Chapter 2: Measurement and Units

Chapter 2: Measurement and Units 2.1 Space and Time 2.2 Mass, Matter, and Atoms 2.3 Experiments and Data

Chapter 2 Objectives • Express lengths in metric and English units. • Convert measurements and calculated quantities between different units. • Calculate the surface area and volume of simple shapes and solids. • Work with time intervals in hours, minutes, and seconds. • Describe two effects you feel every day that are created by mass. • Describe the mass of objects in grams and kilograms. • Use scientific notation to represent large and small numbers. • Design a controlled experiment. • Create and use a graphical model based on data.

element English system experimental variable exponent friction gas graph mixture plasma precision procedure scientific notation SI system solid Chapter 2 Vocabulary • graphical model • independent variable • inertia • length • liquid • mass • metric system • speed • surface area • time interval • variable • volume • weight • x-axis • y-axis

Inv 2.1 Distance and Length Investigation Key Question: How do we accurately communicate length and distance?

2.1 Space and Time • Spacein physics means the three dimensions of up-down, left-right, and front-back. • The three dimensions of space are described with length units, such as meters, inches, and feet. • Time provides another dimension for describing when something occurs.

2.1 Thinking about distance • Measurement • is a quantity and a unit • Distance • is the amount of space between two points • is measured in units of length

2.1 Two common systems of units • Science problem solving requires both: • Metric or S.I. system • English system

2.1 Two common systems of length • Almost all fields of science use metric units. • They make calculations easier because the units are based on factors of ten.

It is often necessary to take a measurement in one unit and convert it into a different unit using conversion factors. 2.1 Converting from one unit to another

Converting length in yards to meters • You are asked for the distance in meters (m). • You are given the distance in yards (yds). • Relationship: 1 yard= 3 feet • 100 yds x 3 ft x 0.3048 m = 91.4 m 1 yd 1 ft A football field is 100 yards long. What is this distance expressed in meters?

2.1 Time Two ways to think about time: What time is it? 11:52 a.m. on March 12, 2010 How much time has passed? 2 hr: 22 min: 42 sec. A quantity of time is often called a time interval.

2.1 How is time measured?

Converting a mixed time toseconds • You are asked for time in seconds. • You are given a time interval in mixed units. 1 hour = 3,600 sec 1 minute = 60 sec • Do the conversion: 1 hour = 3,600 sec 26 minutes = 26 × 60 = 1,560 sec • Add all the seconds: t = 3,600 + 1,560 + 31.25 = 5,191.25 sec How many seconds are in 1 hour, 26 minutes, and 31.25 seconds?

2.1 Time scales in physics • Events in the universe happen over a huge range of time intervals. • In many experiments, you will be observing how things change with time.

Inv 2.2 Time Investigation Key Question: How do we measure and describe time?

2.2 Mass, Matter, and Atoms Mass is the amount of “stuff” an object contains. Two effects mass has on matter: Weight is the force of the Earth’s gravity pulling down. Gravity acts on an object’s mass. Inertia is the tendency of an object to resist changes in motion. Inertia comes from mass.

2.2 Measuring mass Kilogram is the mass of 1 liter of water or 1,000 cubic centimeters of water.

2.2 Very large and very small numbers • Because physics covers such a wide range of values for length, time, and mass you will need a method of working with large and small numbers. • In scientific notation, numbers are written as a value between 1 and 10, multiplied by a power of 10 called the exponent.

A single atom is about 10-10 meters in diameter. Aluminum foil is thin but still more than 200,000 atoms thick. Whether matter is a solid, liquid, or gas depends on how the atoms are organized. 2.2 Matter and atoms

2.2 Matter and atoms Solids - Atoms in a solid stay together because the energy per atom is too low to break the bonds between atoms. Liquids - Liquids flow because atoms have enough energy to move around by temporarily breaking and reforming bonds with neighboring atoms. Gases- Gas atoms have enough energy to completely break bonds with each other. Plasma - In plasma, matter becomes ionized as electrons are broken loose from atoms.

2.2 The diversity of matter There is an incredible diversity of matter around you. This diversity comes from combining elements into compounds, then compounds into mixtures of compounds.

