Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
12/22/12 Chapter 2: Forces and Energy Goals of Period 2 Section 2.1: Section 2.2: Section 2.3: Section 2.4: To define the four fundamental forces To explain the relationship among forces, work, and energy To describe forms of energy To understand the law of conservation of energy 2.1 The Four Fundamental Forces of Nature Why do objects move? Forces can cause objects to move and accelerate. In this period we examine the origins of forces and find that all known forces can be classified as one of four fundamental forces. Based on their properties, all of the currently known forces fall into four types: the gravitational, electromagnetic, strong nuclear, and weak nuclear forces. All forces in the universe are due to one or more of these four fundamental forces. Even though each of these forces has unique properties, at least three of the four forces appear to be related to one another. Scientists continue to search for a grand unified theory that would explain all four fundamental forces in terms of a single underlying force law. The Gravitational Force Although the gravitational force is the weakest of the four fundamental forces, it is the most familiar force in our everyday lives. We experience the gravitational force as the mutual attraction of matter to all other matter. The gravitational force between the Earth and objects near it causes objects to fall to the surface of the Earth. The gravitational force is always an attractive force. The greater the distance between two objects, the smaller the force they exert upon one another. The greater the masses of the objects, the greater the force. The Electromagnetic Force While the electric force and the magnetic force can appear to be distinct and separate forces, they are, in fact, two different aspects of a single force -- the electromagnetic force. The electromagnetic force provides the force that bonds atoms into molecules. Matter is made up of atoms, which are composed of tiny, dense nuclei surrounded by clouds of electrons. The positively charged nucleus of an atom consists of protons and neutrons bound together by the strong nuclear force. The only significant difference between neutrons and protons is their charge – protons have a positive electric charge and neutrons have no charge. The nucleus contains more than 99.9% of the atom’s mass. The negatively charged electron cloud surrounding the nucleus accounts for nearly all of the volume of the atom. Protons and neutrons, called nucleons, have nearly equal mass, about 2,000 times the mass of an electron. 13 12/22/12 The electric charge of protons and electrons is exactly equal in magnitude but opposite in sign. In a neutral atom, the number of negatively charged electrons in the atomic cloud is equal to the number of positively charged protons in the atomic nucleus. There is an attractive electric force between the oppositely charged protons and electrons that draws protons and electrons to each other. Particles with the same electric charge, such as two protons or two electrons, repel each other electrically. Therefore, unlike the gravitational force, which is always attractive, the electric force can be an attractive or repulsive force between charged objects. The larger the charge, the greater the attractive or repulsive force. The greater the distance between charges, the weaker the force. The electromagnetic force holds matter together by providing the force that bonds atoms into molecules. The Strong Nuclear Force If particles with the same charge repel one another, how can positively charged protons exist tightly packed in an atomic nucleus? The strong nuclear force is responsible for holding the neutrons and protons of atomic nuclei together. The strong nuclear force is the strongest of all the forces, but it is effective only over very short distances, such as the diameter of a small atomic nucleus. When the strong nuclear force binds protons and neutrons, the bound object has less mass than the sum of the masses of the unbound protons and neutrons. The difference in mass between the unbound and bound neutrons and protons has been 2 converted into an amount of energy give by Einstein’s famous equation, E = M c . Here, 8 2 M is the decrease in mass, and c is the speed of light, 3 x 10 meters/second. Since c is such a huge number (9 x 1016 = 90 quadrillion m2/s2), converting even a tiny amount of mass will produce a large quantity of energy. The conversion of mass into energy is the energy source for nuclear power plants, nuclear weapons, and stars such as the Sun. While all forces involve an exchange of mass and energy, only the strong nuclear force is strong enough to produce a measurable change in the amount of mass. For example, the atoms in a metal spring are bound together by electromagnetic forces between the positive and negative charges in the atoms. Winding the spring stretches the electromagnetic bonds and increases the strain potential energy of the spring. When the spring is stretched, its increased potential energy is reflected in a very slight increase in the mass of the spring. However, unlike the case of the strong nuclear force, an increase in mass due to the electromagnetic force is too small to measure. When we study the strong nuclear force in Physics 1104, we will find that the change in mass is large enough to be measured by sophisticated scientific equipment. The Weak Nuclear Force The weak nuclear force is responsible for the type of radioactive decay that changes the nucleus of one element into a nucleus of a different element. Like the strong nuclear force, the weak nuclear force is effective only between particles that are extremely close together. Physics 1104 explores the strong and weak nuclear forces in reactions in the sun and in nuclear reactors and the decay of radioactive materials. 