Galileo modeled the behavior of falling objects in order to develop a hypothesis about how objects fall.
Chapter 1 If heavier objects fell faster than slower ones,would two bricks of different masses tied together fall slower (b) or faster (c) than the heavy brick alone (a)? Because of this contradiction, Galileo hypothesized instead that all objects fall at the same rate, as in (d). Section 1 What Is Physics?
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).
Section 2 Measurements in Experiments Chapter 1
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SI Standards Chapter 1 Section 2 Measurements in Experiments
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.
Section 2 Measurements in Experiments Chapter 1 For example, when determining area by multiplying length and width, be sure the measurements are expressed in the same units.
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Dimensions and Units Chapter 1 Section 2 Measurements in Experiments
A typical bacterium has a mass of about 2.0 fg. Express
this measurement in terms of grams and kilograms.
Section 2 Measurements in Experiments Chapter 1 Given: mass = 2.0 fg Unknown: mass = ? g mass = ? kg
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Sample Problem, continued Section 2 Measurements in Experiments Chapter 1 Build conversion factors from the relationships given in Table 3 of the textbook. Two possibilities are: Only the first one will cancel the units of femtograms to give units of grams.
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Sample Problem, continued Section 2 Measurements in Experiments Chapter 1 Take the previous answer, and use a similar process to cancel the units of grams to give units of kilograms.
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.
Section 2 Measurements in Experiments Chapter 1
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Significant Figures, continued Section 2 Measurements in Experiments Chapter 1 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.
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Rules for Determining Significant Zeroes Chapter 1 Section 2 Measurements in Experiments
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Rules for Determining Significant Zeros Chapter 1 Section 2 Measurements in Experiments
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Rules for Calculating with Significant Figures Chapter 1 Section 2 Measurements in Experiments
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Rules for Rounding in Calculations Chapter 1 Section 2 Measurements in Experiments
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Rules for Rounding in Calculations Chapter 1 Section 2 Measurements in Experiments
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.
Chapter 1 Section 3 The Language of Physics
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Data from Dropped-Ball Experiment Chapter 1 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.
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Graph from Dropped-Ball Experiment Chapter 1 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.
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Interpreting Graphs Chapter 1 Section 3 The Language of Physics
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.
Chapter 1 Section 3 The Language of Physics
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Evaluating Physics Equations Chapter 1 Section 3 The Language of Physics
5. A light-year (ly) is a unit of distance defined as the distance light travels in one year.Numerically, 1 ly = 9 500 000 000 000 km. How many meters are in a light-year?
5. A light-year (ly) is a unit of distance defined as the distance light travels in one year.Numerically, 1 ly = 9 500 000 000 000 km. How many meters are in a light-year?
7. 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?
7. 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?
16. 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?
16. 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?
Standardized Test Prep Chapter 1 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.
17. 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.
Standardized Test Prep Chapter 1
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The Scientific Method Chapter 1 Section 1 What Is Physics?
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Hypotheses Chapter 1 Section 1 What Is Physics?
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SI Prefixes Section 2 Measurements in Experiments Chapter 1
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Significant Figures Section 2 Measurements in Experiments Chapter 1
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