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Calculating the distance across a square requires you to know the length of that square's sides. Calculate the distance across a square with help from a high school mathematics tutor in this free video clip.
When calculating distance one thing you need to consider is difference in elevation. Learn about the calculation for distance based upon difference in elevation with help from a high school math tutor and teacher in this free video clip.
You can calculate the number of gallons of gas it will take to drive a certain distance using a very specific formula. Calculate the number of gallons of gas to drive a certain distance with help from an expert in the automotive industry in this free video clip.
A well-performing microwave communication network begins with a properly conducted survey that analyzes the microwave path’s characteristics to identify and mitigate all potential signal obstructions. The need for properly calculating microwave path distances has become more and more important as microwave transmission technology becomes more universally used and popular with wireless phone and data transmission requirements. Surveys can be based on available terrain for long distances or for line-of-sight for shorter distances.
If you have a pumped well, you may need to know the drawdown, which is the distance the water level goes down when the pump is running versus the static level when it is not. You need to know these two measurements. One way to do so is by manually measuring them. If you are at a distance from the well, though, you can still calculate the drawdown if you know these numbers.
Knowing the height of an antenna allows you to calculate the distance that it could transmit a signal. Since antennae send and receive a radio signal, it can be obscured by the curvature of the Earth. The higher an antenna is positioned, the greater the distance the signal can be sent and received without being blocked by the Earth. Other considerations such as signal power and the directionality of the signal will also affect the ability to send and receive with the antenna.
Handrail and guard design is strictly regulated by the national building code. The rails, or spindles, on a guard are the vertical sections that are designed to keep people from slipping under the handrail. They must be built in a way that reduces the likelihood of someone climbing and falling over it. The distance between each spindle is important for safety as well. The common maximum distance between each railing is four inches.
Accidents or collisions between large trucks and automobiles can be dangerous. The difference in mass and gravitational force between the two can result in significant injury and damage. Police officers, emergency personnel and judges view the details of such occurrences frequently as they collect, present and review traffic accidents. According to Engineering Physics for Lawyers, much of the work of accident analysis and reconstruction involves the application of general physical laws to the particular incident such as Newtonian laws of forces and masses. Skids occur when one vehicle is at a position of rest and is struck by another vehicle,…
In map reading the term "azimuth" refers to any direction as expressed in degrees from north (which is both 0 and 360 degrees). The back azimuth refers to the direction 180 degrees opposite the azimuth, or in the exact opposite direction. Keeping track of your back azimuth is important in instances when you have to make your way back to a previous coordinate. It can also be helpful for keeping your bearings by making sure you are traveling in a straight line.
A frequency distribution shows how often each event occurs in an experiment or other study. For example, a frequency distribution of 100 rolls of a die would list the number of times each outcome occurred. A relative frequency distribution shows the proportion of events rather than the absolute number of events.
The Big Bang theory has been the prevailing explanation of our universe's origins. This theory holds that the universe began more than 13 billion years ago, after a violent explosion of matter with extremely high density and temperature. Now scientists have presented alternatives to this theory, explaining the universe in different terms.
Since the origin of the human race, man has been compelled to explore the limits of his known world and beyond. In time, curiosity and technology encouraged and enabled man to explore beyond the bounds of Earth into outer space. While space exploration satiates man's inherent desire to explore beyond the known into the unknown, it is also a costly venture. Maintaining a capable space program requires billions of dollars which many Americans cannot rationalize during times of economic strife. As a result, there is a perpetual debate about the necessity for such an expensive venture.
The stages in the life of a star are important because they provide information about how the solar system operates. Stars aide in measuring distances in space, interpreting the behavior of the sun, dating the galaxy and discovering larger forces at play in the universe. Some stars even maintain consistent characteristics, making them even more reliable sources of information.
Using the astronomical measurement coordinates of the Horizon system, finding the true azimuth of Polaris, known more commonly as the North Star, will only take a compass and a clear, dark, night. Once you locate your position north and find Polaris, you can discover the coordinates without any math at all; the Horizon system uses the astronomer as a reference point to measure the approximate location of the stars based on your time and location. Learning how to use the Horizon system will aid you, as an amateur astronomer, in keeping track of stars and other objects in the sky.
Kinetic energy is the product of an object's mass, or weight, and its velocity. If you throw a ping-pong ball across the room, for example, you exert a force on the ping-pong ball that accelerates the ping-pong ball. This force becomes the kinetic energy of the flying ping-pong ball. Physicists write the formula for kinetic energy (KE) as KE = 1/2mv^2, in which m represents mass and v represents velocity. The units used to measure kinetic energy are Joules.
Astronomers have been observing planets for hundreds of years, not only to track their orbits but to measure distances between them. In the 17th century, Giovanni Cassini calculated the distance between Mars and Earth, and was only 7 percent off. Distances between planets change every moment, but to get a rough number it's best to start with Earth's distance from the Sun and the distance of Mars from the Sun. Then you can easily calculate the relative distance of Mars from Earth.
In complex mathematics, difficulty arises in solving for x in a function when there is a remainder included in the differentiable function. The remainder makes it difficult to find x, because it makes the equation more complex. Linear approximation allows the removal of the remainder to solve for an approximation of x.
Sonar stands for the first letters "S, N and R" from "sound navigation ranging." Sonar is of two types: active and passive. It functions to locate objects under the sea by detecting echoes. For example, whales, porpoises and dolphins make use of natural sonar systems to navigate their way through the waters of the sea. Bats make use of echolocation to find their prey. Passive sonar is capable of receiving echoes without transmitting sound signals of its own. Active sonar sends out what are called "pings" and receives returning sound echoes.
Estimating the capacity of a container can take many routes. Many of these methods rely on your ability to estimate lengths or percentages. By making these estimates, you are able to apply your estimates to volume calculations. An important bit of information you will need is the shape of the container. Each shape uses a different formula to calculate the volume. The job of estimating a container's capacity is usually easier if the container is smaller. You can compare the volume with a container of known capacity.
An angular momentum is a characteristic of an angular motion such as rotation. This value is the mathematical product of the angular velocity and the momentum of inertia. The momentum of inertia plays the same role in the angular motion as the mass does in the linear motion. The momentum of inertia depends upon the shape of the rotating object such as a cylinder, a rod or a sphere as well the location of the rotation axis.
Just a circle is the set of all points in a two-dimensional plane equidistant from a central point and a sphere is the set of all points in three dimensions equidistant from a central point, in mathematics there exist analogous structures, called hyperspheres, in dimensional spaces greater than three that are the set of all points equidistant from a central point. Consequently, just as the the integral volume of a sphere in three dimensions can be derived with calculus, so can the integral volumes of these higher-dimensional figures.
Autonomous underwater vehicles -- underwater robots that follow a predetermined, preprogrammed search pattern -- when properly equipped and programmed, can use the data provided by a terrain-and-object avoidance sonar system, a side-scan sonar system, a sonar imaging camera and the information from an inertial guidance system to match its movements to the location of underwater features. Properly programmed, the unit -- in addition to being autonomous -- will be able to alter its course as required to avoid the seabed and other underwater objects and geological features, providing an effective, multilayered subsea map.
To locate a point in three-dimensional space requires three numbers. Usually, these are given as distances from some point, in terms of east-west, north-south and up-down, which can be called x, y and z, respectively. For example, latitude, longitude and altitude. An alternative system is to use two angles and one distance. These can be labeled theta (the angle from the xy plane in the x-axis), phi (the angle from the z axis) and r (the distance from a central point). (See Reference for a picture and some alternative schemes). It is possible to convert from one to the other.
In mathematics, spherical geometry is the study of lines, angles and shapes on a spherical surface. Spherical geometry differs from the more familiar plane or Euclidean geometry in several important ways, mostly having to do with the behavior of lines and angles. Spherical geometry has a wide range of real-world applications, particularly in mapping the surface of the Earth and other planets.