14 12/22/12 The Frictional Force The frictional force is NOT one of the four fundamental forces. However, it results from the fundamental electromagnetic force. In solids, atoms are held together by atomic forces, which act similarly to springs. Since surfaces are never perfectly smooth, when two objects rub together, the atoms on their surfaces bump into one another and move slightly from their equilibrium positions. These movements result in the frictional force. When the atoms are released, they vibrate back and forth. Their atomic vibrations represent the conversion of the mechanical energy of motion of objects into an increase in the thermal energy of those objects. To experience the frictional force as thermal energy, rub your hands together. 2.2 Forces, Work and Energy Work is done when a force moves an object over some distance in the direction of the force applied to the object. We use the force of our muscles to do work when we push a box across a floor. It takes energy to push the box. Energy is used to do work. Fig 2.1 Work is Done When a Force Moves an Object in the Direction of the Force The box moves in the direction of the force. Force Pushing a box with a force of 1 newton to move it a distance of 1 meter in the direction of the force requires 1 joule of work. In English units, pushing the box with a force of 1 pound to move it 1 foot in the direction of the force requires 1 foot-pound of work. The larger the force and the farther the box moves, the more work done. No work is done unless the box moves. or Work = Force x Distance W = F D where (Equation 2.1) W = work (joules or foot-pounds) F = force applied (newtons or pounds) D = distance moved in the direction of the force (meters or feet) 15 12/22/12 To lift an object, we do work against the downward force of gravity. The force of gravity acting on an object equals the object’s weight: Force of gravity = Weight = M g (Equation 2.2) M = mass of the object (kilograms) g = the acceleration of gravity (9.8 m/s2 ) where To lift an object at a constant velocity, we must exert an upward force equal to the downward force of gravity. The work done to lift the object is the product of the amount of the force of gravity acting on the object and the vertical distance it is raised. The greater the mass of the object and the higher it is lifted, the more work done. Work = force of gravity x change in height or (Equation 2.3) W = F h W = work (joules or foot-pounds) F = force of gravity (newtons or pounds) h = change in vertical height (meters or feet) where Substituting the expression for the force of gravity (Equation 2.2) into the equation for the work done against the force of gravity (Equation 2.3), we find: (Equation 2.4) W = Mg h Ignoring the energy wasted as friction, the work done against the force of gravity to lift an object is equal to the weight of the object times the vertical distance it is lifted. In the case of a falling object, work is done by gravity to make the object fall. For example, if a 5 newton rock falls 2 meters, the work by the force of gravity on the rock is 10 joules. Potential energy is stored energy, which is available to do work. The gravitational potential energy stored in a raised object is proportional to the height it is raised and to the mass of the object. Gravitational potential energy = weight x change in height E pot where = M g h (Equation 2.5) M = mass (kilograms) g = 9.8 m/s2 or 32 ft/s2 h = change in vertical height (meters or feet) If wasted energy is ignored, the work done to raise an object equals the potential energy the object gains. 16 12/22/12 Concept Check a) 2.1 How much work is done against the force of gravity to lift a 3.0 kg box 2.0 meters vertically? ________________ b) If wasted energy is ignored, how much gravitational potential energy does the box gain by being lifted 2.0 meters? _________________ 2.3 Forms of Energy Energy is important because it provides the ability to do work. Work is done when one or more forces move an object over a distance. The objects being moved can be very small, such as molecules, atoms, electrons, or protons, or they can be much larger objects. When forces act on objects and do work, energy is converted from one form to another. Although there are many ways to classify energy, we will discuss eleven forms of energy. The first three forms of energy are related to the energy of motion associated with moving objects, atoms, and molecules. Kinetic Energy (also called Mechanical Energy of Motion): Moving objects exhibit kinetic energy. A ball thrown through the air or a car travelling down a road has kinetic. Thermal Energy: Energy of motion occurs within an object as its atoms and molecules vibrate randomly. Thermal energy is the unorganized energy of motion of vibrating objects too small to see. The faster the atoms and molecules in a substance vibrate, the more thermal energy the substance has and the higher its temperature. Sound Energy: When atoms and molecules vibrate in an organized manner, their vibrations may travel as a wave. Sound is the transmission of vibrations through a solid, liquid, or gas by vibrating atoms or molecules. When sound waves reach our eardrums, the energy in the sound waves causes our eardrums to vibrate. Our brains interpret the vibrations as sounds. Matter contains positive and negative electric charges. Forms of energy that result from the forces between these charges are called electromagnetic energy. We can distinguish three forms of electromagnetic energy. 