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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Conservative Forces and Potential Energy | m42149 | Conservation of Mechanical Energy | Let us now consider what form the work-energy theorem takes when only conservative forces are involved. This will lead us to the conservation of energy principle. The work-energy theorem states that the net work done by all forces acting on a system equals its change in kinetic energy. In equation form, this is |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Nonconservative Forces | m42150 | Nonconservative Forces and Friction | Forces are either conservative or nonconservative. Conservative forces were discussed in Conservative Forces and Potential Energy. A nonconservative force is one for which work depends on the path taken. Friction is a good example of a nonconservative force. As illustrated in [link], work done against friction depends on the length of the path between the starting and ending points. 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. Furthermore, even if the thermal energy is retained or captured, it cannot be fully converted back to work, so it is lost or not recoverable in that sense as well. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Nonconservative Forces | m42150 | 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. [link] compares the effects of conservative and nonconservative forces. We often choose to understand simpler systems such as that described in [link](a) first before studying more complicated systems as in [link](b). |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Nonconservative Forces | m42150 | How the Work-Energy Theorem Applies | Now let us consider what form the work-energy theorem takes when both conservative and nonconservative forces act. We will see that the work done by nonconservative forces equals the change in the mechanical energy of a system. As noted in Kinetic Energy and the Work-Energy Theorem, the work-energy theorem states that the net work on a system equals the change in its kinetic energy, or ${W}_{\text{net}}=\text{ΔKE}$. The net work is the sum of the work by nonconservative forces plus the work by conservative forces. That is, |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Nonconservative Forces | m42150 | Applying Energy Conservation with Nonconservative Forces | When no change in potential energy occurs, applying ${\text{KE}}_{\text{i}}+{\text{PE}}_{\text{i}}+{W}_{\text{nc}}={\text{KE}}_{\text{f}}+{\text{PE}}_{\text{f}}$ amounts to applying the work-energy theorem by setting the change in kinetic energy to be equal to the net work done on the system, which in the most general case includes both conservative and nonconservative forces. But when seeking instead to find a change in total mechanical energy in situations that involve changes in both potential and kinetic energy, the previous equation
${\text{KE}}_{\text{i}}+{\text{PE}}_{\text{i}}+{W}_{\text{nc}}={\text{KE}}_{\text{f}}+{\text{PE}}_{\text{f}}$
says that you can start by finding the change in mechanical energy that would have resulted from just the conservative forces, including the potential energy changes, and add to it the work done, with the proper sign, by any nonconservative forces involved. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Conservation of Energy | m42151 | Law of Conservation of Energy | Energy, as we have noted, is conserved, making it one of the most important physical quantities in nature. The law of conservation of energy can be stated as follows: |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Conservation of Energy | m42151 | Other Forms of Energy than Mechanical Energy | At this point, we deal with all other forms of energy by lumping them into a single group called other energy ($\text{OE}$). Then we can state the conservation of energy in equation form as |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Conservation of Energy | m42151 | Some of the Many Forms of Energy | What are some other forms of energy? You can probably name a number of forms of energy not yet discussed. Many of these will be covered in later chapters, but let us detail a few here. Electrical energy is a common form that is converted to many other forms and does work in a wide range of practical situations. 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. Batteries can in turn produce light, which is a very pure form of energy. 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. Nuclear energy comes from processes that convert measurable amounts of mass into energy. 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. Atoms and molecules inside all objects are in random motion. This internal mechanical energy from the random motions is called thermal energy, because it is related to the temperature of the object. These and all other forms of energy can be converted into one another and can do work. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Conservation of Energy | m42151 | Transformation of Energy | The transformation of energy from one form into others is happening all the time. The chemical energy in food is converted into thermal energy through metabolism; light energy is converted into chemical energy through photosynthesis. In a larger example, the chemical energy contained in coal is converted into thermal energy as it burns to turn water into steam in a boiler. This thermal energy in the steam in turn is converted to mechanical energy as it spins a turbine, which is connected to a generator to produce electrical energy. (In all of these examples, not all of the initial energy is converted into the forms mentioned. This important point is discussed later in this section.) |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Conservation of Energy | m42151 | 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 $\text{Eff}$ of an energy conversion process is defined as |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Power | m42152 | What is Power? | *Power*—the word conjures up many images: a professional football player muscling aside his opponent, a dragster roaring away from the starting line, a volcano blowing its lava into the atmosphere, or a rocket blasting off, as in [link]. