Update physics_info.txt

physics_info.txt

@@ -2,4 +2,258 @@ Physics is the scientific study of matter, its fundamental constituents, its mot
 
 Physics is one of the oldest academic disciplines.[5] Over much of the past two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the Scientific Revolution in the 17th century, these natural sciences branched into separate research endeavors. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences[2] and suggest new avenues of research in these and other academic disciplines such as mathematics and philosophy.
 
-Advances in physics often enable new technologies. For example, advances in the understanding of electromagnetism, solid-state physics, and nuclear physics led directly to the development of technologies that have transformed modern society, such as television, computers, domestic appliances, and nuclear weapons;[2] advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
+Advances in physics often enable new technologies. For example, advances in the understanding of electromagnetism, solid-state physics, and nuclear physics led directly to the development of technologies that have transformed modern society, such as television, computers, domestic appliances, and nuclear weapons;[2] advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
+
+Kinematics - Objects are in motion everywhere we look. Everything from a tennis game to a space-probe flyby of the planet Neptune involves motion. When you are resting, your heart moves blood through your veins. And even in inanimate objects, there is continuous motion in the vibrations of atoms and molecules. Questions about motion are interesting in and of themselves: How long will it take for a space probe to get to Mars? Where will a football land if it is thrown at a certain angle? But an understanding of motion is also key to understanding other concepts in physics. An understanding of acceleration, for example, is crucial to the study of force. Kinematics is the branch of classical mechanics which describes the motion of points, bodies, and systems of bodies without consideration of the masses of those objects, nor the forces that may have caused the motion.
+
+Objects are in motion everywhere we look. Everything from a tennis game to a space-probe flyby of the planet Neptune involves motion. When you are resting, your heart moves blood through your veins. And even in inanimate objects, there is continuous motion in the vibrations of atoms and molecules. Questions about motion are interesting in and of themselves: How long will it take for a space probe to get to Mars? Where will a football land if it is thrown at a certain angle? But an understanding of motion is also key to understanding other concepts in physics. An understanding of acceleration, for example, is crucial to the study of force.
+
+The motion of an American kestrel through the air can be described by the bird’s displacement, speed, velocity, and acceleration. When it flies in a straight line without any change in direction, its motion is said to be one dimensional. (credit: Vince Maidens, Wikimedia Commons)
+Our formal study of physics begins with kinematics which is defined as the study of motion without considering its causes. The word “kinematics” comes from a Greek term meaning motion and is related to other English words such as “cinema” (movies) and “kinesiology” (the study of human motion). In one-dimensional kinematics and Two-Dimensional Kinematics we will study only the motion of a football, for example, without worrying about what forces cause or change its motion. Such considerations come in other chapters. In this chapter, we examine the simplest type of motion—namely, motion along a straight line, or one-dimensional motion. In Two-Dimensional Kinematics, we apply concepts developed here to study motion along curved paths (two- and three-dimensional motion); for example, that of a car rounding a curve.
+
+Position
+In order to describe the motion of an object, you must first be able to describe its position—where it is at any particular time. More precisely, you need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, a rocket launch would be described in terms of the position of the rocket with respect to the Earth as a whole, while a professor’s position could be described in terms of where she is in relation to the nearby white board. In other cases, we use reference frames that are not stationary but are in motion relative to the Earth. To describe the position of a person in an airplane, for example, we use the airplane, not the Earth, as the reference frame.
+
+Displacement
+If an object moves relative to a reference frame (for example, if a professor moves to the right relative to a white board or a passenger moves toward the rear of an airplane), then the object’s position changes. This change in position is known as displacement. The word “displacement” implies that an object has moved, or has been displaced.
+
+Definition: Displacement
+
+Displacement is the change in position of an object:
+
+Δ𝑥=𝑥𝑓−𝑥0,
+ 
+
+where  Δ𝑥
+  is displacement,  𝑥𝑓
+  is the final position, and  𝑥0
+  is the initial position.