17 12/22/12 Electrical Energy: Electrical energy results from the forces between charged particles. These electrical forces exist between charged particles at rest and in motion. Magnetic Energy: Charges moving within some types of materials produce magnetic forces. These magnetic forces are in addition to the electrical forces between moving charges. Magnetic materials are called magnets and attract or repel one another due to their magnetic forces. A coil of wire with charges moving through it acts like a magnet and is called an electromagnet. Electrical and magnetic energy are closely related. Radiant Energy: While vibrations of matter produce thermal and sound energy, radiant energy results from vibrations of electric charges. Radiant energy is another name for waves of electromagnetic energy. For example, the sun’s energy is transported to Earth as waves of radiant energy. Radio waves, microwaves, infrared radiation, light waves, ultraviolet radiation, X-rays and cosmic rays are all waves of radiant energy. Figure 2.2 illustrates the relative sizes of these forms of radiant energy. Figure 2.2: Forms of Radiant Energy Source: http://spaceplace.nasa.gov Stored energy, which can be used to do work, is called potential energy. We consider five types of potential energy. Gravitational Potential Energy: When an object is raised above the Earth and released, the gravitational attraction between that object and the Earth causes the object to fall to the ground. A raised object has gravitational potential energy. 18 12/22/12 Strain Potential Energy: If we stretch or compress a spring and release it, the spring moves back toward its original length. The stretched or compressed spring has strain potential energy because it has the potential to move. Electrical Potential Energy: Electrical potential energy is stored when positive and negative electric charges are separated. The amount of stored energy depends on the number of separated charges and the distance they are separated. Chemical Potential Energy: Chemical potential energy exists because atoms and molecules can take in or give off energy when their chemical bonds are formed or broken. Nuclear Energy: In nuclear reactions, energy is given off or taken in by atomic nuclei. Energy is available from the nuclei of atoms that are radioactive and undergo nuclear changes. Nuclear energy will be discussed in detail later in this course. 2.4 Energy Conversions and Energy Conservation Energy can be converted from one form into another form, but during the conversion process some energy is wasted in undesirable forms. Figure 2.3 shows a box sliding down a ramp. When the box is at rest at the top of a ramp, all of its energy is stored as gravitational potential energy. As the box moves down the ramp, much of its gravitational potential energy is converted into kinetic energy. However, if there is a force of friction between the box and the ramp, some gravitational potential energy is converted into thermal and sound energy as the box moves. Fig. 2.3 A Box Slides down a Ramp At the bottom, the box has only kinetic energy. As it slides, the box has some gravitational potential energy and some kinetic energy. At rest at the top, the box has only potential energy. At the bottom of the ramp, the box has no gravitational potential energy. As the box moves along the floor after it has reached the bottom of the ramp, some of its 19 12/22/12 kinetic energy will continue to be converted into sound energy and some into thermal energy due to friction. Once the box has come to rest, all of its potential energy has been converted into kinetic, sound, and thermal energy. However, in this process, the total amount of energy did not change. The joules of gravitational potential energy that box had at the top of the ramp must equal the sum of its kinetic energy plus the joules of wasted thermal and sound energy at the bottom of the ramp. Once the box has stopped moving across the floor, all of its initial gravitational potential energy will have been converted into the sum of its wasted thermal and sound energy. The initial joules of energy at the beginning of this energy conversion process must equal the total joules of energy at the end of the process. This fact illustrates the law of conservation of energy . The law of conservation of energy tells us that although energy can be converted from one form of energy into another form, the total amount of energy involved in these conversions remains unchanged – energy cannot be created or destroyed. The total amount of energy we have now in the Universe is the same amount of energy that existed at its beginning. Conservation of energy applies not only to gravitational potential energy from the gravitational force, but to conversions involving any of the four fundamental forces. In this period, we will apply conservation of energy to conversions involving gravitational potential, kinetic, electrical, radiant, thermal, and sound energies. Keep in mind