The circle graph or pie chart is a clear way to visually represent categories of data. Each category gets its own slice, with the name of the category and the percentage allotted to it written either directly onto the slice or in a legend to the right of the circle. A good circle graph lists the total number of members in the sample, usually underneath the title of the graph. If you have the relative percentages and the total sample, you can find the exact data for each slice.
The trapezoidal rule is a method for finding the value of a definite integral or area beneath a curve within an interval. The trapezoidal rule states that the value of a definite integral on the interval (a, b) = (Î"x/ 2)[f(x-0) + 2f(x-1) + 2f(x-2) + ... + 2f(x-(n-1)) + f(x-n)], where Î"x = (b - a)/ n, n equals the number of subdivisions of the interval and (x-0) is the initial x-value, (x-1) is the second x-value, etc. The error in the trapezoidal rule is the amount that needs to be added to its approximation to the integral to…
A circle graph or pie chart, is an easy way to visually represent categorical data such as number of votes each candidate got in an election. The percentage of votes each candidate received would be written on each slice of the pie. The circle graph is most helpful when you want to demonstrate how much each individual category contributed to the data set as a whole.
Learn to calculate the size of a cistern to know its water storage capacity. Cisterns are typically used for collection of rain water for use in watering plants, farm fields, and supplying community residents with water. A cistern has a cylindrical shape with a domed or cone shaped top. The volume of the cylindrical portion of the cistern provides a direct measure of its capacity, and the volume depends on the cylinder's height and radius. The radius measures half the total width of the cistern.
Learn to determine the size a Well-Rite pressure tank so you can to find a suitable replacement for an old tank. As long as the volume of the new tank is the same as the old, the shape does not matter. High quality Well-Rite tanks have a protective urethane finish and come in a variety of sizes, so measuring your tank's dimensions for a replacement is crucial. Well-Rite pressure tanks come in a cylindrical shape, so you need the tank height and radius to determine its volume. Cylinder radius equals one-half the tank's diameter or width.
Circle graphs, or pie charts as they are also known, are pictorial representations of the relative frequencies of categorical data. A circle graph that depicts relative frequency displays the percentage of each category on each section of the circle. A pie chart is best to use when you only have a few categories and you want to demonstrate a part-to-whole relationship. Making each slice a different color adds to the visual appeal of this type of graph.
For more than 2,000 years, the phrase "Euclidean geometry" was redundant because there was no other geometry. It was only in the 19th century that mathematicians finally ventured to explore different geometric ideas. Euclidean geometry is based on five postulates, or axioms, and builds up the entire geometric system on the framework of these five postulates. Non-Euclidean geometries accept the first four of these, but change the fifth postulate to build entirely consistent (although non-intuitive) geometries.
Scientists measure the brightness of a light source in units of candles or, when using the metric system, in candelas. The amount of illumination -- or illuminance -- a surface receives depends on the distance from the light source and the intensity of the light source. Illuminance is measured in either foot-candles or the metric system units of lux. You can readily change foot-candles to lux by using a simple numerical conversion factor.
The ampere, like the ohm, volt, coulomb and other SI units, was named for a physicist who contributed to our understanding of electricity. André-Marie Ampère (1775-1836) explored the relationship between electromagnetism and electric current, and in his honor the SI unit used to measure current is called the ampere, or amp for short. You can easily convert amps to electrons per second with a light mathematical equation.
Scientists who work with electricity sometimes compare the flow of current to the flow of water. Just as someone might report the rate of water flowing through a pipe in units of gallons per minute, the scientist describes the flow of electricity in terms of units of charge per second. The coulomb is a common measure of amount of charge and the ampere, or simply "amp," is a unit for the rate of current flow. You can readily convert from amps to coulombs per second since, by definition, an amp is the flow in terms of coulombs per second.
You can measure the length to an object at a distance by using bearings. A bearing is easily obtained by using a standard compass. To find the length to an object, you need to input data into an equation which you then need to solve. You need to first find an object that is some distance away to use as a reference point, such as a tree.
Determining how much oil to fuel is needed depends on the ratio for the engine. A 20:1 ratio needs more oil than a 50:1 ratio. The proper fuel-to-oil ratio is needed when mixing fuel for a 2-cycle engine, such as a snow blower or a boat engine. Calculating the ratio requires determining how much oil you will need to add per gallon of gas. You can easily calculate a fuel-to-oil ratio using simple math.
Measuring the distance to an object that you cannot approach has always been a challenge. The normal method of measuring a straight line from you to the object does not work when there is an impassable gap such as an alligator-infested river or a deep chasm between you and the object. For centuries, surveyors and explorers have used a method called trigonometry, which uses angles to calculate distances, and is ideally suited to measuring distances to inaccessible objects.
Static electricity occurs when an imbalance takes place between positive and negative electrons. You get a buildup of electricity on an item that is unable to conduct electricity, so it becomes static. It can only get discharged when the object containing the electrostatic buildup touches something that feeds to ground, such as a metal water pipe or a metal handle. Several experiments can illustrate static electricity.
Earthquakes are violent, sudden disturbances that generate seismic waves, waves traveling outward from the origin of the earthquake in all directions. When describing an earthquake and its location, geologists often talk about its epicenter and its focus. The epicenter is located above the focus, but the two are different and, depending on the type of earthquake, may be separated by a large or small distance.
Learn to determine the slant height of three-dimensional solid shapes to aid in solving geometry problems. Slant height measures the length of a side of a cone or pyramid. The slant height comes in handy when calculating the volume for a cone or pyramid. The slant height depends on the height of the object and half the width of its base. Slant height can be found in any unit system provided the height and half of the base width are known and measured in the same units.
A legal description of your property is typically found on the land title and deed. If you have an original deed or the land tile there were reference points used to describe the property. A legal description once used measurements of metes, bounds and chains. Drawing a map from a legal description will require you to decipher the geographical locations that were used in the description of the property.
Seismographs are an important tool for measuring the intensity of earthquakes as they occur around the globe. These devices record the various seismic waves that an earthquake produces. They can also provide important information about the location of a quake's epicenter. The vertical space on a seismogram (the paper output of the seismograph) represents the distance the ground moves during a quake at the location of the monitoring device.
Learn to calculate the angular momentum of a particle to aid in solving physics problems involving motion. Angular momentum describes the quality of motion of a particle or object moving on a curved path. The object's angular momentum increases for larger values of its mass and velocity. An example of an object with angular momentum is a planet orbiting the Sun. The angle between the straight line connecting the planet and the direction of velocity, also effect angular momentum. In an orbit, and, in general, angular momentum is conserved for an object, meaning its initial value equals its final value.
Calculating the capacity of a dehydration tower will let you know how much liquid or gas it can treat at one time. A dehydration tower is used to remove water from a liquid or gas to make it pure. An example of dehydration tower use is the removal of water from natural gas. The capacity of a dehydration tower depends on its internal volume, which can be estimated after measuring the required dimensions of the tower.
The moment of the Big Bang is considered by many scientists to be the beginning of time. There is some contention among scientists about when the Big Bang occurred, though estimates place it in the range of a minimum of 13 to 15 billion years ago. As of 2011, the Big Bang Theory is one of the most commonly accepted explanations of how the universe began.
The first scientific instruments sent into space were launched on Feb. 1, 1958, on the Explorer I satellite. In the intervening decades, hundreds of space missions have carried thousands of other scientific instruments into space. The types of instruments used in space are as varied as those used on Earth. A quick review will illustrate the variety.
Energy and work can be measured using the SI unit of the joule, named for the British physicist James Prescott Joule. Electrical charge is measured in another SI unit, the coulomb, named for the French physicist, Charles-Augustin de Coulomb. The two units are linked via electrical potential, which is measured in joules per coulomb. Since electrical potential is measured in volts, it is possible to convert joules to coulombs when the voltage is known.
