Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Objectives List basic SI units and the quantities they describe. Convert measurements into scientific notation. Distinguish between accuracy and precision. Use significant figures in measurements and calculations.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Numbers as Measurements In SI, the standard measurement system for science, there are seven base units. Each base unit describes a single dimension, such as length, mass, or time. The units of length, mass, and time are the meter (m), kilogram (kg), and second (s), respectively. Derived units are formed by combining the seven base units with multiplication or division. For example, speeds are typically expressed in units of meters per second (m/s).

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 SI Standards Section 2 Measurements in Experiments

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 1.What is the SI base unit for length? F. inch G. foot H. meter J. kilometer Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 1.What is the SI base unit for length? F. inch G. foot H. meter J. kilometer Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 SI Prefixes In SI, units are combined with prefixes that symbolize certain powers of 10. The most common prefixes and their symbols are shown in the table.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued Standardized Test Prep Chapter 1 2.A light-year (ly) is a unit of distance defined as the distance light travels in one year.Numerically, 1 ly = km. How many meters are in a light-year? A. 9.5  m B. 9.5  m C. 9.5  m D. 9.5  m

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 2. A light-year (ly) is a unit of distance defined as the distance light travels in one year.Numerically, 1 ly = km. How many meters are in a light-year? A. 9.5  m B. 9.5  m C. 9.5  m D. 9.5  m Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Dimensions and Units Measurements of physical quantities must be expressed in units that match the dimensions of that quantity. In addition to having the correct dimension, measurements used in calculations should also have the same units. For example, when determining area by multiplying length and width, be sure the measurements are expressed in the same units.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Dimensions and Units $125 million dollar mars climate orbiter gets lost in space because contractor Lockheed Martin used English measures when it built the orbiter but NASA assumed they were metric.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Dimensions and Units Section 2 Measurements in Experiments

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Short Response, continued Standardized Test Prep Chapter 1 3. Demonstrate how dimensional analysis can be used to find the dimensions that result from dividing distance by speed.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Short Response, continued Standardized Test Prep Chapter 1 3. Demonstrate how dimensional analysis can be used to find the dimensions that result from dividing distance by speed. Answer:

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Accuracy and Precision Section 2 Measurements in Experiments

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Precision The Precision of a series of measurements is an indication of the agreement among repetitive measurements. A high precision measurement expresses high confidence that the measurement lies within a narrow range of values. Precision depends on the instrument used to make the measurement. The precision of a measurement is one half the smallest division of the instrument for analogue and one significant digit for digital. Typically, imprecision is caused by random variations such as slight changes in ….. pressure, room temperature, supply voltage, friction or pulling force over a distance. Human Interpretation such as how an instrument scale is read between divisions is also a source of random error.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Accuracy Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured. It is sometimes expressed as a percentage deviation from the known value. The known or true value is often based upon reproducible measurements. A common source of systematic error is not zeroing your measuring instrument correctly so that all the data is constantly shifted away from the true value. This can give high precision but poor accuracy. Your instrument might also not be accurate. A two point calibration can be used to check. Does the instrument read zero when it should and give the correct value when measuring the accepted value?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Measurement and Parallax Section 2 Measurements in Experiments

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 4. If you do not keep your line of sight directly over a length measurement, how will your measurement most likely be affected? F. Your measurement will be less precise. G. Your measurement will be less accurate. H. Your measurement will have fewer significant figures. J. Your measurement will suffer from instrument error. Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 4. If you do not keep your line of sight directly over a length measurement, how will your measurement most likely be affected? F. Your measurement will be less precise. G. Your measurement will be less accurate. H. Your measurement will have fewer significant figures. J. Your measurement will suffer from instrument error. Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Significant Figures It is important to record the precision of your measurements so that other people can understand and interpret your results. A common convention used in science to indicate precision is known as significant figures. Significant figures are those digits in a measurement that are known with certainty plus the first digit that is uncertain.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Significant Figures, continued Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Rules for Determining Significant Zeroes Section 2 Measurements in Experiments