+
+In this text the upper case Greek letter size  Δ
+ (delta) always means “change in” whatever quantity follows it; thus, size  Δ𝑥
+  means change in position. Always solve for displacement by subtracting initial position size  𝑥0
+  from final position  𝑥𝑓
+ ​.
+
+Note that the SI unit for displacement is the meter ( 𝑚
+ ) (see Section on Physical Quantities and Units), but sometimes kilometers, miles, feet, and other units of length are used. Keep in mind that when units other than the meter are used in a problem, you may need to convert them into meters to complete the calculation.
+
+The initial and final position of a professor as she moves to the right while writing on a whiteboard. Her initial position is 1 point 5 meters. Her final position is 3 point 5 meters. Her displacement is given by the equation delta x equals x sub f minus x sub 0 equals 2 point 0 meters.
+Figure  2.1.2
+ : A professor paces left and right while lecturing. Her position relative to Earth is given by x. The +2 m displacement of the professor relative to Earth is represented by an arrow pointing to the right.
+View of an airplane with an inset of the passengers sitting inside. A passenger has just moved from his seat and is now standing in the back. His initial position was 6 point 0 meters. His final position is 2 point 0 meters. His displacement is given by the equation delta x equals x sub f minus x sub 0 equals 4 point zero meters.
+Figure  2.1.3
+ : A passenger moves from his seat to the back of the plane. His location relative to the airplane is given by x. The -4 m displacement of the passenger relative to the plane is represented by an arrow toward the rear of the plane. Notice that the arrow representing his displacement is twice as long as the arrow representing the displacement of the professor (he moves twice as far)
+Note that displacement has a direction as well as a magnitude. The professor’s displacement in Figure  2.1.2
+  is 2.0 m to the right, and the airline passenger’s displacement is 4.0 m toward the rear in Figure  2.1.3
+ . In one-dimensional motion, direction can be specified with a plus or minus sign. When you begin a problem, you should select which direction is positive (usually that will be to the right or up, but you are free to select positive as being any direction). The professor’s initial position is size x​0​ = 1.5 m and her final position is x​f ​= 3.5 m. Thus her displacement is
+
+Δ𝑥=𝑥𝑓−𝑥0=3.5𝑚−1.5𝑚=+2.0𝑚.
+ 
+
+In this coordinate system, motion to the right is positive, whereas motion to the left is negative. Similarly, the airplane passenger’s initial position is  𝑥0=6.0𝑚
+  and his final position is  𝑥𝑓=2.0𝑚
+ , so his displacement is
+
+Δ𝑥=𝑥𝑓−𝑥0=2.0𝑚−6.0𝑚=−4.0𝑚.
+ 
+
+His displacement is negative because his motion is toward the rear of the plane, or in the negative size 12{x} {} direction in our coordinate system.
+
+Distance
+Although displacement is described in terms of direction, distance is not. Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Distance has no direction and, thus, no sign. For example, the distance the professor walks is 2.0 m. The distance the airplane passenger walks is 4.0 m.
+
+It is important to note that the distance traveled, however, can be greater than the magnitude of the displacement (by magnitude, we mean just the size of the displacement without regard to its direction; that is, just a number with a unit). For example, the professor could pace back and forth many times, perhaps walking a distance of 150 m during a lecture, yet still end up only 2.0 m to the right of her starting point. In this case her displacement would be +2.0 m, the magnitude of her displacement would be 2.0 m, but the distance she traveled would be 150 m. In kinematics we nearly always deal with displacement and magnitude of displacement, and almost never with distance traveled. One way to think about this is to assume you marked the start of the motion and the end of the motion. The displacement is simply the difference in the position of the two marks and is independent of the path taken in traveling between the two marks. The distance traveled, however, is the total length of the path taken between the two marks.