A coulomb is a unit of charge equal to the charge carried by 6x10^18 electrons. An ampere is a unit of current, or charge per unit time. One ampere is equal to one coulomb of charge per second. In order to convert amperes to coulombs, therefore, it is necessary to know both the amperage of a current and the period of time for which the current ran.
Earthquakes like the devastating Chile earthquake of 2010 and the Japan earthquake of 2011 that resulted in a tsunami are examples of natures tectonic power. The Chile earthquake is one of the largest ever recorded in history. Its magnitude was largely due to the shallow focus of the quake, only 22 miles deep. According to Library Thinkquest, any earthquake at a depth of 43 miles or shallower is considered a shallow focus quake and is likely to cause devastation.
Spherical geometry is a type of geometry that is based on the two-dimensional surface of a sphere. Spherical geometry can differ greatly from the straight line geometry found in a Euclidean geometry, as straightforward concepts such as straight lines can have very different definitions. For example, distance in spherical geometry is measured along what is called a great circle, which is a curved line that follows the radius of the sphere. Measuring distance using the great circle depends on converting the spherical coordinates to the more common Cartesian coordinates, and calculating the distance in this fashion.
Experiments are based upon the testing of a hypothesis and the collection of data. The data is often tabulated in table format which makes it particular difficult to visualize trends. A graph is a visual way of representing data, and the type used depends upon the nature of the data. A circle graph (pie chart), a way of representing proportions, is one of the most popular graph formats, used widely throughout science and statistics.
In July 1997, the Pathfinder launched a rover onto the surface of Mars. Sojourner was the name of the rover, honoring the civil rights leader Sojourner Truth and named by the student winner of a national contest. Make learning about this exciting mission a hands-on affair by introducing Sojourner crafts to students. These crafts can draw inspiration from the rover itself or from the many videos and pictures it transmitted back to Earth.
If you look through a camera focused on a certain point in the distance, everything at that distance will be perfectly clear. Objects just a little bit closer or a little bit further from that point will be less sharp, but not enough for you to notice. As objects get further away from the focus point, they will get less sharp. The range of distance, from closest to furthest away, that objects are still acceptably sharp is called the depth of field, or depth of focus (DOF).
Fatigue life is a concept in material science that deals with a decrease in quality or strength in a substance, such as steel, due to various stresses. The general theory of fatigue is that when an action is repetitive, the object doing the work loses strength, such as knees getting weak after running for a long time. This concept is applied to objects like bridges, springs and airplane wings.
A coulomb is a measure of electrical charge, equivalent to the charge accumulated in one second by a current of one amp. Coulombs are related to the electron because electricity is the movement of electrons and other charged particles. As electrons move from one atom to the next, they create a flow, and that flow is called |electricity. Converting coulombs to electrons is a straightforward process using a scientifically agreed conversion factor.
An ionic compound like sodium chloride (better known as salt) forms a crystalline lattice featuring atoms arranged in well-defined positions with respect to each other. The difference in energy between ions in gas phase and crystal lattice is called lattice energy. You can calculate lattice energy using the Born-Haber cycle. More directly, you can use the Born-Meyer equation, although the calculation will require you to find a number specific for each a given type of crystal structure, the Madelung constant.
A swept area is the part of a circular or elliptical orbit that an object makes as it rotates around a fixed point. This concept has traditionally been applied to planetary motion, but has more recently been used in calculations with wind turbines. Johannes Kepler discovered that as a planetary body is in orbit, the area swept will be equal for equal amounts of time, regardless of the change in the radius of the orbit. This means that an object's velocity must increase as its radius decreases in order to conserve angular momentum.
Cepheid variable stars are a class of stars whose luminous intensity varies with a predictable pattern. They are generally supergiants, 500 to 30,000 times brighter than our sun. The time it takes for the star to go from its brightest to its dimmest and then back to its brightest is called its period of luminosity. This length of time is determined by the brightness of the star, so astronomers can figure out how bright the star is, which is useful in calculating distance.
A circle graph, often called a pie graph, divides a circle into sectors. Each sector represents a fraction of data the whole graph is devoted to. The size of a sector measured in degrees is proportional to the quantity it represents. To figure out percentages using sector sizes, you need to keep in mind that the whole circle measures 360 degrees, while the percentages measured will total to 100.
The calculation for square inches of tubing refers to the exterior surface area of the tubing. This can be useful when determining heat transfer in coils of tubing. The surface area of tubing can be thought of as the exterior surface area of a cylinder and is a function of the outer diameter of the tube.
Astronomers use a technique termed parallax to determine the distance of stellar objects from Earth. The parallax technique is only effective within about 200 parsecs. A parsec is equivalent to 3.26 light years. To grasp the magnitude of a light year, you need to know that the Sun is approximately 91 million miles (91 X 10^6) from Earth, and light travels from the Sun to the Earth in about eight minutes. One light year is 65,700 minutes, so that yields that a light year represents approximately 6 X 10^12 miles. To measure distances beyond the 200-parsec limit of the parallax…
A storm usually brings with it plenty of lightning and thunder. If you have a stopwatch and a calculator, you can use the time delay between the flash of lightning and its accompanying thunderclap to calculate the distance of the storm with remarkable precision. Since the light from a lightning flash reaches you almost instantaneously (light travels over 185,000 miles per second), all you need to know is the speed of sound and the time it took the sound to reach your ears to determine the distance to the thunder cloud.
Marine protected areas (MPAs) and marine reserves are both areas of protected habitat in oceans, lakes, and other waterways. They have similar features and serve a similar purpose, but also have several fundamental differences. Marine reserves, along with wildlife refuges, ocean parks, and marine sanctuaries, are actually specific types of marine protected areas.
Sound is a wave and as such has a different velocity depending on the medium that it passes through. For example, the speed of sound in air is different than the speed of sound in water. In fact, it is much faster in water than air. The density and temperature of a liquid make a significant difference in the speed a sound wave travels through the medium. It is sometimes necessary to measure this speed for an experiment.
Though Christopher Columbus is often credited with the discovering the earth is a sphere in 1492, the fact was well known by Greek intellectuals centuries earlier. The first recorded estimation of the earth's shape dates to the 3rd century B.C. and Aristotle's essay "On the Heavens," which states the earth's round shadow across the moon proves that the planet is round. The spherical nature of the earth must be taken into account when calculating the relative elevation of two peaks.
An earthquake is a ground movement caused by rocks breaking within the Earth's crust. As they break, large sections of rock slide alongside each other -- upward, downward and sideways -- along areas of weakness within the Earth known as geological faults. This movement releases energy which travels in the form of waves both through and on the surface of the Earth. A seismograph is a scientific instrument which measures the movement of the ground during an earthquake. A seismogram is a printout of this movement against recorded time. After an earthquake, the first unusual large trace on the seismogram…
Rho, also known as Spearman's rho, is an ordinal measure of correlation. That is, it expresses the strength of relationship between two ordinal variables. Ordinal variables are those that have an order such "none,'" "a little," "some" and "a lot." It also can be used for variables that are interval level. This corresponds to those that have equal intervals (such as weight or height) if there are outliers (subjects who have very unusual values such as very thin or fat people, or very short or tall people).
Percentages are fractions expressed in an alternative and often more easily comprehended way. For example, 342/1,000 is easier to understand when expressed as 34.2 percent. Calculating a percentage of a circle is straightforward and has applications in statistics and the creating of circle graphs. The math involved is basic, but using a calculator may simplify the calculations and increase the reliability of the results.
The slant height refers to the vertical height from a point anywhere on the circle base of a right circular cone. It is simply the vertical height from the ground to the highest point of a slanted line which, for a right circular cone, is the apex. A simpler example would be a ladder leaning against a house. The ladder is the slanted line and the vertical distance from the ground to the top of the ladder is the slant height. To find the slant height of a slanted line is a simple procedure using a well known formula, the…
The study of ballistic trajectories has important applications in the field of engineering. Their aspects are subject to the laws of physics, and as such, can be predicted to a reasonable degree of accuracy using mathematical formulas. To calculate the time of flight of a launched projectile, you will need to know two things ahead of time: how fast it is moving when it is launched, and the angle of its launch. As a working example, assume that you are launching a projectile at a velocity of 100 meters per second and at an angle of 45 degrees.