2.2 The diversity of matter Each type of matter is called an element. Each element has is own properties, such as mass and the ability to combine with other elements. There are about 92 different types of atoms in ordinary matter.

2.2 The diversity of matter A compound is a substance that contains two or more different elements bonded together. Water is an example of a compound. If you could look at water with a powerful atomic microscope you would find each particle of water is made from one oxygen atom and two hydrogen atoms.

2.2 The diversity of matter Another compound, glucose, is a sugar in food. A single glucose molecule is made of carbon, oxygen, and hydrogen atoms.

2.2 Matter and atoms • The matter you normally experience is made of mixtures of compounds. • Wood is a mixture that contains water and more than 100 other compounds.

Inv 2.3 Matter and Mass Investigation Key Question: How is mass described?

2.3 Experiments and Data • Data are the measurements and calculations that you make during the experiment. • Things you measure in experiments are fundamental quantities. • Derived quantities can be measured but are often calculated from things you originally measured.

2.3 Speed • Speed • is a derived quantity calculated from measurements of distance and time. • Other derived quantities include frequency, density, acceleration, intensity, and energy. • Each of these units can be broken down into combinations of the fundamental units of length, mass, and time.

Converting a speed from cm/s to mi/h • You are asked for speed in mi/h. • You are given speed in cm/s. • Relationships: • speed = distance ÷ time • 1 hour = 3,600 s • 1 mile = 1,609 m • 1 meter = 100 cm • A car on a ramp is measured to go 45 cm in 1.5 s. What is the speed in miles per hour? 4.

2.3 Area and volume • A solid object has surface area as well as volume. • Surface area • is the measurement of the extent of an object’s surface or area without including its thickness.

2.3 Area and volume • Volume • is a measure of the space occupied by an object.

Calculating area and volume • You are asked for surface area and volume. • You are given the radius. • Relationships: area: A = 4π r2; volume: V = (4/3)π r3 • Solve: Surface area Volume A= 4(3.14)(12.5)2 = 1,963 cm2 V= 4 (3.14)(12.5)3 8,181 cm)3 A basketball has a radius of 12.5 cm. Calculate the surface area and volume of the ball.

2.3 Density • Density describes how much mass is in a given volume of a material. • The units of density are mass divided by volume. • Identically-sized cubes of iron, polyethylene, and glass contain different amount of mass.

2.3 Density • Solids range in density from cork, with a density of 120 kg/m3, to platinum, a precious metal with a density of 21,500 kg/m3.

2.3 Accuracy and precision Accuracy is the quality of being exact and free from error. is how close a measurement is to the true value. Precision means how small a difference a measurement can show.

2.3 Variables and relationships • Factors that affect the results of an experiment are called variables. • The science of physics can be thought of as “the search for the relationships between all the variables that describe everything.” • To learn about something specific in nature, scientists instead select a small set of related variables and define it as a system.

2.3 Variables for a car on a ramp

We do experiments to find out what happens when we change a variable. The variable that is changed is called the experimental variable. The variables that are kept the same are called the control variables. When you change one variable and control all of the others, we call it a controlled experiment. Controlled experiments are the best way to get reliable data. 2.3 Experimental design

2.3 Experimental design • The procedure is a collection of all the techniques you use to do an experiment. • Your experimental techniqueis how you actually do the experiment. • Each repetition of the experiment is called a trial.

2.3 Graphical data • A graph shows how two variables are related. • By convention, graphs are drawn a certain way. • The dependent variable goes on the y-axis which is vertical. • The independent variable goes on the horizontal or x-axis.

2.3 Graphical models • A graph is a form of a mathematical model because it shows the connection between two variables. • A graphical model uses a graph to make predictions based on the relationship between the variables on the x- and y-axes.

2.3 Graphical models

2.3 How to make a graph Decide what to put on the x and y axes. Make a scale by counting boxes to fit your largest value (multiples of 1, 2, 5 or 10 are best). Plot your points. Draw a best fit curve. Create a title andlabel each axis.

2.3 Recognizing relationships in data • When there is a relationship between the variables, a graph shows a clear pattern.

2.3 Recognizing relationships in data • You can tell how strong the relationship is from the pattern. • If the relationship is weak, even a big change in one variable has little effect on the other.

Chapter 2: Measurement and Units