+
+  is the initial position and xf is the final position. In this text, the Greek letter  Δ
+  (delta) always means “change in” whatever quantity follows it. The SI unit for displacement is the meter (m). Displacement has a direction as well as a magnitude.
+
+When you start a problem, assign which direction will be positive.
+Distance is the magnitude of displacement between two positions.
+Distance traveled is the total length of the path traveled between two positions.
+
+There is more to motion than distance and displacement. Questions such as, “How long does a foot race take?” and “What was the runner’s speed?” cannot be answered without an understanding of other concepts. In this section we add definitions of time, velocity, and speed to expand our description of motion.
+
+Snails leaving slime trails as they race each other along a flat surface.
+Figure  2.3.1
+ : The motion of these racing snails can be described by their speeds and their velocities. (credit: tobitasflickr, Flickr)
+Time
+As discussed in Physical Quantities and Units, the most fundamental physical quantities are defined by how they are measured. This is the case with time. Every measurement of time involves measuring a change in some physical quantity. It may be a number on a digital clock, a heartbeat, or the position of the Sun in the sky. In physics, the definition of time is simple—time is change, or the interval over which change occurs. It is impossible to know that time has passed unless something changes.
+
+The amount of time or change is calibrated by comparison with a standard. The SI unit for time is the second, abbreviated s. We might, for example, observe that a certain pendulum makes one full swing every 0.75 s. We could then use the pendulum to measure time by counting its swings or, of course, by connecting the pendulum to a clock mechanism that registers time on a dial. This allows us to not only measure the amount of time, but also to determine a sequence of events.
+
+How does time relate to motion? We are usually interested in elapsed time for a particular motion, such as how long it takes an airplane passenger to get from his seat to the back of the plane. To find elapsed time, we note the time at the beginning and end of the motion and subtract the two. For example, a lecture may start at 11:00 A.M. and end at 11:50 A.M., so that the elapsed time would be 50 min. Elapsed time  Δ𝑡
+  is the difference between the ending time and beginning time,
+
+Δ𝑡=𝑡𝑓−𝑡0
+ ,
+
+where  Δ𝑡
+  is the change in time or elapsed time,  𝑡𝑓
+  is the time at the end of the motion, and  𝑡0
+  is the time at the beginning of the motion. (As usual, the delta symbol,  Δ
+ , means the change in the quantity that follows it.)
+
+Life is simpler if the beginning time  𝑡0
+  is taken to be zero, as when we use a stopwatch. If we were using a stopwatch, it would simply read zero at the start of the lecture and 50 min at the end. If  𝑡0=0
+ , then
+
+Δ𝑡=𝑡𝑓≡𝑡.(2.3.1)
+
+In this text, for simplicity’s sake,
+
+motion starts at time equal to zero ( 𝑡0=0
+ )
+the symbol  𝑡
+  is used for elapsed time unless otherwise specified ( Δ𝑡=𝑡𝑓≡𝑡
+ )
+Velocity
+Your notion of velocity is probably the same as its scientific definition. You know that if you have a large displacement in a small amount of time you have a large velocity, and that velocity has units of distance divided by time, such as miles per hour or kilometers per hour.
+
+Definition: AVERAGE VELOCITY
+
+Average velocity is displacement (change in position) divided by the time of travel,
+
+𝑣¯=Δ𝑥Δ𝑡=𝑥𝑓−𝑥0𝑡𝑓−𝑡0.(2.3.2)
+
+where  𝑣¯
+  is the average (indicated by the bar over the  𝑣
+ ) velocity,  Δ𝑥
+  is the change in position (or displacement), and  𝑥𝑓
+  and  𝑥0
+  are the final and beginning positions at times  𝑡𝑓
+  and  𝑡0
+ , respectively. If the starting time  𝑡0
+  is taken to be zero, then the average velocity is simply
+
+𝑣¯=Δ𝑥𝑡.(2.3.3)
+
+Notice that this definition indicates that velocity is a vector because displacement is a vector. It has both magnitude and direction. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph), and cm/s, are in common use. Suppose, for example, an airplane passenger took 5 seconds to move −4 m (the negative sign indicates that displacement is toward the back of the plane). His average velocity would be
+
+𝑣¯=Δ𝑥𝑡=−4𝑚5𝑠=−0.8𝑚/𝑠.(2.3.4)
+The minus sign indicates the average velocity is also toward the rear of the plane.