When metals and nonmetals form compounds, the metal atoms donate electrons to the nonmetal atoms. The metal atoms thereby assume positive charges due to their loss of negatively charged electrons, and the nonmetal atoms assume negative charges. Chemists refer to charged atoms as "ions." Ions exhibit attractive forces for ions of opposite charge -- hence the adage that "opposites attract." The force of attraction between oppositely charged ions, or of repulsion between like-charged ions, follows Coulomb's law, expressed mathematically as F = k * q1 * q2 / d^2, where F represents the force of attraction in Newtons, q1 and…
The term aquatic pertains water in general. However, marine is specific to those things in and around ocean or sea water. Marine life encompasses a broad range of plants and animals living in various ocean ecological systems throughout the world. Numerous things can affect marine life, including pollution, temperature, ocean currents and the sea's chemical balance.
A pie chart is a circle graphic that displays triangular slices proportional to the whole. The mean is the total of all the observations, divided by the count of the number of observations -- the "typical score." While it may, therefore, seem impossible to make a pie chart of the mean since one is a summary statistic and the other is a proportion of a whole, there are certain circumstances in which this can be done. An example would be if a baker wants to know the proportions of flour, sugar and milk he used on average over the last…
Trapezoidal approximation is a numerical integration technique used in scientific computing. It is a simple and relatively accurate numerical approximation of a definite integral, which is important when working with computers that can't perform symbolic integration and when there is no known integral for a function. Although there is some error associated with trapezoidal approximation, it can be negligible depending on the application. Sampling the function in question more frequently can also reduce it.
Mathematics is can often seem dry and difficult, but it holds many of the explanations and secrets of life. From simple daily tasks to complex construction projects to theoretical physics, math is at the center of the fundamentals of nature. There are many branches of mathematics, two of which are algebra and calculus.
The force on an object is equal to its mass times its acceleration. Momentum, by contrast, is mass times velocity, or p = M x V, where p is momentum, M is mass and V is velocity. The law of conservation of momentum says that if a system doesn't have any external forces acting on it, the momentum of this system doesn't change. Finding the change in momentum is pretty straightforward--it's proportional to the change in velocity.
Bakers struggle sometimes with cutting pies into equal portions when the portions are an odd number. Dividing a pie into two parts is easy; cut the pie down the middle (either horizontally or vertically). Similarly easy is creating four equal portions; cut down the center both vertically and horizontally. Cutting a pie with mathematical precision into five equal pieces can be done in three ways. Alternatively, if you do not want mathematical precision but just satisfied pie eaters, there is an easy way to cut the pie into five fairly equal pieces.
If you build or repair radio equipment, you may come across an inductor value not commonly stocked by electronics suppliers. Unlike other components which need industrial processes to produce, you can make decent inductors in your home workshop. An inductor is simply a coil of magnet wire wound around a cylindrical plastic form. Magnet wire has a thin coating of electrically insulating varnish. Since the varnish is thin, you can wind very tight coils with magnet wire. Some simple calculations will tell you how many turns of wire the inductor needs for a given inductance value.
Determine the interior volume of a length of tubing to know how much liquid it can hold. Volume tells you which tube is right for a specific job. Plastic or rubber tubing used for fluid transport have the shape of a hollow cylinder. The volume of the tubing depends on its length, diameter and thickness. Diameter measures the width of the tubing as seen from its circular end. Measure diameter along a line that passes through the center of the tube's circular end. Thickness determines the width of the tubing's walls.
A Scottish engineer named William Playfair first used pie graphs, or pie charts, to display a "Statistical Representation of the United States of America," in 1801. Pie graphs graphically represent data sets as segments of a circle. The entire 360 degrees of the circle represents the total data available, and the sizes of the individual segments are proportional to the percentage of the total made up by each data set. Creating a pie graph involves basic math and access to drawing equipment.
Knowing how to calculate distances between coordinates can help you in case of an emergency or to satisfy your own curiosity. Even with a GPS or tracking device, the exact distance is actually an estimate, sometimes off by a couple of miles. By simply knowing the coordinates from where you are, and where you need to be, you can find the exact distance between them.
Although science fiction writers make it look easy, there are still several problems that must be overcome before space travel is as common in life as it is in the movies. Space exploration requires humans to be able to travel long distances through space and survive in space for long periods of time. The demands of even beginning to explore these possibilities are testing humans' physical, psychological and technological mettle. Pushing further into space exploration means overcoming huge costs, technical problems, the limitations of the human body and the contents of space itself.
Many mysteries and unexplored locations exist in the ocean. Using sonar to scan the ocean floor is a useful way to map and explore these remote areas. Sonar transducers transmit sound waves from ships and sometimes use underwater transducers called towfish. Sound waves bounce off the underwater objects and return to the sonar device. Readings from the device determine the depth of the sea floor or layout of basic structures, such as geological formations and shipwrecks.
Marine environments are very diverse in terms of habitat and inhabitants. Marine life that inhabits a particular area in the ocean is adapted to survival there, but even the slightest change in that environment can have a huge impact on marine organisms. Natural factors such as pH balance and salinity can affect the marine environment as well as human factors such as toxic waste and boating pollution.
Whales are majestic, elusive creatures and most people only hope to catch a glimpse of one. These large, powerful mammals rely on their hearing to navigate through ocean waters, find food and communicate with other whales. In some ways, the Navy is similar to marine life. Sailors navigate through the ocean looking for enemy vessels, hidden explosives and other aquatic threats. Unfortunately, potential life-saving technology for humans is damaging and possibly deadly to water mammals.
Add two points to a map and determine the distance between them, so you know how long you going to travel. Knowing the distance of your route traveling by car helps in planning for stopping to rest, buying gas and getting a bite to eat. On the other hand, knowing how to determine distances while hiking could mean the difference between a hot shower and meal and getting stuck in the wilderness at night. All maps include a scale that relates distances on the map to distances in real life.
The term "deflection" is used in engineering to describe the degree to which a load bearing structure will deform under stress. In other words, it is the amount a steel beam or tube will bend or twist when a certain amount of force is exerted on it. It is always important to determine the deflection of steel tubes whenever you are using them to support weight. Even though a certain amount of deflection is inevitable, too much can cause your structure to collapse.
Deflection refers to the extent to which a building material can bend and flex during its lifetime. Deflection criteria for metal buildings become important if relatively fragile materials, such as glass, stucco or vinyl siding, are applied to the building structure.
Marine hoses are used on ships and boats to pump water around or to clean parts of the vessel. Bending stiffness is a property of an object that describes the relationship between the bending moment to the consequent deflection of the object due to the bending moment. In this context, the bending moment is the force applied, multiplied by the distance between the point at which the force is applied and the point of interest.
The process by which a spacecraft shifts from one orbit to another is called transfer orbit. This maneuver requires a shift in the spacecraft's speed, which is attained by two short engine impulses. The craft is sent on an extremely elliptical orbit so that when it reaches the aphelion (the furthest point in its solar orbit), it uses the transfer orbit to transfer to the orbit of the nearest planet. Orbital transfers are used for getting satellites into their geosynchronous or geostationary orbits, and also for space probes for interplanetary missions.
Calculate the rate a compressor discharges air to be able to determine the time required to inflate objects. An air compressor utilizes a motor and fan system to create a difference in pressure, which forces air out through a hose. The flow rate of a compressor is measured in how many cubic inches of air it moves per second. You can determine the flow rate of an air compressor using an object of known volume, or air capacity, and a few tools.
