Chapter 1 Measurement and Problem Solving © 2010 Pearson Education, Inc.

Units of Chapter 1 Why and How We Measure SI Units of Length, Mass, and Time More about the Metric System Unit Analysis Unit Conversions Significant Figures Problem Solving © 2010 Pearson Education, Inc.

1.1 Why and How We Measure Physics attempts to describe nature in an objective way through measurement. Measurements are expressed in units; officially accepted units are called standard units. Major systems of units: Metric British (used by the U.S., but no longer by the British!) © 2010 Pearson Education, Inc.

1.2 SI Units of Length, Mass, and Time Length, mass, and time are fundamental quantities; combinations of them will form all the units we will use through Chapter 14. In this text, we will be using the SI system of units, which is based on the metric system. © 2010 Pearson Education, Inc.

1.2 SI Units of Length, Mass, and Time SI unit of length: the meter. The original definition is on the left, the modern one is on the right. Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level), © 2010 Pearson Education, Inc.

1.2 SI Units of Length, Mass, and Time SI unit of mass: the kilogram Originally, the kilogram was the mass of 0.10 m3 of water. Now, the standard kilogram is a platinum-iridium cylinder kept at the French Bureau of Weights and Measures. © 2010 Pearson Education, Inc.

1.2 SI Units of Length, Mass, and Time SI unit of time: the second The second is defined as a certain number of oscillations of the cesium-133 atom. © 2010 Pearson Education, Inc.

1.2 SI Units of Length, Mass, and Time In addition to length, mass, and time, base units in the SI system include electric current, temperature, amount of substance, and luminous intensity. These seven units are believed to be all that are necessary to describe all phenomena in nature. © 2010 Pearson Education, Inc.

1.3 More about the Metric System The British system of units is used in the U.S., with the basic units being the foot, the pound (force, not mass), and the second. However, the SI system is virtually ubiquitous outside the U.S., and it makes sense to become familiar with it. © 2010 Pearson Education, Inc.

Learning Check Give a couple of major differences between the SI and the British system. One major difference is the decimal versus duodecimal basis. Another difference is that SI basic units are meters, kilograms and seconds, whereas the British system uses feet, pounds and seconds.

1.3 More about the Metric System In the metric system, units of the same type of quantity (length or time, for example) differ from each other by factors of 10. Here are some common prefixes: © 2010 Pearson Education, Inc.

1.3 More about the Metric System The basic unit of volume in the SI system is the cubic meter. However, this is rather large for everyday use, so the volume of a cube 0.1 m on a side is called a liter. Recall the original definition of a kilogram; one kilogram of water has a volume of one liter. © 2010 Pearson Education, Inc.

Which of the following has the greatest volume? Learning Check Which of the following has the greatest volume? 2000 mL 1qt 2000 µl 1 L 1 quart=946.35 mL

Learning Check Explain why 1 ml is equivalent to 1 cm3. 1 L=1000 mL and 1 L=1000 cm^3

1.4 Unit Analysis A powerful way to check your calculations is to use unit analysis. Not only must the numerical values on both sides of an equation be equal, the units must be equal as well. © 2010 Pearson Education, Inc.

1.4 Unit Analysis Units may be manipulated algebraically just as other quantities are. Example: Therefore, this equation is dimensionally correct. © 2010 Pearson Education, Inc.

1.5 Unit Conversions A conversion factor simply lets you express a quantity in terms of other units without changing its physical value or size. The fraction in blue is the conversion factor; its numerical value is 1. © 2010 Pearson Education, Inc.

1.6 Significant Figures Calculations may contain two types of numbers: exact numbers and measured numbers. Exact numbers are part of a definition, such as the 2 in d = 2r. Measured numbers are just that—for example, we might measure the radius of a circle to be 10.3 cm, but that measurement is not exact. © 2010 Pearson Education, Inc.

1.6 Significant Figures SIGNIFICANT FIGURES Significant figures are the numbers in a measurement that represent the certainty of the measurement, plus one number representing an estimate. COUNTING ZEROS AS SIGNIFICANT FIGURES Leading zeros are never significant figures. Buried zeros are always significant figures. Trailing zeros are generally significant figures（with decimal) .

1.6 Significant Figures Significant figures in calculations: 1. When multiplying and dividing quantities, leave as many significant figures in the answer as there are in the quantity with the least number of significant figures. © 2010 Pearson Education, Inc.

1.6 Significant Figures 2. When adding or subtracting quantities, leave the same number of decimal places (rounded) in the answer as there are in the quantity with the least number of decimal places.

Learning Check What volume in liters is a cube 40  cm on a side? Express your answer using two significant figures 64 L

1.7 Problem Solving The flowchart at left outlines a useful problem-solving strategy. It can be used for most types of physics problems. © 2010 Pearson Education, Inc.

1.7 Problem Solving The table at left describes several types of examples that are used in the text. © 2010 Pearson Education, Inc.

Learning Check A corner construction lot has the shape of a right triangle. If the two sides perpendicular to each other are 35  long and 46.3  long, what is the length of the hypotenuse? Express your answer using two significant figures. 58.04

Accuracy and Precision The accuracy of a measurement signifies how close it comes to the true (or accepted) value- that is, how nearly correct it is.

Precision refers to the agreement among repeated measurements-that is, the “spread” of the measurements or how close they are together. The more precise a group of measurements, the closer together they are.

Review of Chapter 1 SI units of length, mass, and time: meter, kilogram, second Liter: 1000 cm3; one liter of water has a mass of 1 kg Unit analysis may be used to verify answers to problems Significant figures – digits known with certainty, plus one © 2010 Pearson Education, Inc.

Review of Chapter 1 Problem-solving procedure: 1. Read the problem carefully and analyze it. 2. Where appropriate, draw a diagram. 3. Write down the given data and what is to be found. (Make unit conversions if necessary.) 4. Determine which principle(s) are applicable. 5. Perform calculations with given data. 6. Consider if the results are reasonable. © 2010 Pearson Education, Inc.