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Rules for Determining Significant Zeros Section 2 Measurements in Experiments

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Rules for Calculating with Significant Figures Section 2 Measurements in Experiments

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 5. If you measured the length of a pencil by using the meterstick shown in the figure and you report your measurement in centimeters, how many significant figures should your reported measurement have? A. one B. two C. three D. four Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 5. If you measured the length of a pencil by using the meterstick shown in the figure and you report your measurement in centimeters, how many significant figures should your reported measurement have? A. one B. two C. three D. four Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Short Response Standardized Test Prep Chapter 1 6. Determine the number of significant figures in each of the following measurements. A kg B g C m D  10 3 m

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Short Response Standardized Test Prep Chapter 1 6. Determine the number of significant figures in each of the following measurements. A kg B g C m D  10 3 m Answers: A. 2; B. 3; C. 3; D. 4

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Short Response, continued Standardized Test Prep Chapter 1 7. Calculate the following sum, and express the answer in meters. Follow the rules for significant figures. ( km) + (1024 m) + (3.0  10 2 cm)

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Short Response, continued Standardized Test Prep Chapter 1 7. Calculate the following sum, and express the answer in meters. Follow the rules for significant figures. ( km) + (1024 m) + (3.0  10 2 cm) Answer: m

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 8. A room is measured to be 3.6 m by 5.8 m.What is the area of the room? (Keep significant figures in mind.) F m 2 G. 2  10 1 m 2 H. 2.0  10 1 m 2 J. 21 m 2 Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 8. A room is measured to be 3.6 m by 5.8 m.What is the area of the room? (Keep significant figures in mind.) F m 2 G. 2  10 1 m 2 H. 2.0  10 1 m 2 J. 21 m 2 Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 2 Measurements in Experiments Chapter 1 Mistakes Mistakes on the part of the individual such as…. misreading scales (using equipment incorrectly). Poor arithmetic and computational skills. wrongly transferring raw data to the final report. Using the wrong theory and equations. These are a source of error but ARE NOT considered a source of experimental error

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Section 3 The Language of Physics Chapter 1 Objectives Interpret data in tables and graphs, and recognize equations that summarize data. Distinguish between conventions for abbreviating units and quantities. Use dimensional analysis to check the validity of equations. Perform order-of-magnitude calculations.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Mathematics and Physics Tables, graphs, and equations can make data easier to understand. For example, consider an experiment to test Galileo’s hypothesis that all objects fall at the same rate in the absence of air resistance. –In this experiment, a table-tennis ball and a golf ball are dropped in a vacuum. –The results are recorded as a set of numbers corresponding to the times of the fall and the distance each ball falls. –A convenient way to organize the data is to form a table, as shown on the next slide. Section 3 The Language of Physics

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Data from Dropped-Ball Experiment Section 3 The Language of Physics A clear trend can be seen in the data. The more time that passes after each ball is dropped, the farther the ball falls.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Graph from Dropped-Ball Experiment Section 3 The Language of Physics One method for analyzing the data is to construct a graph of the distance the balls have fallen versus the elapsed time since they were released. The shape of the graph provides information about the relationship between time and distance.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Interpreting Graphs Section 3 The Language of Physics It is important to be able to recognize the shape of a graph and be able to relate that shape to a mathematical function. You can then compare this function to your model. Some functions found in physics are shown on the next two slides! Independent y = k y does not depend on x Direct y  x y = kx k = slope of the line y is directly proportional to x Note: If the line does not go through (o,o) it is linear y = kx + b b = y intercept b

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Interpreting Graphs Section 3 The Language of Physics Inverse Proportional y  1/x y = k/x y = k x -1 y is inversely proportional to x Square y  x 2 y = kx 2 y is proportional to the square of x Square root y  √x y = k √ x Y = k x 1/2 Y is proportional to the square root of x Note: all these functions are all power functions as they fit the general expression, y = A x B where A and B are constants