Calculate the size of the intake pipe on a home heating system to ensure enough air reaches the device. Each heating system specifies a required size, in cubic inches, for air intake. Its job is to take in room temperature air that is then heated and sent throughout the home. The volume, or capacity, of an air intake pipe depends on the dimensions of its cylindrical shape. (See Reference 1) These dimensions include its length as well as radius. On the circular opening of the pipe, radius extends from the center to the edge. (See Reference 2)
Test duct-work volume to be sure enough hot or cool air flows through your home. Furnaces and heat pumps, for controlling the temperature in a home, need air ducts to to move air throughout a home. Having too small of a duct may limit the heating ability of a furnace. Air ducts are cylindrical in shape therefore a cylinder volume calculation yields their air capacity. The volume of a cylinder depends not only on its length, but also its radius. (See References 1) Radius measures the distance from the center of the duct to its edge. (See References 2)
Gauge the drilling ability of an auger by determining the volume between its flights. Augers allow cylindrical holes to be dug in the ground by the spinning of a long metal shaft with flights attached. An auger flight is one of the many corkscrew-like blades that extend from the shaft. Since an auger produces a cylindrical hole, determining the space of the cylindrical section between flights yields volume. This volume measurement depends on the distance between the flights as well as the how far the flights protrude form the shaft.
Inductors regulate current flow in electrical circuits. The inductor consists of wire wrapped around a cylinder made of plastic. When an electrical current is sent through the inductor, a magnetic field is induced within the cylinder. This magnetic field in turn creates a current in the coil opposing the initial current effective reducing its value. The diameter of a inductor measures the width of the circular end of the coil on a line passing through its center. The diameter also equals twice the radius of the inductor.
Eratosthenes of Cyrene is attributed with the first scientific estimation of the Earth's radius--and he did it without even leaving Egypt by using the angle of a shadow cast by a stick. He was surprisingly accurate, having a margin of error of only one percent. Since that time, we have learned that the Earth is not a perfect sphere, so there is no single value for its radius. Rather, the radius of the Earth ranges from 6,353 to 6,384 kilometers, or 3,947 to 3,968 miles. Still, you can calculate the distance from the center of the Earth using relatively simple…
Test the size of duct work to ensure its capability to transport the amount of air stated by the manufacturer. Ducts commonly carry air from heating and cooling systems throughout a home or office. The size of duct work is determined from its interior volume or empty space contained within. Because the duct has the shape of a cylinder, like a large straw, finding ducts' length and radius allows calculation of its volume. Radius measures the distance from the center of the duct's circular end to its edge.
Know precisely the size of hole an auger creates by determining its blade volume. Auger blades resemble a long corkscrew made of metal. The sides of the corkscrew are sharp to allow the auger to easily burrow through tough soil. A spinning auger blade has the shape of a cylinder and therefore creates cylindrical-shaped holes. The volume of the auger blade depends on its length as well as its radius. The radius of a cylinder measures the distance from its central axis to its edge.
Just as an object being held above the ground has mechanical potential energy, individual charges have what is called electric potential energy. This value is measured in volts, is a scalar value (meaning it has a magnitude but no direction) and calculating the electric potential energy isn't difficult with the right information available.
The shortest distance between two points along the surface of a sphere is known as the great circle distance. This measurement is used regularly in navigation for plotting the shortest route across the sea or through the air. The distance is calculated using the latitude and longitude in radians for each of the two points on the sphere. The output is also given in radians, but it can be easily converted into a hard unit by multiplying the radians by the radius of the sphere.
Determine the radius of your cable tray to get an idea just how much wire can wrap around it. A cable tray resembles a spool and stores long lengths of cable, wire or chain depending on its radius. The radius of a cable tray extends from the center of one of its circular ends to its edge. It is more accurate, though, to first determine the circumference, or distance around, of the tray, then calculate the radius. This avoids confusion over finding the exact center of the cable tray for a radius measurement.
Figure out exactly how much concrete you need before making a purchase. Not only will this save you money by preventing overbuying but it will also keep you from wasting concrete. Volume relates the amount of concrete needed to fill a given block mold to the interior dimensions of the mold. A block's volume is the amount of space it will occupy in cubic inches once formed. Concrete blocks provide an economical and easy solution for do-it-yourself projects such as walls or walkways.
Know exactly how much fluid your water or fuel tank overflow pipe can carry before a malfunction occurs. The overflow pipe takes fluid out of the tank when the system backs up to prevent spillage out of the top or bottom of the tank onto the floor. The size of the overflow pipe is found by determining the volume of a cylinder, since pipes have a cylindrical shape. Measurements of the physical dimensions of the pipe allow calculation of volume.
If you have watched a top whirl, you might have noticed the peg makes small circles as the top spins. Watch long enough, and those circles will get larger and faster as the top slows and nears the tipping point. The path traveled by the peg is called a precession cycle. Deducing the mathematics behind this physical problem might sound like a mere intellectual curiosity, but the axis of our planet spins in a similar pattern. Understanding the relationship between Earth's axis and the sun can aid in making predictions about future climate change.
Calculate the capacity of a heating oil tank before refilling to know the exact amount of fuel you need to purchase. Fuel oil tanks, found in the basements of homes, are cylindrical in shape. The capacity in gallons, or volume, of such a tank depends on its dimensions. The pertinent dimensions are its length and its radius. Radius is measured from the center of one of the tank's circular ends to its edge. A larger volume means more storage capacity for the tank.
Lenses need to be measured for a variety of reasons. For example, you might want to replace it in a gun scope, telescope or flashlight. You will need to know the diameter of the lens before you can replace it. The measurement has to be precise. There is a tool that is specially designed for the job: a dial caliper. The caliper will give you a reading that is accurate to 1/1,000 of an inch.
Acceleration is the rate of change in velocity (speed) with respect to time. It quantifies how quickly an object is speeding up or slowing down, described by units of meters per second squared (m/s^2) or feet per second squared. Although acceleration can be given as an average increase in speed over a specified time interval, the instantaneous acceleration is often the more useful quantity in considering the distance covered for the duration of the speed change. To determine this distance, some knowledge of introductory calculus and integration methods is a prerequisite.
The capacity of an object that carries gases or liquids grows when its physical dimensions increases. Scientists and engineers refer to the capacity of a tank or hose as its volume, or amount of empty space inside the object. A pressure hose's interior shape comprises a long, empty cylinder that carries forced air or water. The volume of this cylinder is related to the length of the hose, as well as its inner radius. Looking at the circular end of the hose, the radius measures the distance from the circle's center to its edge.
Overflow tanks collect excess liquid that spills out of a main reservoir. Many examples exist, including the coolant overflow tank that is part of an automobile engine, as well as cylindrical sewage overflow tanks. To have a diameter, an overflow tank must be cylindrical in shape. The ends of a cylinder are circles that have a diameter or width as measured on a line that passes through their center. Half of the diameter's length is the radius, which is related to the distance around the cylinder's side, called circumference.
The diagonal of a square is a line drawn from one corner to the corner across and at the other side of the square. The length of the diagonal of any rectangle equals the square root of the sum of the squares of its length and width. A square is a rectangle with all sides of equal length, so the diagonal's length is the square root of twice the square of a side, which simplifies to the square root of two multiplied by the length of a side. You can compute the length of the diagonal merely by multiplying the…
The acronym FCC stands for "Face Centered Cubic." It is a specific subset of crystalline lattice configurations that describes the geometry of the atomic constituents of a solid whose primitive unit cell takes the form of a cube. The FCC structure describes an arrangement in which atoms are fixed at all eight corners of a cube, with an additional atom fixed at the center of each of the six cube faces. The planes of this structure take the shape of an equilateral triangle with three corner atoms fixed at each vertex. The distance between planes is simply the perpendicular length…
An electric field is a force field surrounding electrically charged particles. Mathematically, the strength of an electric field at any given point is defined as F / q, where F is the force a particle experiences and q is its charge. Since like charges repel, all the net charge of a conductor is on its surface, so for nonpoint charges you can often use Gauss's Law to evaluate the strength of the electric field. The following steps show how to calculate this field for a charged sphere.