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Power | m42152 | Calculating Power from Energy | It is impressive that this woman’s useful power output is slightly less than 1 horsepower $\left(\text{1 hp}=\text{746 W}\right)$! People can generate more than a horsepower with their leg muscles for short periods of time by rapidly converting available blood sugar and oxygen into work output. (A horse can put out 1 hp for hours on end.) Once oxygen is depleted, power output decreases and the person begins to breathe rapidly to obtain oxygen to metabolize more food—this is known as the *aerobic* stage of exercise. If the woman climbed the stairs slowly, then her power output would be much less, although the amount of work done would be the same. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Power | m42152 | Examples of Power | Examples of power are limited only by the imagination, because there are as many types as there are forms of work and energy. (See [link] for some examples.) Sunlight reaching Earth’s surface carries a maximum power of about 1.3 kilowatts per square meter $\left({\text{kW/m}}^{2}\right)\text{.}$ A tiny fraction of this is retained by Earth over the long term. Our consumption rate of fossil fuels is far greater than the rate at which they are stored, so it is inevitable that they will be depleted. Power implies that energy is transferred, perhaps changing form. It is never possible to change one form completely into another without losing some of it as thermal energy. For example, a 60-W incandescent bulb converts only 5 W of electrical power to light, with 55 W dissipating into thermal energy. Furthermore, the typical electric power plant converts only 35 to 40% of its fuel into electricity. The remainder becomes a huge amount of thermal energy that must be dispersed as heat transfer, as rapidly as it is created. A coal-fired power plant may produce 1000 megawatts; 1 megawatt (MW) is ${\text{10}}^{6}{\rule{0.25em}{0ex}}\text{W}$ of electric power. But the power plant consumes chemical energy at a rate of about 2500 MW, creating heat transfer to the surroundings at a rate of 1500 MW. (See [link].) |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Power | m42152 | 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. The power consumption rate is $P=W/t=E/t$, where $E$ is the energy supplied by the electricity company. So the energy consumed over a time $t$ is |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Work, Energy, and Power in Humans | m42153 | Energy Conversion in Humans | Our own bodies, like all living organisms, are energy conversion machines. Conservation of energy implies that the chemical energy stored in food is converted into work, thermal energy, and/or stored as chemical energy in fatty tissue. (See [link].) The fraction going into each form depends both on how much we eat and on our level of physical activity. If we eat more than is needed to do work and stay warm, the remainder goes into body fat. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Work, Energy, and Power in Humans | m42153 | Power Consumed at Rest | The *rate* at which the body uses food energy to sustain life and to do different activities is called the metabolic rate. The total energy conversion rate of a person *at rest* is called the basal metabolic rate (BMR) and is divided among various systems in the body, as shown in [link]. The largest fraction goes to the liver and spleen, with the brain coming next. Of course, during vigorous exercise, the energy consumption of the skeletal muscles and heart increase markedly. About 75% of the calories burned in a day go into these basic functions. The BMR is a function of age, gender, total body weight, and amount of muscle mass (which burns more calories than body fat). Athletes have a greater BMR due to this last factor. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | Work, Energy, and Power in Humans | m42153 | Power of Doing Useful Work | Work done by a person is sometimes called useful work, which is *work done on the outside world*, such as lifting weights. Useful work requires a force exerted through a distance on the outside world, and so it excludes internal work, such as that done by the heart when pumping blood. Useful work does include that done in climbing stairs or accelerating to a full run, because these are accomplished by exerting forces on the outside world. Forces exerted by the body are nonconservative, so that they can change the mechanical energy ($\text{KE}+\text{PE}$) of the system worked upon, and this is often the goal. A baseball player throwing a ball, for example, increases both the ball’s kinetic and potential energy. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | World Energy Use | m42154 | Renewable and Nonrenewable Energy Sources | The principal energy resources used in the world are shown in [link]. The fuel mix has changed over the years but now is dominated by oil, although natural gas and solar contributions are increasing. Renewable forms of energy are those sources that cannot be used up, such as water, wind, solar, and biomass. About 85% of our energy comes from nonrenewable fossil fuels—oil, natural gas, coal. The likelihood of a link between global warming and fossil fuel use, with its production of carbon dioxide through combustion, has made, in the eyes of many scientists, a shift to non-fossil fuels of utmost importance—but it will not be easy. