Measurement

1. Measurement

2. Measurements • What can we measure? • We can measure mass, time, length, and temperature. • What is the difference between a calculation and a measurement? • What can we calculate? • Area, Volume, Work, Pressure, Torque, Resistance, Energy, ………

3. Measurements • What is included in a measurement? • A measurement should always include 2 things: a number and a unit. • What can be determined by knowing the unit(s)? • In most cases, you can deduct what has been measured.

4. Units • Units are used to define measurements so that everyone knows exactly how much. Some examples of units are meter, foot, inch, centimeter or a mile. • If a planner draws a bridge and says it is 1000 long and the builder looks at the plans and says it is one short, this is a problem! Are they talking about a meter, a foot or an inch?

5. Units • Units are very important! Some examples everyone may know include things like: there are 20 minutes until lunch; it takes 5 days to drive across the country; a desk top is 20 inches wide and 25 inches long; a recipe uses 2 cups of flour; it is 45 degrees Celsius outside today. Each of these measurements includes a number and a unit.

6. Mass • Everything, whether it is a solid, liquid, or a gas has mass. It is a measure of how much of the substance is there - how many molecules. • Sometimes mass is expressed as weight, even though they are not the same.

7. SI and Customary Systems • In the SI (metric) system, the units for mass are grams, kilograms (1000 grams) or milligrams (1/1000 grams). • In the American unit (called the Customary (English) system), the weight of the substance is used, in pounds or ounces. A pound is 16 ounces.

8. SI and Customary Systems • Often abbreviations are used for the units: a gram is g, a kilogram is kg, a milligram is mg, a pound is lb. and an ounce is oz.

9. Time • The easiest way to think of time is how long it takes something to happen. It may take 10 minutes to drive to school; it may take an hour to eat dinner. The units for time are the same around the world: seconds, hours, days, years. A common example of time measurement is how long it takes an object to go from one point to another or from point A to point B.

10. Length • Length is a quality used to define an object. A pencil is 7 inches long. A student is 6 feet tall. A swimming pool is 2 meters deep.

11. Length in SI and Customary Measurement Systems • The most common units for the SI or metric system are a centimeter, a meter (100 centimeters) and a kilometer (1000 meters). • In the Customary or English system, that most Americans use, common units are the inch, a foot (12 inches), or a mile (5280 feet).

12. Length in SI and Customary Measurement Systems • These units may be abbreviated: centimeter as cm, meter as m, kilometer as km, inch as in, foot or feet as ft, and a mile as mi.

13. Area • In addition to the length of an object, it is often useful to know the area or volume of the object in question. The area is how much room is on a surface like the floor of the classroom or the surface of a wing. Area is found by multiplying one length by another length. The result is called "square units".

14. How to Calculate Area • If a room is 20 feet by 25 feet long you would multiply 20ft X 25ft = 500 square feet (ft2). Many common measurements in science and engineering include square feet or square meters. Another common measurement is an acre, 40,000 square feet.

15. Volume • The volume of an object can either be how much space is available inside an object, like a fuel tank or how much actual material is inside a specific place. Volume has three measurements, length, height and width (all of these can be called lengths). Multiplying these together equal volume. The result is cubed.

16. How to Calculate Volume • A 12 inch long section of a 2 inch by 4 inch board (2 in X 4 in X 12 in) would have a volume of 96 cubic inches (in3). Cubic feet, cubic meters, gallons, liters, and cubic centimeters (cc for short) are all common units for volume.

17. Temperature • The quality of temperature is a measure of how hot or cold something is. A thermometer is commonly used to determine the temperature of an object. Everything has a temperature: the rocks, trees, people, air. The weather report in the newspaper usually gives the high and low temperatures of the air each day.

18. Temperature in the SI and Customary System • The common units for temperature are degrees Fahrenheit or degrees Celsius (what used to be Centigrade). • In America, almost everyone uses the Fahrenheit scale. • In science and engineering, however, temperatures can be reported using either scale. • The way this is shown is either 85° F or 85° C.

19. Pressure • Pressure is measured as force per unit area (square inches, square meters). In metric units, pressure is measured in Newtons per square meter (N / m2). In the English system, pressure is usually measured in pounds per square inch. • Example: The atmosphere (air) presses on your skin at 14.7 pounds per square inch (psi).

20. Pressure • Pressure can be powerful. A small pressure, spread over a very large area, can add up to be a very large force. Air pressure decreases as the altitude increases; pressure also decreases when the speed of the fluid (air, water) increases. When the temperature of a fluid increases, so does the pressure.

21. Density • Density is a measure of how much mass (the amount of molecules) is included in a given object or volume. Another way to think about it is how tightly the molecules are packed in a volume or object. When we talk about the density of fluid, we often refer to a specific volume, such as a cubic meter or a cubic foot.