Angular momentum is a fundamental aspect of the universe. It is what holds solar systems together and it is responsible for keeping gyroscopes upright while they spin. Figure skaters change the orientation of their bodies to change their angular momentum when they spin. It is a property that is conserved in a system with no external torque. While an object moving linearly has momentum that is equal to its mass multiplied by its velocity, angular momentum is calculated using an object's moment of inertia and its angular velocity.
A handheld GPS receives extremely accurate position information from an array of 24 satellites that orbit the Earth. According to Garmin, their GPS devices are accurate to within 50 feet. GPS devices cannot only be used in automobiles for driving directions, but also on foot while hiking. A person walking can use a GPS to determine the dimensions of a large shape or tract of land outdoors by noting the distance traveled.
Many people wince at the thought of calculating math formulas, dreading a return to this nemesis of their High School days. However, though you may never need to apply math formulas in many occupations, there are a number of formulas that are always handy to learn and remember. The radius of a sphere is the length of the center point to the outside edge. You may encounter this formula if purchasing replacement pool or billiard balls; fortunately the formula is simple and easily worked out using a calculator.
A wheel rolling over a surface overcomes static friction. If it could not, the wheel would stop rolling. Static friction depends on many things such as the wheel material, axle friction and the surface rolled upon. It does not depend on the mass of the vehicle, however. The combination of a few rules of physics will allow you to calculate the distance an object, such as how far a car will roll before coming to a stop.
Air compressor tanks hold air at high pressure for delivery to paint sprayers or tire inflation. The volume of the air compressor's tank equals the amount of air the tank can hold. The key to determining the tank's volume, in gallons, is realizing that it has a cylindrical shape when you exclude the rounded top and bottom. The top and bottom hold very little air when compared to the rest of the container, so a cylinder approximates the tank's shape very well. Cylinder volume depends on length as well as radius, which is half of the tank's rounded width.
Electrostatic potential is important in understanding physical systems. Calculating electrostatic potential requires multiplication, exponent manipulation and "reading" unit prefixes. The most basic calculation of electrostatic potential is that for a single point charge.
It is easy enough to figure out the length of a vertical or horizontal line on a graph or other plotting system; you can just compare it against the markings on the grid. For diagonal lines, though, it's a bit trickier. This is where the Pythagorean Theorem comes in. Pythagoras was a Greek mathematician who discovered the formula the sum of the squares of the two shorter sides of a right triangle--a triangle with a 90-degree angle in it--is equal to the square of the longest side, called the hypotenuse. You can apply the same principle to calculate the length…
Calculating the distance between two circles may seem like an exercise designed to frustrate trigonometry students, but it has many real-world applications. Computer programmers use it to calculate where to place characters or objects in a game so that they won't run into each other, while engineers may use it to calculate where to launch satellites or how to build runways so that two planes can safely circle the airport at the same time. You can calculate the distance between two circles with only a few pieces of information and a knowledge of geometry.
The simplest way to calculate the distance between two objects is to measure it directly. However, that is not always feasible, such as with distant, inaccessible objects. Perhaps you are hiking and wish to know the distance across a river or ravine. A simple technique called triangulation allows you to calculate the distance without ever stepping foot into the river.
Catapults can be effective weapons for throwing stones at or over walls, as was often done in the Middle Ages. Nowadays we don't use catapults in this fashion, but you can learn something about physics by calculating the distance a projectile travels using a model catapult.
Topographic maps are maps that show not only standard features such as lakes, rivers and roads, but the land's actual shape as well. Topographic maps were developed for military use, but they are popular with hikers, hunters and geologists. Standard symbols are used to indicate various land shapes so that anyone reading the map will understand the features. A slope is indicated by a series of lines. The closer together the lines are, the steeper the slope.
Thunderstorms can be dangerous, so it is always a good idea to be aware of their approach. If you have ever noticed a flash of lightning and, a few seconds later, heard the rumble of thunder, you've already assembled all the tools you need to estimate the distance to the storm.
The epicenter is the point on the Earth's surface immediately above the center of underground movement sensed as an earthquake. This movement sends out shock waves of many kinds, which move at different speeds. The different waves can be detected by sensitive instruments called seismographs. From the time difference between the first recorded occurrence of different kinds of waves of the same earthquake, a scientist studying the seismograph record can determine the distance to the earthquake's epicenter but cannot determine the direction. By using three or more seismographs, however, a scientist can triangulate a location.
Calculating distance is measuring the length covered by a moving object without considering the direction in which the object traveled. To calculate acceleration, you must know both the velocity and the distance. Velocity is the distance an object has traveled per unit time. Acceleration can be described as the rate at which an object changes the velocity. Therefore, to calculate acceleration, the distance must be measured as well as the velocity.
Determining the distance between latitude-longitude points is not as straightforward as calculating the distance between XY points because the distance between lines of longitude varies with latitude. The haversine formula for great-circle distances is generally used for this calculation.
Where lumens measure the amount of light a light source emits, lux tells how much that light source illuminates an object or workspace that is one square meter in area and placed one meter away from the light source. Lux meters, or light meters, determine the amount of available light in either luxes or in foot-candles (illuminance of one square foot area, located one foot from a light source). Lux meters contain a central unit housing the computerized electronics that operate the meter a light sensor and a digital or analog display.
The pressure difference between two places is measured by physicists using a U-shaped manometer. A manometer consists of a U-shaped tube connected at one end to a closed reservoir, with the other side open to the surrounding atmosphere. By placing a liquid of known density, or compactness, into the U-shaped portion, you can calculate the pressure difference between the closed reservoir and the air outside the manometer by measuring the height difference between the liquid in the left and right parts of the U-tube. In science, pressure is measured in pascals, so metric measurements must be made.
Lumens and candlepower measure light emission--measured at the light source--and visual perception of light as it reflects off objects. Candlepower generally describes the light's radiance or intensity while lumens indicate the light's luminance.
Physicists and mathematicians denote the net change in linear position of an object by the capital Greek letter delta followed by an "x." Another name for "delta x" is displacement. Displacement quantifies the difference in the starting and ending positions of a moving object. It is important to note displacement may be positive or negative, since it is measured from a fixed point of reference. The location of the point of reference is known as the origin and is denoted by the number zero. Measurements made to the left of the origin are negative, while measurements made to the right…
In photography, the working distance measures the distance between your lens and the object you're photographing. You often can't choose your working distance, and you choose a lens that best suits your set working distance. If you must use a lens with a particular focal length; however, you can calculate the ideal working distance for focusing on your subject.
You can use a regular map to calculate the distance from one point to another, but if there are hills along the way, the path along the ground might actually be longer. With a topographic map, you can calculate the distance more accurately, taking into consideration the extra length required to ascend or descend hills. The precision of your calculations will depend on how many separate measurements you take. A simple measurement from the top of each hill to the bottom, ignoring smaller irregularities, may be accurate enough, but the same technique can be applied to each change in slope…
You can easily calculate the horizontal distance that a projectile will travel if you know the right equation to use. The distance of a projectile is dependent upon three critical factors: its initial velocity, the angle at which it was launched, and the acceleration due to gravity. Initial velocity and gravity are important because the faster the projectile travels, the farther it will go before gravity pulls it back to Earth. The launch angle determines how much the projectile will travel vertically versus horizontally. These three factors can be combined into one equation to calculate the distance of a projectile.
Measuring the distance between two points on a curved surface, such as the globe, is not as straightforward as it is for a flat surface. There are a number of different trigonometry formulas that can do it. The most precise one, especially for fairly short distances, is called the Haversine formula.
Finding the distance between two points in three-dimensional (3-D) space is a common problem in mathematics (for example, in linear algebra) and in programming. A programmer would want to find the distance between two points for collision detection---for example, you might want to find out when a ball will hit a wall or other solid surface in a computer game. A general formula helps you to find the distance for any situation.