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | World Energy Use | m42154 | The World’s Growing Energy Needs | World energy consumption continues to rise, especially in the developing countries. (See [link].) Global demand for energy has tripled in the past 50 years and might triple again in the next 30 years. While much of this growth will come from the rapidly booming economies of China and India, many of the developed countries, especially those in Europe, are hoping to meet their energy needs by expanding the use of renewable sources. Although presently only a small percentage, renewable energy is growing very fast, especially wind energy. For example, Germany plans to meet 65% of its power and 30% of its overall energy needs with renewable resources by the year 2030. (See [link].) Energy is a key constraint in the rapid economic growth of China and India. In 2003, China surpassed Japan as the world’s second largest consumer of oil. However, over 1/3 of this is imported. Unlike most Western countries, coal dominates the commercial energy resources of China, accounting for 2/3 of its energy consumption. In 2009 China surpassed the United States as the largest generator of ${\text{CO}}_{2}$. In India, the main energy resources are biomass (wood and dung) and coal. Half of India’s oil is imported. About 70% of India’s electricity is generated by highly polluting coal. Yet there are sizeable strides being made in renewable energy. India has a rapidly growing wind energy base, and it has the largest solar cooking program in the world. China has invested substantially in building solar collection farms as well as hydroelectric plants. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | World Energy Use | m42154 | Energy and Economic Well-being | Economic well-being is dependent upon energy use, and in most countries higher standards of living, as measured by GDP (gross domestic product) per capita, are matched by higher levels of energy consumption per capita. This is borne out in [link]. Increased efficiency of energy use will change this dependency. A global problem is balancing energy resource development against the harmful effects upon the environment in its extraction and use. |
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College Physics for AP® Courses 2e | Work, Energy, and Energy Resources | World Energy Use | m42154 | Conserving Energy | As we finish this chapter on energy and work, it is relevant to draw some distinctions between two sometimes misunderstood terms in the area of energy use. As has been mentioned elsewhere, the “law of the conservation of energy” is a very useful principle in analyzing physical processes. It is a statement that cannot be proven from basic principles, but is a very good bookkeeping device, and no exceptions have ever been found. It states that the total amount of energy in an isolated system will always remain constant. Related to this principle, but remarkably different from it, is the important philosophy of energy conservation. This concept has to do with seeking to decrease the amount of energy used by an individual or group through (1) reduced activities (e.g., turning down thermostats, driving fewer kilometers) and/or (2) increasing conversion efficiencies in the performance of a particular task—such as developing and using more efficient room heaters, cars that have greater miles-per-gallon ratings, energy-efficient compact fluorescent lights, etc. |
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College Physics for AP® Courses 2e | Linear Momentum and Collisions | Connection for AP® courses | m55108 | |||
College Physics for AP® Courses 2e | Linear Momentum and Collisions | Linear Momentum and Force | m42156 | Linear Momentum | The scientific definition of linear momentum is consistent with most people’s intuitive understanding of momentum: a large, fast-moving object has greater momentum than a smaller, slower object. Linear momentum is defined as the product of a system’s mass multiplied by its velocity. In symbols, linear momentum is expressed as |
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College Physics for AP® Courses 2e | Linear Momentum and Collisions | Linear Momentum and Force | m42156 | Momentum and Newton’s Second Law | The importance of momentum, unlike the importance of energy, was recognized early in the development of classical physics. Momentum was deemed so important that it was called the “quantity of motion.” Newton actually stated his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. Using symbols, this law is |
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College Physics for AP® Courses 2e | Linear Momentum and Collisions | Impulse | m42159 | |||
College Physics for AP® Courses 2e | Linear Momentum and Collisions | Conservation of Momentum | m42162 | Subatomic Collisions and Momentum | The conservation of momentum principle not only applies to the macroscopic objects, it is also essential to our explorations of atomic and subatomic particles. Giant machines hurl subatomic particles at one another, and researchers evaluate the results by assuming conservation of momentum (among other things). |
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College Physics for AP® Courses 2e | Linear Momentum and Collisions | Elastic Collisions in One Dimension | m42163 | |||
College Physics for AP® Courses 2e | Linear Momentum and Collisions | Inelastic Collisions in One Dimension | m42164 | |||
College Physics for AP® Courses 2e | Linear Momentum and Collisions | Collisions of Point Masses in Two Dimensions | m42165 | Elastic Collisions of Two Objects with Equal Mass | Some interesting situations arise when the two colliding objects have equal mass and the collision is elastic. This situation is nearly the case with colliding billiard balls, and precisely the case with some subatomic particle collisions. We can thus get a mental image of a collision of subatomic particles by thinking about billiards (or pool). (Refer to [link] for masses and angles.) First, an elastic collision conserves internal kinetic energy. Again, let us assume object 2 $\left({m}_{2}\right)$ is initially at rest. Then, the internal kinetic energy before and after the collision of two objects that have equal masses is |