22. Density • A fluid with a lot of molecules tightly packed together has a high density; one that has fewer molecules would have a lower density. Water, for example, has a much higher density than air. A 10 gallon fish tank with water in it has much more mass in it than a 10 gallon tank with air in it. Since it has more mass, it will weigh more.

23. Density • Density is also used to define whether a fluid is incompressible or compressible. If the density of the fluid is fixed (constant), the fluid is incompressible; neither the mass or the volume can change. Water is an incompressible fluid. The amount of volume and mass will stay the same, even under pressure.

24. Density • Gases (like air), are compressible, they will expand to fill a new volume. The mass doesn't change, but the volume increases, so the density of the gas decreases in the new volume.

25. Force • Forces have been defined as pushes or pulls on an object. To determine the units of force, scientists and engineers use various mathematical formulas to measure force. • An interesting point about the force is that in addition to a value and units, it also has a direction associated with it.

26. Force • Let us assume a force is applied to the left side of a box, the motion will be to the right. If the force were applied down on the top of the box, no motion would occur. Since the box is already on the ground, it can't move any further. No matter how large the force was, there would be no motion. So, defining a direction for a force is very important.

27. Weight and Gravity • In other countries, objects are measured in terms of their mass, in grams or kilograms. In the United States, however, people use the terms for weight to also mean mass. This works okay near the earth's surface because gravity is constant, so the units of "weight and mass" stay the same.

28. Weight and Gravity • Acceleration of gravity in the SI system of measurement is equal to 32.174 feet per second, at sea level. • Acceleration of gravity in the Standard system of measurement is equal to 32.174 feet per second, at sea level.

29. Weight and Gravity • Because of gravity, weight is actually a force and not the true mass of an object. If an object is taken up high in the atmosphere, the force of gravity is less. Therefore, the "force" of weight is less. An object will weigh less, at high altitude, but the mass will remain the same.

30. Weight and Gravity • Scientists must be able to separate weight and mass. Therefore, the units are: kg of mass or Newtons of force. Mass will not change. Newtons will change with altitude. Acceleration of an object at high altitudes is less, due to gravity, therefore the weight (force from gravity) of the object is less.

31. Weight and Gravity • This is why an object on the moon weighs less than the same object on the earth. The gravitational attraction on the moon is less than that of earth, so the acceleration due to gravity is less (about 1/6th that of the earth). When an object is weighed on the moon, it will weigh about 1/6th as much as the same object on earth. Example: A 60 pound child would weigh 10 pounds on the moon!

32. Velocity • How fast an object moves is measured by its velocity. Velocity is calculated by dividing the distance traveled (a length) by the time it takes to travel the distance. The units of velocity are, for example, meters per second (m/s) or feet per minute (ft/min). If a person runs 15 kilometers in 2 hours, his or her velocity is 7.5 kilometers per hour (km/hr).

33. Velocity • If a car travels from Los Angeles, CA, to San Diego, CA , a distance of 120 miles, in 2 hours, its velocity is 60 miles per hour (120/2hrs=60 mph). One exception to these units is a term held over from sailing days, the knot. In aeronautics, the velocity of the air is often measured in knots. One knot is equal to about 1.7 feet per second (ft/s) or 1.15 miles per hour (mph).

34. Velocity • Rate and speed are two of the many terms used interchangeably with velocity. When engineers work with velocities, they must know the direction of the motion as well as the numerical value. They will sometimes call the numerical value the rate or speed, and then define a direction: the box was moved at a rate of 3 ft/s to the right, or the rocket traveled upwards at a speed of 120 m/s.

35. Acceleration • Acceleration is a measure of how the velocity of an object is changing over time. It can be found by computing the difference in velocities at first one time, then some time later, and dividing that by the difference in time. a = (vf - vi) / t

36. Acceleration • Example: A car is traveling at 60 mph at the first mile post. One mile (and one minute) later the car is traveling at 70 mph. 70 - 60=10 divided by 1/60 hr. = 600 mph2 (if acceleration continued at the same rate for the next 59 minutes). The units for acceleration are meters per second2 (m/s2); feet per second2 (f/s2); miles per hour (mph2); kilometers per hour (km/hr2).

37. Newton’s First Law: • Newton’s First Law states that a body of mass in a state of rest tend to stay at rest and a body in motion tends to remain in motion, unless acted upon by another force.

38. Newton’s Second Law: • Newton’s Second Law states that an unbalance or force on a body tends to produce an acceleration in the direction of the force.

39. Newton’s Third Law: • Newton’s Third Law states that for every acting force there is an equal and opposite reacting force.