+
+The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he goes to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals.
+
+Airplane shown from the outside. Vector arrows show paths of each individual segment of the passenger’s trip to the back of the plane.
+Figure  2.3.2
+ : A more detailed record of an airplane passenger heading toward the back of the plane, showing smaller segments of his trip.
+The smaller the time intervals considered in a motion, the more detailed the information. When we carry this process to its logical conclusion, we are left with an infinitesimally small interval. Over such an interval, the average velocity becomes the instantaneous velocity or the velocity at a specific instant. A car’s speedometer, for example, shows the magnitude (but not the direction) of the instantaneous velocity of the car. (Police give tickets based on instantaneous velocity, but when calculating how long it will take to get from one place to another on a road trip, you need to use average velocity.) Instantaneous velocity  𝑣
+  is the average velocity at a specific instant in time (or over an infinitesimally small time interval).
+
+Mathematically, finding instantaneous velocity,  𝑣
+ , at a precise instant  𝑡
+  can involve taking a limit, a calculus operation beyond the scope of this text. However, under many circumstances, we can find precise values for instantaneous velocity without calculus.
+
+Speed
+In everyday language, most people use the terms “speed” and “velocity” interchangeably. In physics, however, they do not have the same meaning and they are distinct concepts. One major difference is that speed has no direction. Thus speed is a scalar. Just as we need to distinguish between instantaneous velocity and average velocity, we also need to distinguish between instantaneous speed and average speed.
+
+Instantaneous speed is the magnitude of instantaneous velocity. For example, suppose the airplane passenger at one instant had an instantaneous velocity of −3.0 m/s (the minus meaning toward the rear of the plane). At that same time his instantaneous speed was 3.0 m/s. Or suppose that at one time during a shopping trip your instantaneous velocity is 40 km/h due north. Your instantaneous speed at that instant would be 40 km/h—the same magnitude but without a direction. Average speed, however, is very different from average velocity. Average speed is the distance traveled divided by elapsed time.
+
+We have noted that distance traveled can be greater than displacement. So average speed can be greater than average velocity, which is displacement divided by time. For example, if you drive to a store and return home in half an hour, and your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero, because your displacement for the round trip is zero. (Displacement is change in position and, thus, is zero for a round trip.) Thus average speed is not simply the magnitude of average velocity.
+
+A house and a store, with a set of arrows in between showing that the distance between them is 3 point 0 kilometers and the total distance traveled, delta x total, equals 0 kilometers.
+Figure  2.3.3
+ : During a 30-minute round trip to the store, the total distance traveled is 6 km. The average speed is 12 km/h. The displacement for the round trip is zero, since there was no net change in position. Thus the average velocity is zero.
+Another way of visualizing the motion of an object is to use a graph. A plot of position or of velocity as a function of time can be very useful. For example, for this trip to the store, the position, velocity, and speed-vs.-time graphs are displayed in Figure  2.3.4
+ . (Note that these graphs depict a very simplified model of the trip. We are assuming that speed is constant during the trip, which is unrealistic given that we’ll probably stop at the store. But for simplicity’s sake, we will model it with no stops or changes in speed. We are also assuming that the route between the store and the house is a perfectly straight line.)