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College Physics for AP® Courses 2e | Linear Momentum and Collisions | Introduction to Rocket Propulsion | m42166 | |||
College Physics for AP® Courses 2e | Statics and Torque | Connection for AP® Courses | m55175 | |||
College Physics for AP® Courses 2e | Statics and Torque | The First Condition for Equilibrium | m42170 | |||
College Physics for AP® Courses 2e | Statics and Torque | The Second Condition for Equilibrium | m42171 | |||
College Physics for AP® Courses 2e | Statics and Torque | Stability | m42172 | |||
College Physics for AP® Courses 2e | Statics and Torque | Applications of Statics, Including Problem-Solving Strategies | m42173 | |||
College Physics for AP® Courses 2e | Statics and Torque | Simple Machines | m42174 | |||
College Physics for AP® Courses 2e | Statics and Torque | Forces and Torques in Muscles and Joints | m42175 | |||
College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Connection for AP® Courses | m55182 | |||
College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Angular Acceleration | m42177 | |||
College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Kinematics of Rotational Motion | m42178 | |||
College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Dynamics of Rotational Motion: Rotational Inertia | m42179 | Rotational Inertia and Moment of Inertia | Before we can consider the rotation of anything other than a point mass like the one in [link], we must extend the idea of rotational inertia to all types of objects. To expand our concept of rotational inertia, we define the moment of inertia
$I$ of an object to be the sum of
${\text{mr}}^{2}$ for all the point masses of which it is composed. That is,
$I=\sum {\text{mr}}^{2}$. Here
$I$ is analogous to
$m$ in translational motion. Because of the distance
$r$, the moment of inertia for any object depends on the chosen axis. Actually, calculating
$I$ is beyond the scope of this text except for one simple case—that of a hoop, which has all its mass at the same distance from its axis. A hoop’s moment of inertia around its axis is therefore
${\text{MR}}^{2}$, where
$M$ is its total mass and $R$ its radius. (We use $M$ and $R$ for an entire object to distinguish them from $m$ and $r$ for point masses.) In all other cases, we must consult [link] (note that the table is piece of artwork that has shapes as well as formulae) for formulas for $I$ that have been derived from integration over the continuous body. Note that $I$ has units of mass multiplied by distance squared ($\text{kg}\cdot {\text{m}}^{2}$), as we might expect from its definition. |
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College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Rotational Kinetic Energy: Work and Energy Revisited | m42180 | How Thick Is the Soup? Or Why Don’t All Objects Roll Downhill at the Same Rate? | One of the quality controls in a tomato soup factory consists of rolling filled cans down a ramp. If they roll too fast, the soup is too thin. Why should cans of identical size and mass roll down an incline at different rates? And why should the thickest soup roll the slowest? |
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College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Angular Momentum and Its Conservation | m42182 | Conservation of Angular Momentum | We can now understand why Earth keeps on spinning. As we saw in the previous example, $\text{Δ}L=\left(\text{net}{\rule{0.25em}{0ex}}\tau \right)\text{Δ}t$. This equation means that, to change angular momentum, a torque must act over some period of time. Because Earth has a large angular momentum, a large torque acting over a long time is needed to change its rate of spin. So what external torques are there? Tidal friction exerts torque that is slowing Earth’s rotation, but tens of millions of years must pass before the change is very significant. Recent research indicates the length of the day was 18 h some 900 million years ago. Only the tides exert significant retarding torques on Earth, and so it will continue to spin, although ever more slowly, for many billions of years. |
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College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Collisions of Extended Bodies in Two Dimensions | m42183 | |||
College Physics for AP® Courses 2e | Rotational Motion and Angular Momentum | Gyroscopic Effects: Vector Aspects of Angular Momentum | m42184 | |||
College Physics for AP® Courses 2e | Fluid Statics | Connection for AP® Courses | m55199 | |||
College Physics for AP® Courses 2e | Fluid Statics | What Is a Fluid? | m42186 | |||
College Physics for AP® Courses 2e | Fluid Statics | Density | m42187 | |||
College Physics for AP® Courses 2e | Fluid Statics | Pressure | m42189 | |||
College Physics for AP® Courses 2e | Fluid Statics | Variation of Pressure with Depth in a Fluid | m42192 | |||
College Physics for AP® Courses 2e | Fluid Statics | Pascal’s Principle | m42193 | Application of Pascal’s Principle | One of the most important technological applications of Pascal’s principle is found in a *hydraulic system*, which is an enclosed fluid system used to exert forces. The most common hydraulic systems are those that operate car brakes. Let us first consider the simple hydraulic system shown in [link]. |
