College Physics, 7th Edition Lecture Outline Chapter 1 College Physics, 7th Edition Wilson / Buffa / Lou © 2010 Pearson Education, Inc.

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. Before standards how did you measure? Major systems of units: Metric – The sliding scale or powers of 10 British (“English” system used by the U.S., but no longer by the British!) – Stubborn Americans © 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 nearly all the units. We will be using the SI system of units, which is based on the metric system. Where are these standard kept or international? US? © 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. How do you think the “modern” one was first calculated? Late 1600s. © 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. NIST is the American equivalent © 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. How was it first “calculated”? © 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. What is the US equivalent for mass? However, the SI system is virtually ubiquitous outside the U.S., and it makes sense to become familiar with it. – Stubborn Americans © 2010 Pearson Education, Inc.

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. Easy way to memorize… © 2010 Pearson Education, Inc.

1.3 More about the Metric System Easy way to memorize… 103 to 10-3 King Henry Decided (to) Drink Chocolate Milk © 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.

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. Sanity check! © 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.

1.5 Unit Conversions Practice example Convert 45 mi/h to m/s What do you need to achieve this? Conversion factor(s). You should know the ones for time… 1 meter = 0.000621 miles Answer is… 20.12 m/s © 2010 Pearson Education, Inc.

1.5 Unit Conversions Practice example A student takes 5 measurements of the exact same object with different scales. They are 3.25 g, 3.26g, 3.30g, 3.20g, and 0.00311kg. Are these measurements precise? Are the accurate? What is the average of all of his measurements? © 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. Remember that precision ONLY comes from the instrument doing the measuring. © 2010 Pearson Education, Inc.

1.6 Significant Figures When dealing with measured numbers, it is useful to consider the number of significant figures. The significant figures in any measurement are the digits that are known with certainty, plus one digit that is uncertain. It is easy to create answers that have many digits that are not significant using a calculator. For example, 1/3 on a calculator shows as 0.33333333333. But if we’ve just cut a pie in three pieces, how well do we really know that each one is 1/3 of the whole? © 2010 Pearson Education, Inc.

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. 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. © 2010 Pearson Education, Inc.

1.7 Problem Solving I’m using a different method from the book. IDGUESS Use IDGUESS on this problem. The potential difference, or voltage, across a circuit equals the current multiplied by the resistance in the circuit. That is, V (volts) = I (amperes) × R (ohms). What is the resistance of a light bulb that has a 0.75 amperes current when plugged into a 120-volt outlet? © 2010 Pearson Education, Inc.

Graphing Data I have added a section on graphing. Its extremely important to understand. Especially in physics and if you are to go to physics in college and use calculus.

Graphing Data Identifying Variables A variable is any factor that might affect the behavior of an experimental setup. It is the key ingredient when it comes to plotting data on a graph. The independent variable is the factor that is changed or manipulated during the experiment. The dependent variable is the factor that depends on the independent variable. Typically the measured outcome.

Graphing Data Graphing Data

Graphing Data Linear Relationships Scatter plots of data may take many different shapes, suggesting different relationships.

Graphing Data Linear Relationships When the line of best fit is a straight line the dependent variable varies linearly with the independent variable. This relationship between the two variables is called a linear relationship. The relationship can be written as an equation.

Graphing Data Linear Relationships The slope is the ratio of the vertical change to the horizontal change. To find the slope, select two points, A and B, on the line. The vertical change, or rise, Δy, is the difference between the vertical values of A and B. The horizontal change, or run, Δx, is the difference between the horizontal values of A and B.

Graphing Data Linear Relationships The slope of a line is equal to the rise divided by the run, or the change in y divided by the change in x. If y gets smaller as x gets larger, then Δy/Δx is negative, and the line slopes downward. The y-intercept, b, is the point at which the line crosses the y-axis, and it is the y-value when the value of x is zero.

Graphing Data Nonlinear Relationships When the graph is not a straight line, it means that the relationship between the dependent variable and the independent variable is not linear. There are many types of nonlinear relationships. Two of the most common are the quadratic and inverse relationships. Check this vocabulary term.

Graphing Data Nonlinear Relationships The graph shown in the figure is a quadratic or exponential relationship. A quadratic relationship exists when one variable depends on the square of another. A quadratic relationship can be represented by the following equation:

Graphing Data Nonlinear Relationships The graph in the figure shows how the current in an electric circuit varies as the resistance is increased. This is an example of an inverse relationship. In an inverse relationship, a hyperbola (hi-per-bola) results when one variable depends on the inverse of the other. An inverse relationship can be represented by the following equation:

Graphing Data Nonlinear Relationships There are various mathematical models available apart from the three relationships you have learned. Combinations of different mathematical models represent even more complex phenomena.

Graphing Data Predicting Values Relations, either learned as formulas or developed from graphs, can be used to predict values you have not measured directly. Physicists use models to accurately predict how systems will behave: what circumstances might lead to a solar flare, how changes to a circuit will change the performance of a device, or how electromagnetic fields will affect a medical instrument.

Graphing Data Proportionalities Two variables are proportional if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant. The constant is called the coefficient of proportionality. "y is proportional to x," we write as an equation y = kx, for some real constant k. The relation is often denoted, using the ∝ symbol, as y ∝ x and where k = y/x. Summary: = means there is a constant and ∝ means there are no constants

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.