Gauss's law and Coulomb's law are two alternative ways of obtaining the electric field strength from a distribution of charge. An electric field is generated from and exerts forces on charged particles. The electric field is a vector field that is directed away from positive charge toward the negative. In Coulombs law, the magnitude of the electric field E at a point in space is proportional to the charge q over the distance s, from the source, squared: E = k*|q|/s^2, where k = 8.988e9 Nm^2/C^2. Gauss's law states that the total electric flux out of any closed imaginary surface…
In algebra, points are commonly defined using Cartesian coordinates. Coordinates "X" and "Y" of a point are given in brackets following the style (X, Y): for example (5,8). The distance formula based on the well-known Pythagorean theorem permits you to easily calculate the required distance from the differences of the coordinates of the two points. For instance, compute the distance between points with coordinates (-3.4, 6.5) and (2.7, 10.2).
Concave (sunken) mirrors in the shape of a parabola have the property of being able to focus light at a great distance to a point. This property is exploited in most large visible-light telescopes. The distance from the center of the mirror to the point of focus is called the "focal length." The parabola has the form y=x^2, where ^2 means "squared." From this, you can derive the focal length of a mirror by measuring how wide and sunken it is.
The angular distance traveled around a circle is the number of radians around the circle the object goes. There are 2π radians in one revolution around a circle, so three revolutions is an angular distance of 6π radians. If the motion is rectilinear, it's hard to determine the angular distance traversed. If the motion is curvilinear, the angular distance is easier to determine.
A car's tires are designed to provide friction between the car and the road. This friction allows the car to accelerate from a stop and to decelerate from high speed. The tires provide grip, allowing the car to safely navigate roadways. When a driver wants to stop the car, he makes a mental estimation of the required stopping distance and applies the brakes at a rate that allows him to stop safely. In emergencies, the driver can apply the brakes firmly to stop in a shorter distance. Today, anti-lock brakes prevent wheels from locking, which could make the car skid.
Geodesic distance, or "great circle" distance, is the shortest distance from one point on the earth's surface to another. This distance is "as the crow flies," meaning it does not take into account the terrain between the two points. For long distances, such as the ground track for an intercontinental flight, you must take the curvature of the earth into account. If you assume the earth is spherical, the calculation is fairly easy and accurate enough for many applications.
Calculating distances to the stars is a very complex procedure, normally undertaken only by professional astronomers with cutting-edge instruments. Even the most accurate star-distance measurements are only very good approximations. However, if you have access to an astronomer, a professional telescope, or an accurate data feed from other researchers, you can use time-tested procedures to calculate distances to the stars.
You can calculate the height of a structure too tall to measure directly, such as a flagpole or a building, by geometric or trigonometric methods. In the former case, you compare the shadow of the measured structure to the shadow of a directly measurable object. In the latter case, you view the top of the object through an instrument measuring the angle of view.
A parabolic mirror has the property of reflecting light from a great distance---that is essentially parallel---to a point. The distance of this point is called the "focal length." Because of this property, parabolic mirrors are used in most large visible-light telescopes. You can easily determine a parabolic mirror's focal length with a simple formula.
The slope or grade refers to the change in the elevation of land over a distance. In other words, it is the measurement of how much higher an incline, or how much lower a decline, is at a specific points compared to where you are currently standing. People use slope or grade measurements from everything to building construction to simply putting a slide in your backyard.
The grade of a slope is the amount of the rise of a slope as a proportion of distance. It is commonly expressed as a percentage for highway use. For example, when driving through a mountain pass, you may see signs for 6% grades or higher. This means that for every 100 feet of distance, the road goes up or down 6 feet. A 0% grade is flat, and a 100% grade would be a 45 degree angle, where the distance and rise are equal (for instance, 10 inches long with a 10 inch rise). You can figure out the…
When using mechanical machinery that uses pulley systems, it is imperative to calculate shaft deflection. Shaft deflection refers to how much the pulley bends or stretches in accordance with how much weight is placed on it. Accurately calculating shaft deflection is important in making sure the pulley will be able to handle the weight involved and will not stretch or bend to too great a degree, which could cause the pulley system to break entirely. Once the variable numbers are identified, calculating the angle of shaft deflection requires only the usage of a straightforward formula.
Depth of field is a photography term that refers to the space in which the subjects of a photograph will be in-focus. Any objects further from the lens or closer to the lens than the depth of field range with be out-of-focus. The plane of in-focus objects will be determined by the near focus limit and far focus limit, which must be calculated independently. Each of the focus limits are determined by the lens' focal length, aperture and the distance between the photographer and his subject.
The term "light-year" refers not to a length of time, but instead a unit of distance often used in astronomy. Astronomers define a light-year as the distance light travels in one year. To calculate this distance, or the distance that light travels in any amount of time, you must know the speed of light and how to manipulate the equation for speed in general. The speed of light is roughly 300,000 kilometers per second (km/s), or 186,000 miles per second (mi/s). Speed is equal to distance traveled divided by the time it took to travel that distance.
You can easily calculate falling distance from the time that an object took to fall that distance by using equations derived from Newton’s second law of motion, as discussed in “Fundamentals of Physics.” Specifically, the gravitational force acting on a falling body is F=mg, where m is the body’s mass and g is the acceleration due to the force of gravity. Integrating twice gives the an equation well-known to freshman physics students: y(t) = y(0) + v(0)xt - 0.5x9.8xt^2. Here, v(0) is the initial vertical velocity and y(t) is the vertical position after time t. The acceleration here is in…
A circle graph, also known as a pie chart, is a graph used to visually display proportions. Usually, these proportions are displayed in percentages, although they can be displayed also as fractions or ratios. It does not take a very advanced knowledge of math to be able to plug your own circle graph, but you will need the right tools and at least an elementary knowledge of proportions.
Slant height is the distance, from bottom to top, along any surface that is slanted in relationship to its base. So the measurement from the base of a pyramid up to its tip, along one of the sides, would be slant height. The measurement from the base of a ramp straight up to its top would also be considered slant height. The easiest way to calculate slant height is by using the Pythagorean theorem as if the slanted side were one side of a right triangle.
You certainly have experienced the decrease in a sound's intensity as you get farther from the source of the sound. What you may not know is that the intensity does not decrease in a linear fashion as you move away; it occurs relative to the square of the distance from the source, which means it decays very fast. This is because the sound power is dispersed in a spherical fashion from its source and is why sounds can seem very loud when you are right next to them but very soft when you move a short distance away.
Volume is the measurement of the amount of space in an object, and is calculated in cubic units, such as cubic feet or cubic centimeters. Calculating the volume of a hole is often necessary when determining the amount of material needed to fill it or planning a well. Using the volume formulas for basic geometric shapes, it is easy to calculate the approximate volume of round and rectangular holes. A short hole can be measured with a yard stick or tape measure, while deeper holes will require an alternative method.
GPS technology has numerous applications both for personal and commercial use. A GPS unit receives satellite signals and provides real-time location data. This information can then be plotted onto maps using geographic information system (GIS) software for additional applications and interpretations. Several factors affect the accuracy of the GPS data. Land features such as tree cover or hilly terrain can interfere with satellite signals. Also, a GPS unit measures distances between points "as the crow flies" and does not factor in changes in distances due to topography. For best results, minimize whatever factors you can control.
While not a substitute for a compass and map, a GPS unit makes navigation easy whether on the road or on a trail. At any given time, it is possible to know your precise location and its coordinates in latitude and longitude. There are several methods for calculating distance with a GPS unit. Refer to your device's user manual for instructions on setting coordinate systems. Different systems may be required, depending on the method you choose to calculate GPS distances.
In the third century B.C., Eratosthenes was able to mathematically calculate the earth's diameter by comparing differences in the angle of the sun's rays at two separate geographic points. He noticed the difference in the angle of a shadow in his location at Syene, which is present-day Aswan in Egypt, and that of a shadow in Alexandria was about 7.2 degrees. Since he knew the distance between the locations, he was able to determine the circumference of the earth, and therefore the diameter and radius as well. You can do this, too, by following the methods he devised.