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College Physics for AP® Courses 2e | Fluid Statics | Pascal’s Principle | m42193 | Relationship Between Forces in a Hydraulic System | We can derive a relationship between the forces in the simple hydraulic system shown in [link] by applying Pascal’s principle. Note first that the two pistons in the system are at the same height, and so there will be no difference in pressure due to a difference in depth. Now the pressure due to ${F}_{1}$ acting on area ${A}_{1}$ is simply ${P}_{1}=\frac{{F}_{1}}{{A}_{1}}$, as defined by $P=\frac{F}{A}$. According to Pascal’s principle, this pressure is transmitted undiminished throughout the fluid and to all walls of the container. Thus, a pressure ${P}_{2}$ is felt at the other piston that is equal to ${P}_{1}$. That is ${P}_{1}={P}_{2}$. |
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College Physics for AP® Courses 2e | Fluid Statics | Gauge Pressure, Absolute Pressure, and Pressure Measurement | m42195 | |||
College Physics for AP® Courses 2e | Fluid Statics | Archimedes’ Principle | m42196 | Floating and Sinking | Drop a lump of clay in water. It will sink. Then mold the lump of clay into the shape of a boat, and it will float. Because of its shape, the boat displaces more water than the lump and experiences a greater buoyant force. The same is true of steel ships. |
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College Physics for AP® Courses 2e | Fluid Statics | Archimedes’ Principle | m42196 | Density and Archimedes’ Principle | Density plays a crucial role in Archimedes’ principle. The average density of an object is what ultimately determines whether it floats. If its average density is less than that of the surrounding fluid, it will float. This is because the fluid, having a higher density, contains more mass and hence more weight in the same volume. The buoyant force, which equals the weight of the fluid displaced, is thus greater than the weight of the object. Likewise, an object denser than the fluid will sink. |
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College Physics for AP® Courses 2e | Fluid Statics | Archimedes’ Principle | m42196 | More Density Measurements | One of the most common techniques for determining density is shown in [link]. |
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College Physics for AP® Courses 2e | Fluid Statics | Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action | m42197 | Cohesion and Adhesion in Liquids | Children blow soap bubbles and play in the spray of a sprinkler on a hot summer day. (See [link].) An underwater spider keeps his air supply in a shiny bubble he carries wrapped around him. A technician draws blood into a small-diameter tube just by touching it to a drop on a pricked finger. A premature infant struggles to inflate her lungs. What is the common thread? All these activities are dominated by the attractive forces between atoms and molecules in liquids—both within a liquid and between the liquid and its surroundings. |
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College Physics for AP® Courses 2e | Fluid Statics | Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action | m42197 | Surface Tension | Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension. Molecules on the surface are pulled inward by cohesive forces, reducing the surface area. Molecules inside the liquid experience zero net force, since they have neighbors on all sides. |
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College Physics for AP® Courses 2e | Fluid Statics | Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action | m42197 | Adhesion and Capillary Action | Why is it that water beads up on a waxed car but does not on bare paint? The answer is that the adhesive forces between water and wax are much smaller than those between water and paint. Competition between the forces of adhesion and cohesion are important in the macroscopic behavior of liquids. An important factor in studying the roles of these two forces is the angle $\theta$ between the tangent to the liquid surface and the surface. (See [link].) The contact angle $\theta$ is directly related to the relative strength of the cohesive and adhesive forces. The larger the strength of the cohesive force relative to the adhesive force, the larger $\theta$ is, and the more the liquid tends to form a droplet. The smaller $\theta$ is, the smaller the relative strength, so that the adhesive force is able to flatten the drop. [link] lists contact angles for several combinations of liquids and solids. |
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College Physics for AP® Courses 2e | Fluid Statics | Pressures in the Body | m42199 | Pressure in the Body | Next to taking a person’s temperature and weight, measuring blood pressure is the most common of all medical examinations. Control of high blood pressure is largely responsible for the significant decreases in heart attack and stroke fatalities achieved in the last three decades. The pressures in various parts of the body can be measured and often provide valuable medical indicators. In this section, we consider a few examples together with some of the physics that accompanies them. |
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College Physics for AP® Courses 2e | Fluid Statics | Pressures in the Body | m42199 | Blood Pressure | Common arterial blood pressure measurements typically produce values of 120 mm Hg and 80 mm Hg, respectively, for systolic and diastolic pressures. Both pressures have health implications. When systolic pressure is chronically high, the risk of stroke and heart attack is increased. If, however, it is too low, fainting is a problem. Systolic pressure increases dramatically during exercise to increase blood flow and returns to normal afterward. This change produces no ill effects and, in fact, may be beneficial to the tone of the circulatory system. Diastolic pressure can be an indicator of fluid balance. When low, it may indicate that a person is hemorrhaging internally and needs a transfusion. Conversely, high diastolic pressure indicates a ballooning of the blood vessels, which may be due to the transfusion of too much fluid into the circulatory system. High diastolic pressure is also an indication that blood vessels are not dilating properly to pass blood through. This can seriously strain the heart in its attempt to pump blood. |
