cannot be created or destroyed, but it change from one form to another. Pendulum experiment. The pendulum will eventually come to a stop. Where did the energy go? Of course, friction is involved. In most practical situations, Kinetic and Potential energies of objs eventually ended up as heat. Heat is transferred energy that becomes associated with kinetic and potential energies on molecular level. The gravitational potential energy of water is used to generate electricity in hydroelectric. Electricity may be described in terms of electrical force and electrical energy. This energy is associated with the motions of electric charges. Electrical forces hold atoms and molecules together, and there is potential energy in these holds or bonds. When fuel is burned, a rearrangement of the electrons and atoms in the fuel occurs, and energy chemical energy is released. Our main fossil fuels ( coal, petroleum, gas) are indirectly the result of the sun’s energy. This radiant energy or light from the sun is electromagnetic radiation. Visible lights, radio waves, tv waves and microwaves are examples of electromagnetic. A recent entry into the energy sweepstakes is Nuclear energy. In this case, mass is considered to be a form of energy. As we go about our daily lives, each of us is constantly using and giving off energy from body heat. The source of this energy is food. An adult radiates heat energy at about the same rate as a 100 w light bulb. The commercial sources of energy on a national scale are mainly coal, oil (petroleum), and natural gas. Nuclear and hydroelectric energies are about the only other significant commercial sources. The United States does have large reserves of coal. It is its major energy source for generation of electricity. Energy Consumption Although the United States has less than 5% of world’s population, it accounts for 26% of the world’s annual energy consumption of fossil fuels: coal, oil, and natural gas. How many common forms of energy are there? What are they? There are 6 common, or conventional forms of energy, chemical, electrical, nuclear, gravitational, radiant, and thermal.

What are the two leading fuels consumed in the US, and which is used more in the generation of electricity? Oil and coal are the leading fuels consumed in the Us. Almost half the electricity consumed is generated by burning coal 4.6 Alternative and Renewable Energy Sources. Fossil- fuel combustion contributes to pollution and possible climate change. The amount of fossil fuels is limited. They will be depleted someday. Alternative energy sources are energy sources that are not based on the burning of fossil fuels and nuclear process Renewable energy sources are energy sources from natural processes that are constantly replenished. In large part these energy sources overlap. It is estimated that they account for about 7-8% of the energy consumption in the united states Hydropower Its used to produce electricity. Falling water generates electricity cleanly and efficiently. However, most of the best sites for dams have already been developed. The damming of rivers usually results in the loss of agricultural land and alters ecosystems. Wind Power Windmills for pumping water were once common on American farms. Nowadays there are more modern wind turbines. Wind power generates electricity directly. The wind is free and nonpolluting. However, the limited availability of sites with sufficient wind (at least 20 km/h) prevents widespread development of wind power, and the wind does not blow continuously. Solar Power The sun is our major source of energy and one of the most promising sources of energy for the future. Solar heating and cooling systems are used in some homes and businesses, and other technologies focus on concentrating solar radiation for energy production. One of the most environmentally promising solar applications is the photovoltaic cell. These cells convert sunlight directly into electricity. The light meter used in photography is a photocell, photocell arrays are used on earth satellites. Efficiency has been a problem with photocells. Electricity from photocells costs 30 cents per kWh, which is not economically competitive with electricity produced from fossil average 10 cents.

Geothermal Geothermal hotspots and volcanic features can be found around the world. The earth interior is hot, and heat is energy. Steam from geysers in California and Italy are used to generate electricity. Such systems are relatively inefficient and costly Tides (mares) Unlike the weather problems with wind and solar energy production, tidal energy production is steady. There is constant water motion and thus a constant energy source. Biofuels A mixture of gasoline an ethanol called gasohol is used to run cars. Ethanol is advertised as reducing air pollution when mixed and burned with gasoline. Some pollution is reduced, but there are still emissions. There is also biodiesel that is made by the chemically reacting of vegetable oil with an alcohol. Algae use photosynthesis to produce energy for rapid growth and can double in weight several times on a sunny day. Alga produce oils which can be harvested as biofuels. Biomass Biomass is any organic matter available on a renewable basis. It includes agricultural crops, wood, and wood wastes, animal wastes, municipal wastes, and aquatic plants. Processed and capable of being burned, biomass constitutes a source of energy some of which can be used in transportation fuels or chemicals. In addition to alternative energy resources, emphasis is placed on using our available energy more efficiently. Appliances come with energy guide labels that compare energy costs or usage. What is the difference between alternative and renewable energy sources? Alternative energy sources are those not based on fossil fuels and nuclear processes: biofuels are an example. Renewable energy sources are those that cannot be exhausted; solar and wind are examples Why are solar power and wind power somewhat unreliable? Solar power (sunlight) varies bc of weather conditions and seasonal changes. Wind power varies bc the wind does not blow continuously....