Orbits have several important components, namely the period, the semi-major axis, the inclination and the eccentricity. You can only compute the eccentricity and the inclination from observations of the orbit itself over time, but the semi-major axis and the period are related mathematically. If you know one of these parameters, usually determined originally from observations, you can determine the other. It is possible to find the semi-major axis of many orbits from information tables about astronomical objects. Once you have the semi-major axis, you can find the period of an orbit.
Bucket trucks make a great photographic platform when you need a higher point of view above the ground but not as high as you could get with an airplane or helicopter. This solution is a great option for large group portraits. A bucket truck is also excellent when taking photos in low light conditions from an elevated platform as the truck is a stationary platform, unlike an aircraft. This article will briefly explain the steps to use a bucket truck for photography.
A screw is a simple machine that works as a modified incline plane. As the screw is turned, the screw enters deeper into the substrate. Once inside the substrate, the frictional force of the thread is intended to prevent the screw from rotating back out of the substrate. The thread of the screw may be viewed as an inclined plane wrapped around the shaft of the screw. The slope of the screw is the distance for one complete rotation around the screw while the height of the inclined plane is the distance between the threads, known as pitch. The relationship…
Maps are used to represent a larger area in a scaled-down format so people can get a birds' eye view of the area. The map scale shows how the distance on the map compares to the distance in real life. The scale will depend on the size of the area being show on the map. For example, an inch may represent a mile on a local map but on a national map an inch may represent 300 miles.
River miles are distance measurements by the U.S. Army Corps of Engineers that measure miles along a navigable waterway. The mile numbers begin with zero (at the mouth) and increase with each mile you travel upstream. You use river miles to locate places along the river, relative to the location of the mouth. While most rivers in the United States already are marked, you can mark river miles along smaller channels, too, using simple tools and calculations.
The distance formula stems from the Pythagorean Theorem and is primary used to calculate separation between any two points that are given in Cartesian coordinates. According to the formula the distance equals to sqrt((X2 - X1)^2 + (Y2 - Y1)^2); X1,Y1 and X2,Y2 are Cartesian coordinates of the two points and "sqrt" is an abbreviation for the root square math operation. It is also possible to compute a geometrical shape perimeter, for example, the circle circumference based on the distance formula.
Whether you're gazing at the moon, Saturn, the Orion Nebula or a distant object, the magnification of the telescope plays an important role in your experience. Calculating magnification is relatively easy, and it can help in decision-making when purchasing and using your telescope and eyepieces.
The azimuth of an object is its direction in the sky, measured in degrees. It corresponds to the cardinal direction on land, namely north (0 or 360 degrees), east (90 degrees), south (180 degrees) and west (270 degrees). Astronomers use azimuth and altitude (the height of an object above the horizon) to describe the location of a specific object. Because of the Earth's rotation, the azimuth and altitude both change over time as the stars appear to move across the night sky. Satellite dishes also use azimuth and altitude for pointing at the appropriate broadcasting satellites in the sky.
GPS stands for global positioning system. It is a satellite-driven means of navigation. As ubiquitous as GPS is in our everyday lives, on May 1, 2000, former President Clinton halted the intentional degradation of GPS signals. Prior to the proclamation, handheld GPS units were ten times less accurate. This means that a GPS could lead you within 100 feet of a destination, plenty of room for inaccuracy. Now a handheld GPS can have accuracies of within 10 feet, depending upon conditions.
Mars is a rocky planet, smaller than Earth, measuring 4,221 miles in diameter, making it slightly more than half the size of Earth. An orbit occurs when one object travels around another object. The sun's gravity, interacting with each planets' gravity, form an equilibrium, which creates the orbital plane. Mars' orbital plane is 1.8 degrees above the equator of the sun.
In the first half of the 1960s, evidence of the concept of sea floor spreading, resulted in the acceptance of plate tectonics. Dr. Robert Dietz, in 1961, and Dr. Harry Hess, in 1962, proposed the idea of sea floor spreading: the sea floor is continually created volcanically at mid-oceanic ridges and then spreads away, carrying the continents with them. Because of reversals of the Earth's magnetic field, the magnetic pattern of the sea floor can be used to date a piece of oceanic crust. Geologists at Smith College estimate that sea floor spreading throughout the world's oceans ranges between 1…
Chromatography is a method of substance separation. It is implemented using a narrow tube (column) packed with a specific material. A mixture of compounds is forced through the column using pressure. Each compound comes out from the column during certain times, graphically representing a peak on a chromatogram. The position of the peak maximum, called a retention time, is specific for each compound. Performance of chromatographic columns is expressed as a number of theoretical plates. A theoretical plate is an imaginary layer within a column that helps to interpret the separation process. A higher number of theoretical plates corresponds to…
The relative distance between two points on a map is the same as the relative distance between two points in the real world. Maps show the scale to which they are drawn, such as "one inch equals five miles." You can use a map's scale to calculate both straight-line map distances and map driving distances.
A clinometer is a scientific instrument used to measure angles and is used by scientists, engineers and other professionals to gather data during field work. For example, an engineer might use a clinometer, also known as an inclinometer, to survey land, determine its slope or calculate the height of objects such as trees. There are multiple types of clinometers, but all perform measurements and provide data for use in a set of related formulas.
The distance between two points can be calculated from Cartesian coordinates of these points abbreviated here as X1,Y1 and X2,Y2. The coordinate differences "X2-X1" and "Y2-Y2," as well as the distance, form the right triangle (see Figure). Hence, the distance (diagonal) can be calculated using the Pythagorean theorem as sqrt((X2-X1)^2+(Y2-Y1)^2). "Sqrt" is an abbreviation for the root square math operation. As an example, calculate the distance between two points with coordinates X1=2, Y1=13 and X2=10, Y2=19.
When a photographer wants to get the greatest depth of field in an image, he needs to focus at the hyperfocal distance. The area in focus in a picture is called the focal plane. One-third of the focal plane is ahead of the object being focused on and two-thirds behind. When a photographer is focusing at the hyperfocal distance, everything in her image will be sharp, from a near object in the foreground to the furthest object in the background, also called infinity.
Ancient astronomers knew that the earth is round, a sphere, even though the mariners of the Middle Ages forgot and were sure that the earth was flat. The ancients figured out how to measure the earth's circumference and used that information to create a system of concentric circles to divide the earth into sections. They called the lines defined by these circles lines of latitude. Later geographers assigned upper, middle and lower zones to name the various groups of latitudes. Lower latitudes are closest to the equator.
Sound navigation and ranging, or sonar, is an umbrella term for technology and methods that use sound to detect objects, usually underwater, much the same way bats rely on sound for catching food in the air. The basic principles on which sonar relies are that sound moves at a steady rate through a given medium, such as air or water, and that certain types of objects produce certain types of sounds. With this knowledge, calculations can determine the distance to an object and identify it with reasonable certainty. The Navy mainly uses sonar to detect vessels, torpedoes and mines. Commercial…
The Big Bang theory is one of many proposed theories on the origins of the universe. It sets up a cosmological model which aims to show that the universe began from an initial "bang." According to the theory, this release of hot and dense matter sent the universe into unstoppable expansion.
Velocity, acceleration and motion are some of the very basic physics topics first year physics students will see. Some of these concepts and formulas are based on things we do every day. So, let the mystery be gone, because today you will learn how to solve for velocity in physics in just a few simple steps. Read on to learn more.
Anemometers are used to measure either wind speed or air pressure, depending on the style of anemometer. The most familiar form, the cup anemometer, was invented in 1846 by John Thomas Romney Robinson and features four hemispheric cups arranged at 90-degree angles. Making this form of anemometer is a common school science project, but reading it requires a bit of mathematical skill.