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College Physics for AP® Courses 2e | Fluid Statics | Pressures in the Body | m42199 | Pressure in the Eye | The shape of the eye is maintained by fluid pressure, called intraocular pressure, which is normally in the range of 12.0 to 24.0 mm Hg. When the circulation of fluid in the eye is blocked, it can lead to a buildup in pressure, a condition called glaucoma. The net pressure can become as great as 85.0 mm Hg, an abnormally large pressure that can permanently damage the optic nerve. To get an idea of the force involved, suppose the back of the eye has an area of $6\text{.}0{\rule{0.25em}{0ex}}{\text{cm}}^{2}$, and the net pressure is 85.0 mm Hg. Force is given by
$F=\text{PA}$. To get
$F$ in newtons, we convert the area to
${\text{m}}^{2}$ (
${\text{1 m}}^{2}={\text{10}}^{4}{\rule{0.25em}{0ex}}{\text{cm}}^{2}$). Then we calculate as follows: |
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College Physics for AP® Courses 2e | Fluid Statics | Pressures in the Body | m42199 | Pressure Associated with the Lungs | The pressure inside the lungs increases and decreases with each breath. The pressure drops to below atmospheric pressure (negative gauge pressure) when you inhale, causing air to flow into the lungs. It increases above atmospheric pressure (positive gauge pressure) when you exhale, forcing air out. |
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College Physics for AP® Courses 2e | Fluid Statics | Pressures in the Body | m42199 | Other Pressures in the Body | null |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Connection for AP® Courses | m55221 | |||
College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Flow Rate and Its Relation to Velocity | m42205 | |||
College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Bernoulli’s Equation | m42206 | Bernoulli’s Equation | The relationship between pressure and velocity in fluids is described quantitatively by Bernoulli’s equation, named after its discoverer, the Swiss scientist Daniel Bernoulli (1700–1782). Bernoulli’s equation states that for an incompressible, frictionless fluid, the following sum is constant: |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Bernoulli’s Equation | m42206 | Bernoulli’s Equation for Static Fluids | Let us first consider the very simple situation where the fluid is static—that is, ${v}_{1}={v}_{2}=0$. Bernoulli’s equation in that case is |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Bernoulli’s Equation | m42206 | Bernoulli’s Principle—Bernoulli’s Equation at Constant Depth | Another important situation is one in which the fluid moves but its depth is constant—that is, ${h}_{1}={h}_{2}$. Under that condition, Bernoulli’s equation becomes |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Bernoulli’s Equation | m42206 | Applications of Bernoulli’s Principle | There are a number of devices and situations in which fluid flows at a constant height and, thus, can be analyzed with Bernoulli’s principle. |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | The Most General Applications of Bernoulli’s Equation | m42208 | Torricelli’s Theorem | [link] shows water gushing from a large tube through a dam. What is its speed as it emerges? Interestingly, if resistance is negligible, the speed is just what it would be if the water fell a distance $h$ from the surface of the reservoir; the water’s speed is independent of the size of the opening. Let us check this out. Bernoulli’s equation must be used since the depth is not constant. We consider water flowing from the surface (point 1) to the tube’s outlet (point 2). Bernoulli’s equation as stated in previously is |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | The Most General Applications of Bernoulli’s Equation | m42208 | Power in Fluid Flow | Power is the *rate* at which work is done or energy in any form is used or supplied. To see the relationship of power to fluid flow, consider Bernoulli’s equation: |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Viscosity and Laminar Flow; Poiseuille’s Law | m42209 | Laminar Flow and Viscosity | When you pour yourself a glass of juice, the liquid flows freely and quickly. But when you pour syrup on your pancakes, that liquid flows slowly and sticks to the pitcher. The difference is fluid friction, both within the fluid itself and between the fluid and its surroundings. We call this property of fluids *viscosity*. Juice has low viscosity, whereas syrup has high viscosity. In the previous sections we have considered ideal fluids with little or no viscosity. In this section, we will investigate what factors, including viscosity, affect the rate of fluid flow. |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Viscosity and Laminar Flow; Poiseuille’s Law | m42209 | Laminar Flow Confined to Tubes—Poiseuille’s Law | What causes flow? The answer, not surprisingly, is pressure difference. In fact, there is a very simple relationship between horizontal flow and pressure. Flow rate *$Q$* is in the direction from high to low pressure. The greater the pressure differential between two points, the greater the flow rate. This relationship can be stated as |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Viscosity and Laminar Flow; Poiseuille’s Law | m42209 | Flow and Resistance as Causes of Pressure Drops | You may have noticed that water pressure in your home might be lower than normal on hot summer days when there is more use. This pressure drop occurs in the water main before it reaches your home. Let us consider flow through the water main as illustrated in [link]. We can understand why the pressure ${P}_{1}$ to the home drops during times of heavy use by rearranging |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | The Onset of Turbulence | m42210 | |||
