Vern J. Ostdiek Donald J. Bord Chapter 1 The Study of Motion (Section 1) Drag Racing • Acceleration, pure and simple • That’s the point of drag racing • Increase the speed of the dragster as quickly as possible so it will travel the one-quarter of a mile (about 400 meters) faster than your opponent. • The elite machines have engines that are much more powerful than those on the largest airplanes in World War II (about 6,000 horsepower). Drag Racing • From a standing start, they reach speeds of more than 300 mph in times shorter than it took you to read this sentence. • And, they subject their drivers to average accelerations over four times that of gravity. • At the end of their brief run, another critical feat must be accomplished: • They have to be brought to a stop safely. • How do you slow a vehicle that is going much faster than a passenger jet when it lands? • You deploy a parachute Drag Racing • This chapter is an introduction to the study of motion. • One key concept in this area of physics is acceleration, which is used to describe changes in motion. • • Drag racing is one of the most dramatic examples of human beings deliberately accelerating themselves. The large attendance at these events suggests that many people are thrilled to watch it happen. • Two types of acceleration are involved in drag racing: • speeding up and slowing down • Is there another type of acceleration? • Can a car accelerate without changing its speed? Drag Racing • Most of this chapter is an introduction to the branch of physics called mechanics—the study of motion and its causes. • The main topic of this chapter is motion and how it is described using the concepts of speed, velocity, and acceleration—something called kinematics. • • Both examples and graphs are used to illustrate and define these three concepts. An important example treated in detail is the motion of a body undergoing free fall. • We conclude with a brief account of the work of two men who made important contributions to the development of mechanics. 1.1 Fundamental Physical Quantities • Our main task here is to take a closer look at motion—what it is, how one quantifies it, what the simplest kinds of motion are, and so on. • Fortunately for beginners, most of the concepts and terms are familiar because motion is such an important part of our everyday world. • We have a sense of how fast 60 miles per hour (or 97 kilometers per hour) is and how to compute speed if we know the distance traveled and the time elapsed. • The unit of measure pretty much tells us how to do that: “miles per hour” means divide the distance in miles by the time in hours. 1.1 Fundamental Physical Quantities • But there are some important subtleties that must be examined, and our basic ideas about velocity and acceleration need to be expanded. • The ways that we will express relationships throughout the text, oftentimes involving things not so familiar as motion, will be presented. 1.1 Fundamental Physical Quantities • In physics, there are three basic aspects of the material universe that we must describe and quantify in various ways: space, time, and matter. • All physical quantities used in this textbook involve measurements (or combinations of measurements) of space, time, and the properties of matter. • The units of measure of all of these quantities can be traced back to the units of measure of distance, time, and two properties of matter called mass and charge. • We will not deal with charge until Chapter 7. 1.1 Fundamental Physical Quantities • Distance, time, and mass—known as fundamental physical quantities—are such basic concepts that it is difficult to define them, particularly time. • Distance represents a measure of space in one dimension. • Length, width, and height are examples of distance measurements. 1.1 Fundamental Physical Quantities • The table lists the common distance units of measure, in both the metric system and the English system, and their abbreviations. 1.1 Fundamental Physical Quantities • Why are there so many different units in each system? • Generally, it is easier to use a unit that fits the scale of the system being considered. • • The meter is good for measuring the size of a house, the millimeter for measuring the size of a coin, and the kilometer for measuring the distance between cities. Eighty kilometers is the same as 80,000 meters, but the former measurement is easier to conceptualize and to use in calculations. 1.1 Fundamental Physical Quantities • Similarly, it might be correct to say that a coin is 0.000019 kilometers in diameter, but 19 millimeters is a more convenient measure. 1.1 Fundamental Physical Quantities • The sizes of all of the distance units, including the English units, are defined in relation to the meter. • In this book, we will use meters most often in our examples. • You should try to get used to distance measurements expressed in meters and have an idea, for example, of how long 25 and 0.2 meters are. 1.1 Fundamental Physical Quantities • The table shows some representative distances expressed in both metric and English units. 1.1 Fundamental Physical Quantities • It is a rather simple matter to convert a distance expressed in, say, meters to a distance expressed in another unit. • • For example, you might solve a problem and find that the answer is, “The sailboat travels 23 meters in 10 seconds.” Just how far is 23 meters? • Think of any numerical measurement as a number multiplied by a unit of measure. • In this case, 23 meters equals 23 times 1 meter. 1.1 Fundamental Physical Quantities • Then the 1 meter can be replaced by the corresponding number of feet—a conversion factor found in the back inside cover of the textbook. 