+
+Three line graphs. First line graph is of position in kilometers versus time in hours. The line increases linearly from 0 kilometers to 6 kilometers in the first 0 point 25 hours. It then decreases linearly from 6 kilometers to 0 kilometers between 0 point 25 and 0 point 5 hours. Second line graph shows velocity in kilometers per hour versus time in hours. The line is flat at 12 kilometers per hour from time 0 to time 0 point 25. It is vertical at time 0 point 25, dropping from 12 kilometers per hour to negative 12 kilometers per hour. It is flat again at negative 12 kilometers per hour from 0 point 25 hours to 0 point 5 hours. Third line graph shows speed in kilometers per hour versus time in hours. The line is flat at 12 kilometers per hour from time equals 0 to time equals 0 point 5 hours.
+Figure  2.3.4
+ : Position vs. time, velocity vs. time, and speed vs. time on a trip. Note that the velocity for the return trip is negative.
+
+If you have spent much time driving, you probably have a good sense of speeds between about 10 and 70 miles per hour. But what are these in meters per second? What do we mean when we say that something is moving at 10 m/s? To get a better sense of what these values really mean, do some observations and calculations on your own:
+
+calculate typical car speeds in meters per second
+estimate jogging and walking speed by timing yourself; convert the measurements into both m/s and mi/h
+determine the speed of an ant, snail, or falling leaf
+ 
+
+The SI unit for velocity is m/s.
+Velocity is a vector and thus has a direction.
+Instantaneous velocity  𝑣
+  is the velocity at a specific instant or the average velocity for an infinitesimal interval.
+Instantaneous speed is the magnitude of the instantaneous velocity.
+Instantaneous speed is a scalar quantity, as it has no direction specified.
+Average speed is the total distance traveled divided by the elapsed time. (Average speed is not the magnitude of the average velocity.) Speed is a scalar quantity; it has no direction associated with it.
+
+In everyday conversation, to accelerate means to speed up. The accelerator in a car can in fact cause it to speed up. The greater the acceleration, the greater the change in velocity over a given time. The formal definition of acceleration is consistent with these notions, but more inclusive.
+
+An airplane flying very low to the ground, just above a beach full of onlookers, as it comes in for a landing.
+
+The average acceleration is the rate at which velocity changes,
+
+Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are  𝑚/𝑠2
+ , meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second.
+
+Recall that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction. For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both.
+
+Acceleration is a vector in the same direction as the change in velocity,  Δ𝑣
+ . Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both.
+
+Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. This is known as deceleration.
+
+A subway train arriving at a station. A velocity vector arrow points along the track away from the train. An acceleration vector arrow points along the track toward the train.
+Figure  2.4.2
+ : A subway train in Sao Paulo, Brazil, decelerates as it comes into a station. It is accelerating in a direction opposite to its direction of motion. (credit: Yusuke Kawasaki, Flickr)
+MISCONCEPTION ALERT: DECELERATION VS. NEGATIVE ACCELERATION
+
+Deceleration always refers to acceleration in the direction opposite to the direction of the velocity. Deceleration always reduces speed. Negative acceleration, however, is acceleration in the negative direction in the chosen coordinate system. Negative acceleration may or may not be deceleration, and deceleration may or may not be considered negative acceleration. If acceleration has the same sign as the velocity, the object is speeding up. If acceleration has the opposite sign as the velocity, the object is slowing down. 
+
+Four separate diagrams of cars moving. Diagram a: A car moving toward the right. A velocity vector arrow points toward the right. An acceleration vector arrow also points toward the right. Diagram b: A car moving toward the right in the positive x direction. A velocity vector arrow points toward the right. An acceleration vector arrow points toward the left. Diagram c: A car moving toward the left. A velocity vector arrow points toward the left. An acceleration vector arrow points toward the right. Diagram d: A car moving toward the left. A velocity vector arrow points toward the left. An acceleration vector arrow also points toward the left.