that the law of conservation of energy requires all of the energy put into a conversion process be accounted for at the end – no energy can be lost or destroyed. Fig. 2.4 Conservation of Energy for the Box Sliding Down the Ramp Gravitational Potential Energy In Useful Kinetic Energy Out Wasted Thermal & Sound Energy Out Grav. Potential Energy In = Kinetic Energy Out + Thermal and Sound Energy Out 20 12/22/12 From the law of conservation of energy, we know that the total energy input to an energy conversion process must equal the total energy output. However, not all of the energy out is useful. In all energy conversions, some energy is wasted. The amount of the total energy in that is converted into useful energy out is the efficiency of the conversion process. Efficiency Useful Energy Out Total Energy In (Equation 2.6) When a series of energy conversions are required to produce the desired form of energy, energy is wasted in each step of the process. The overall efficiency of a series of energy conversion processes can be quite low. The overall efficiency is the product of the efficiencies of each step in the process. Overall Efficiency = (Efficiency of step 1) x (Efficiency of step 2) x (Efficiency of step 3) x … or Overall Efficiency = Efficiency1 x Efficiency2 x Efficiency3 x ….. (Equation 2.7) Often the form of energy most readily available is not the most useful form. Coal can be burned to provide heat, but converting the chemical energy stored in coal into electrical energy requires a series of intermediate steps. In each step of the conversion process, some energy is wasted. In the process of using electricity, such as to light bulb, also wastes energy. The series of energy conversions from the chemical energy in coal to radiant energy from a light bulb can have a low efficiency. Concept Check 2.2 a) A series of two energy conversions has efficiencies of 25% and 60%. What is the overall efficiency of this series of two conversions? ________________ b) A third energy conversion is added to the process described in part a). The efficiencies of the three conversions are 25%, 60%, and 50%. What is the overall efficiency of this series of three conversions? ________________ c) Explain why the overall efficiency decreased when a third energy conversion was added. 21 12/22/12 Period 2 Summary 2.1: All forces currently known can be classified into four fundamental forces: 1) the Gravitational force, an attractive force between all objects. 2) the Electromagnetic force, electric and magnetic forces that arise from charged particles. 3) the Strong Nuclear Force that holds atomic nuclei together. 4) the Weak Nuclear Force, responsible for some nuclear decays 2.2: Work is done when a force moves an object over a distance in the direction of the force. Work = Force x Distance, or W = F D One joule of work is done when a force of 1 newton moves an object a distance of 1 meter in the direction of the force. The work needed to raise an object vertically against the force of gravity is W = M g h One joule is the amount of work done against the force of gravity when a 1 newton weight is lifted a vertical distance of 1 meter. Potential energy is stored energy, which is available to do work. The gravitational potential energy stored in a raised object is proportional to the height it is raised and to the mass of the object. E pot = M g h If wasted energy is ignored, the work done to raise an object equals the potential energy the object gains. 2.3: Energy provides the ability to do work. Energy takes many different forms. Eleven forms of energy are defined on pages 17 – 19. 2.4: The law of conservation of energy states that energy can be converted from one form into another, but energy cannot be created nor destroyed. The total amount of energy put into a conversion process must equal the total amount of energy out in all forms. When a raised object slides down a ramp, some of its stored gravitational potential energy is converted into the kinetic energy of the moving object and some energy is wasted as sound energy and as thermal energy from the friction between the object and the ramp. Conservation of energy requires that all of the original gravitational potential energy be accounted for: Potential energy in = kinetic energy out + sound and thermal energy out. 22 12/22/12 Period 2 Summary, Continued The efficiency of an energy conversion process is the ratio of the useful energy that results from the process to the total energy put into the process. Efficiency of an energy conversion = Useful Energy Out Total Energy In In many situations, producing the desirable form of energy requires a series of energy conversion processes. For a series of energy conversions, the overall efficiency is the produce of the efficiencies of the individual steps. Overall Efficiency = Efficiency1 x Efficiency2 x Efficiency3 … Solutions to Chapter 2 Concept Checks 2.1 a) W = M g h = 3.0 kg x 9.8 m/s2 x 2.0 m = 58.8 joules b) If we assume no energy is wasted, the gravitational potential energy gained by the lifted box equals the work done to lift it: 58.8 joules a) Overall Efficiency = Eff1 x Eff2 = 0.25 x 0.60 = 0.15 = 15% b) Overall Efficiency = Eff1 x Eff2 x Eff3 = 0.25 x 0.60 x 0.50 = 0.75 =7.5% c) In every energy conversion process, some energy is wasted so the efficiency of the process is less than 100%. Multiplying a value by a number less than 1 results in a product smaller than the original value. 2.2 23