College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Motion of an Object in a Viscous Fluid | m42211 | |||
College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes | m42212 | Diffusion | There is something fishy about the ice cube from your freezer—how did it pick up those food odors? How does soaking a sprained ankle in Epsom salt reduce swelling? The answer to these questions are related to atomic and molecular transport phenomena—another mode of fluid motion. Atoms and molecules are in constant motion at any temperature. In fluids they move about randomly even in the absence of macroscopic flow. This motion is called a random walk and is illustrated in [link]. Diffusion is the movement of substances due to random thermal molecular motion. Fluids, like fish fumes or odors entering ice cubes, can even diffuse through solids. |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes | m42212 | The Rate and Direction of Diffusion | If you very carefully place a drop of food coloring in a still glass of water, it will slowly diffuse into the colorless surroundings until its concentration is the same everywhere. This type of diffusion is called free diffusion, because there are no barriers inhibiting it. Let us examine its direction and rate. Molecular motion is random in direction, and so simple chance dictates that more molecules will move out of a region of high concentration than into it. The net rate of diffusion is higher initially than after the process is partially completed. (See [link].) |
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College Physics for AP® Courses 2e | Fluid Dynamics and Its Biological and Medical Applications | Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes | m42212 | Osmosis and Dialysis—Diffusion across Membranes | Some of the most interesting examples of diffusion occur through barriers that affect the rates of diffusion. For example, when you soak a swollen ankle in Epsom salt, water diffuses through your skin. Many substances regularly move through cell membranes; oxygen moves in, carbon dioxide moves out, nutrients go in, and wastes go out, for example. Because membranes are thin structures (typically $6\text{.}5×{\text{10}}^{-9}$ to $\text{10}×{\text{10}}^{-9}$ m across) diffusion rates through them can be high. Diffusion through membranes is an important method of transport. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Connection for AP® Courses | m55232 | |||
College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Temperature | m42214 | Temperature Scales | Thermometers are used to measure temperature according to well-defined scales of measurement, which use pre-defined reference points to help compare quantities. The three most common temperature scales are the Fahrenheit, Celsius, and Kelvin scales. A temperature scale can be created by identifying two easily reproducible temperatures. The freezing and boiling temperatures of water at standard atmospheric pressure are commonly used. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Temperature | m42214 | Temperature Ranges in the Universe | [link] shows the wide range of temperatures found in the universe. Human beings have been known to survive with body temperatures within a small range, from $\text{24}\text{º}\text{C}$ to $\text{44}\text{º}\text{C}$ $\left(\text{75}\text{º}\text{F}$ to $\text{111}\text{º}\text{F}$). The average normal body temperature is usually given as $\text{37}\text{.}0\text{º}\text{C}$ ($\text{98}\text{.}6\text{º}\text{F}$), and variations in this temperature can indicate a medical condition: a fever, an infection, a tumor, or circulatory problems (see [link]). |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Thermal Expansion of Solids and Liquids | m42215 | Thermal Expansion in Two and Three Dimensions | Objects expand in all dimensions, as illustrated in [link]. That is, their areas and volumes, as well as their lengths, increase with temperature. Holes also get larger with temperature. If you cut a hole in a metal plate, the remaining material will expand exactly as it would if the plug was still in place. The plug would get bigger, and so the hole must get bigger too. (Think of the ring of neighboring atoms or molecules on the wall of the hole as pushing each other farther apart as temperature increases. Obviously, the ring of neighbors must get slightly larger, so the hole gets slightly larger). |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Thermal Expansion of Solids and Liquids | m42215 | Thermal Stress | Thermal stress is created by thermal expansion or contraction (see Elasticity: Stress and Strain for a discussion of stress and strain). Thermal stress can be destructive, such as when expanding gasoline ruptures a tank. It can also be useful: for example, when two parts are joined together by heating one in manufacturing, then slipping it over the other and allowing the combination to cool. Thermal stress can explain many phenomena, such as the weathering of rocks and pavement by the expansion of ice when it freezes. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | The Ideal Gas Law | m42216 | Moles and Avogadro’s Number | It is sometimes convenient to work with a unit other than molecules when measuring the amount of substance. A mole (abbreviated mol) is defined to be the amount of a substance that contains as many atoms or molecules as there are atoms in exactly 12 grams (0.012 kg) of carbon-12. The actual number of atoms or molecules in one mole is called Avogadro’s number$\left({N}_{\text{A}}\right)$, in recognition of Italian scientist Amedeo Avogadro (1776–1856). He developed the concept of the mole, based on the hypothesis that equal volumes of gas, at the same pressure and temperature, contain equal numbers of molecules. That is, the number is independent of the type of gas. This hypothesis has been confirmed, and the value of Avogadro’s number is |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | The Ideal Gas Law | m42216 | The Ideal Gas Law Restated Using Moles | A very common expression of the ideal gas law uses the number of moles, $n$, rather than the number of atoms and molecules, $N$. We start from the ideal gas law, |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | The Ideal Gas Law | m42216 | The Ideal Gas Law and Energy | Let us now examine the role of energy in the behavior of gases. When you inflate a bike tire by hand, you do work by repeatedly exerting a force through a distance. This energy goes into increasing the pressure of air inside the tire and increasing the temperature of the pump and the air. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature | m42217 | Distribution of Molecular Speeds | The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This distribution is called the *Maxwell-Boltzmann distribution*, after its originators, who calculated it based on kinetic theory, and has since been confirmed experimentally. (See [link].) The distribution has a long tail, because a few molecules may go several times the rms speed. The most probable speed ${v}_{\text{p}}$ is less than the rms speed ${v}_{\text{rms}}$. [link] shows that the curve is shifted to higher speeds at higher temperatures, with a broader range of speeds. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Phase Changes | m42218 | *PV* Diagrams | We can examine aspects of the behavior of a substance by plotting a graph of pressure versus volume, called a *PV* diagram. When the substance behaves like an ideal gas, the ideal gas law describes the relationship between its pressure and volume. That is, |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Phase Changes | m42218 | Phase Diagrams | The plots of pressure versus temperatures provide considerable insight into thermal properties of substances. There are well-defined regions on these graphs that correspond to various phases of matter, so $\text{PT}$ graphs are called phase diagrams. [link] shows the phase diagram for water. Using the graph, if you know the pressure and temperature you can determine the phase of water. The solid lines—boundaries between phases—indicate temperatures and pressures at which the phases coexist (that is, they exist together in ratios, depending on pressure and temperature). For example, the boiling point of water is $\text{100}\text{º}\text{C}$ at 1.00 atm. As the pressure increases, the boiling temperature rises steadily to $\text{374}\text{º}\text{C}$ at a pressure of 218 atm. A pressure cooker (or even a covered pot) will cook food faster because the water can exist as a liquid at temperatures greater than $\text{100}\text{º}\text{C}$ without all boiling away. The curve ends at a point called the *critical point*, because at higher temperatures the liquid phase does not exist at any pressure. The critical point occurs at the critical temperature, as you can see for water from [link]. The critical temperature for oxygen is $–\text{118}\text{º}\text{C}$, so oxygen cannot be liquefied above this temperature. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Phase Changes | m42218 | Equilibrium | Liquid and gas phases are in equilibrium at the boiling temperature. (See [link].) If a substance is in a closed container at the boiling point, then the liquid is boiling and the gas is condensing at the same rate without net change in their relative amount. Molecules in the liquid escape as a gas at the same rate at which gas molecules stick to the liquid, or form droplets and become part of the liquid phase. The combination of temperature and pressure has to be “just right”; if the temperature and pressure are increased, equilibrium is maintained by the same increase of boiling and condensation rates. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Phase Changes | m42218 | Vapor Pressure, Partial Pressure, and Dalton’s Law | Vapor pressure is defined as the pressure at which a gas coexists with its solid or liquid phase. Vapor pressure is created by faster molecules that break away from the liquid or solid and enter the gas phase. The vapor pressure of a substance depends on both the substance and its temperature—an increase in temperature increases the vapor pressure. |
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College Physics for AP® Courses 2e | Temperature, Kinetic Theory, and the Gas Laws | Humidity, Evaporation, and Boiling | m42219 | |||
College Physics for AP® Courses 2e | Heat and Heat Transfer Methods | Connection for AP® Courses | m55253 | |||
College Physics for AP® Courses 2e | Heat and Heat Transfer Methods | Heat | m42223 | Mechanical Equivalent of Heat | It is also possible to change the temperature of a substance by doing work. Work can transfer energy into or out of a system. This realization helped establish the fact that heat is a form of energy. James Prescott Joule (1818–1889) performed many experiments to establish the mechanical equivalent of heat—*the work needed to produce the same effects as heat transfer*. In terms of the units used for these two terms, the best modern value for this equivalence is |
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College Physics for AP® Courses 2e | Heat and Heat Transfer Methods | Temperature Change and Heat Capacity | m42224 | |||
College Physics for AP® Courses 2e | Heat and Heat Transfer Methods | Phase Change and Latent Heat | m42225 | Problem-Solving Strategies for the Effects of Heat Transfer | null |
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College Physics for AP® Courses 2e | Heat and Heat Transfer Methods | Heat Transfer Methods | m42226 | |||
College Physics for AP® Courses 2e | Heat and Heat Transfer Methods | Conduction | m42228 |
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