+Figure  2.4.3
+ : (a) This car is speeding up as it moves toward the right. It therefore has positive acceleration in our coordinate system. (b) This car is slowing down as it moves toward the right. Therefore, it has negative acceleration in our coordinate system, because its acceleration is toward the left. The car is also decelerating: the direction of its acceleration is opposite to its direction of motion. (c) This car is moving toward the left, but slowing down over time. Therefore, its acceleration is positive in our coordinate system because it is toward the right. However, the car is decelerating because its acceleration is opposite to its motion. (d) This car is speeding up as it moves toward the left. It has negative acceleration because it is accelerating toward the left. However, because its acceleration is in the same direction as its motion, it is speeding up (not decelerating).
+Example  2.4.1
+ : Calculating Acceleration: A Racehorse Leaves the Gate
+
+A racehorse coming out of the gate accelerates from rest to a velocity of 15.0 m/s due west in 1.80 s. What is its average acceleration?
+
+Two racehorses running toward the left.
+Figure  2.4.4
+ : Two racehorses running toward the left. (credit: Jon Sullivan, PD Photo.org)
+Strategy
+
+First we draw a sketch and assign a coordinate system to the problem. This is a simple problem, but it always helps to visualize it. Notice that we assign east as positive and west as negative. Thus, in this case, we have negative velocity.
+
+An acceleration vector arrow pointing west, in the negative x direction, labeled with a equals question mark. A velocity vector arrow also pointing toward the left, with initial velocity labeled as 0 and final velocity labeled as negative fifteen point 0 meters per second.
+Figure  2.4.5
+ .
+We can solve this problem by identifying  Δ𝑣
+  and  Δ𝑡
+  from the given information and then calculating the average acceleration directly from the Equation  ???
+ :
+
+𝑎¯=Δ𝑣Δ𝑡=𝑣𝑓−𝑣0𝑡𝑓−𝑡0.
+ 
+
+Solution
+
+Identify the knowns.  𝑣0=0,𝑣𝑓=−15.0𝑚/𝑠
+  (the negative sign indicates direction toward the west),  Δ𝑡=1.80𝑠
+ .
+Find the change in velocity. Since the horse is going from zero to  −15.0𝑚/𝑠
+ , its change in velocity equals its final velocity:
+Δ𝑣=𝑣𝑓=−15.0𝑚/𝑠.
+ 
+Plug in the known values (  Δ𝑣
+  and  Δ𝑡
+  ) and solve for the unknown  𝑎¯
+ .
+𝑎¯=Δ𝑣Δ𝑡=−15.0𝑚/𝑠1.80𝑠=−8.33𝑚/𝑠2
+ .
+
+Discussion
+
+The negative sign for acceleration indicates that acceleration is toward the west. An acceleration of  8.33𝑚/𝑠2
+  due west means that the horse increases its velocity by 8.33 m/s due west each second, that is, 8.33 meters per second per second, which we write as  8.33𝑚/𝑠2
+ . This is truly an average acceleration, because the ride is not smooth. We shall see later that an acceleration of this magnitude would require the rider to hang on with a force nearly equal to his weight.
+
+Instantaneous Acceleration
+Instantaneous acceleration  𝑎
+ , or the acceleration at a specific instant in time, is obtained by the same process as discussed for instantaneous velocity in Time, Velocity, and Speed—that is, by considering an infinitesimally small interval of time. How do we find instantaneous acceleration using only algebra? The answer is that we choose an average acceleration that is representative of the motion. Figure  2.4.6
+  shows graphs of instantaneous acceleration versus time for two very different motions. In Figure  2.4.6𝑎
+ , the acceleration varies slightly and the average over the entire interval is nearly the same as the instantaneous acceleration at any time. In this case, we should treat this motion as if it had a constant acceleration equal to the average (in this case about  1.8𝑚/𝑠2
+ ). In Figure  2.4.6𝑏
+ , the acceleration varies drastically over time. In such situations it is best to consider smaller time intervals and choose an average acceleration for each. For example, we could consider motion over the time intervals from 0 to 1.0 s and from 1.0 to 3.0 s as separate motions with accelerations of  +3.0𝑚/𝑠2
+  and  –2.0𝑚/𝑠2
+ , respectively.