23 meters = 23 ×1 meter • But 1 meter = 3.28 feet; therefore: 23 meters = 23 × 1 meter = 23 × 3.28 feet 23 meters = 75.4 feet 1.1 Fundamental Physical Quantities • Two other physical quantities that are closely related to distance are area and volume. • Area commonly refers to the size of a surface, such as the floor in a room or the outer skin of a basketball. • The concept of area can apply to surfaces that are not flat and to “empty,” two-dimensional spaces such as holes and open windows. 1.1 Fundamental Physical Quantities • Area is a much more general idea than “length times width,” an equation you may have learned that applies only to rectangles. • The area of something is just the number of squares 1 inch by 1 inch (or 1 meter by 1 meter, or 1 mile by 1 mile, etc.) that would have to be added or placed together to cover it. 1.1 Fundamental Physical Quantities • In a similar manner, the volume of a solid is the number of cubes 1 inch or 1 centimeter on a side needed to fill the space it occupies. • For common geometric shapes such as a rectangular box or a sphere, there are simple equations to compute the volume. • We use volume measures nearly every time we buy food in a supermarket. 1.1 Fundamental Physical Quantities • Area and volume are examples of physical quantities that are based on other physical quantities—in this case, just distance. • Their units of measure are called derived units because they are derived from more basic units: • 1 square meter = 1 meter × 1 meter = 1 meter2 1.1 Fundamental Physical Quantities • The measure of time is based on periodic phenomena—processes that repeat over and over at a regular rate. • The rotation of Earth was originally used to establish the universal unit of time, the second. • The time it takes for one rotation was set equal to 86,400 seconds (24 × 60 × 60). • Both the metric system and the English system use the same units for time. 1.1 Fundamental Physical Quantities • Clocks measure time by using some process that repeats. Many mechanical clocks use a swinging pendulum. • The time it takes to swing back and forth is always the same. • This is used to control the speed of a mechanism that turns the hands on the clock face. • Mechanical wristwatches and stopwatches use an oscillating balance wheel for the same purpose. • Quartz electric clocks and digital watches use regular vibrations of an electrically stimulated crystal made of quartz. 1.1 Fundamental Physical Quantities • The first step in designing a clock is to determine exactly how much time it takes for one cycle of the oscillation. • If it were 2 seconds for a pendulum, for example, the clock would then be designed so that the second hand would rotate once during 30 oscillations. 1.1 Fundamental Physical Quantities • The period of oscillation in that case is 2 seconds. • • Period: The time for one complete cycle of a process that repeats. It is abbreviated T, and the units are seconds, minutes, and so forth. 1.1 Fundamental Physical Quantities • But there is another way to look at this. The clock designer must determine how many cycles must take place before 1 second (or 1 minute or 1 hour) elapses. • In our example, one-half of a cycle takes place during each second. • This is called the frequency of the oscillation. • • • Frequency: The number of cycles of a periodic process that occur per unit time. It is abbreviated f and has units s–1 or hertz (Hz). The standard unit of frequency is the hertz (Hz), which equals 1 cycle per second: 1 Hz = 1/s = 1 s–1 1.1 Fundamental Physical Quantities • The frequency of AM radio stations is expressed in kilohertz (kHz) and those of FM stations in megahertz (MHz). • • Mega- is the metric prefix signifying 1 million. So, 91.5 MHz equals 91,500,000 Hz. • Another metric prefix, giga-, is also commonly used with hertz. • For example, the “speed” of a computer’s processor—actually, the frequency of the electrical signal it uses—might be 2 gigahertz, which is 2 billion (2,000,000,000) hertz. 1.1 Fundamental Physical Quantities • The relationship between the period of a cyclic phenomenon and its frequency is simple: • the period equals 1 divided by the frequency, and vice versa 1 period = frequency 1 T= f 1 f = T 1.1 Fundamental Physical Quantities Example 1.1 • A mechanical stopwatch uses a balance wheel that rotates back and forth 10 times in 2 seconds. What is the frequency of the balance wheel? frequency = number of cycles per time 10 cycles f = 2s = 5 Hz • What is the period of the balance wheel? period = time for one cycle = 1 divided by the frequency 1 T= 5 Hz = 0.2 s • The balance wheel oscillates 300 times each minute. 1.1 Fundamental Physical Quantities • The third basic physical quantity is mass. • The mass of an object is basically a measure of how much matter it contains. • This statement illustrates the sort of circular definition that arises when one tries to define fundamental concepts. • We know intuitively that a large body such as a locomotive has a large mass because it is composed of a great deal of material. 1.1 Fundamental Physical Quantities • Mass is also a measure of what we sometimes refer to in everyday speech as inertia. • The larger the mass of an object, the greater its inertia and the more difficult it is to speed up or slow down. • Mass is not in common use in the English system; note the unfamiliar unit, the slug. • Weight, a quantity that is related to, but is not the same as mass, is used instead. 1.1 Fundamental Physical Quantities • We can contrast the two ideas: • • When you try to lift a shopping cart, you are experiencing its weight. When you try to speed it up or slow it down, you are experiencing its mass.