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Interpreting Graphs Section 3 The Language of Physics

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued The graph shows the relationship between time and distance for a ball dropped vertically from rest. Use the graph to answer questions 11–12. Standardized Test Prep Chapter 1 9. About how far has the ball fallen after 0.20 s? A cm B cm C cm D cm

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued The graph shows the relationship between time and distance for a ball dropped vertically from rest. Use the graph to answer questions 11–12. Standardized Test Prep Chapter 1 9. About how far has the ball fallen after 0.20 s? A cm B cm C cm D cm

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued Standardized Test Prep Chapter 1 10.Which statement best describes the relationship between the variables? F. For equal time intervals, the change in position is increasing. G. For equal time intervals, the change in position is decreasing. H. For equal time intervals, the change in position is constant. J. There is no clear relationship between time and change in position.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued Standardized Test Prep Chapter 1 10.Which statement best describes the relationship between the variables? F. For equal time intervals, the change in position is increasing. G. For equal time intervals, the change in position is decreasing. H. For equal time intervals, the change in position is constant. J. There is no clear relationship between time and change in position.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Physics Equations Physicists use equations to describe measured or predicted relationships between physical quantities. Variables and other specific quantities are abbreviated with letters that are boldfaced or italicized. Units are abbreviated with regular letters, sometimes called roman letters. Two tools for evaluating physics equations are dimensional analysis and order-of-magnitude estimates. Section 3 The Language of Physics

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Evaluating Physics Equations Section 3 The Language of Physics

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 11. What technique can help you determine the power of 10 closest to the actual numerical value of a quantity? A. rounding B. order-of-magnitude estimation C. dimensional analysis D. graphical analysis Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 11. What technique can help you determine the power of 10 closest to the actual numerical value of a quantity? A. rounding B. order-of-magnitude estimation C. dimensional analysis D. graphical analysis Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 1 Equation from Dropped-Ball Experiment We can use the following equation to describe the relationship between the variables in the dropped-ball experiment: (change in position in meters) = 4.9  (time in seconds) 2 With symbols, the word equation above can be written as follows :  y = 4.9(  t) 2 The Greek letter  (delta) means “change in.” The abbreviation  y indicates the vertical change in a ball’s position from its starting point, and  t indicates the time elapsed. This equation allows you to reproduce the graph and make predictions about the change in position for any time. Section 3 The Language of Physics

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 12. Which of the following statements is true of any valid physical equation? F. Both sides have the same dimensions. G. Both sides have the same variables. H. There are variables but no numbers. J. There are numbers but no variables. Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Multiple Choice, continued 12. Which of the following statements is true of any valid physical equation? F. Both sides have the same dimensions. G. Both sides have the same variables. H. There are variables but no numbers. J. There are numbers but no variables. Standardized Test Prep Chapter 1

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Extended Response Standardized Test Prep Chapter You have decided to test the effects of four different garden fertilizers by applying them to four separate rows of vegetables. What factors should you control? How could you measure the results?

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Extended Response Standardized Test Prep Chapter You have decided to test the effects of four different garden fertilizers by applying them to four separate rows of vegetables. What factors should you control? How could you measure the results? Sample answer: Because the type of fertilizer is the variable being tested, all other factors should be controlled, including the type of vegetable, the amount of water, and the amount of sunshine. A fifth row with no fertilizer could be used as the control group. Results could be measured by size, quantity, appearance, and taste.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Extended Response, continued Standardized Test Prep Chapter In a paragraph, describe how you could estimate the number of blades of grass on a football field.

Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Extended Response, continued Standardized Test Prep Chapter In a paragraph, describe how you could estimate the number of blades of grass on a football field. Answer: Paragraphs should describe a process similar to the following: First, you could count the number of blades of grass in a small area, such as a 10 cm by 10 cm square. You would round this to the nearest order of magnitude, then multiply by the number of such squares along the length of the field, and then multiply again by the approximate number of such squares along the width of the field.