Chapter 4: Problem Solving

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Presentation transcript:

Chapter 4: Problem Solving When you analyze a problem, you first separate what is known from what is unknown. Then you decide on a strategy that uses the known data to solve for the unknown. After you solve a problem, you need to evaluate your answer to decide if it makes sense.

A Problem Solving Strategy

A Problem Solving Strategy

A Problem Solving Strategy

A Problem Solving Strategy

Dimensional Analysis Dimensional analysis is a method of problem-solving that focuses on the units used to describe matter. For example, if you want to convert a temperature in degrees Celsius to a temperature in kelvins, you focus on the relationship between the units in the two temperature scales.

Dimensional Analysis A conversion factor is a ratio of equivalent values used to express the same quantity in different units.

Dimensional Analysis A conversion factor is always equal to 1. Because a quantity does not change when it is multiplied or divided by 1, conversion factors change the units of a quantity without changing its value.

Dimensional Analysis Dimensional analysis often uses conversion factors. Suppose you want to know how many meters are in 48 km. You need a conversion factor that relates kilometers to meters. You know that 1 km is equal to 1000 m.

Dimensional Analysis Because you are going to multiply 48 km by the conversion factor, you want to set up the conversion factor so the kilometer units will cancel out.

Using Multiple Conversion Factors It is common in scientific problems to use dimensional analysis to convert more than one unit at a time. For example, what is a speed of 550 meters per second in kilometers per minute?

Using Multiple Conversion Factors First convert meters to kilometers. Set up the conversion factor so that the meter units will cancel out. Next convert seconds to minutes. Set up the conversion factor so that the seconds cancel out.

Assessment Questions Question 1 Your friend is 1.56 m tall. How many millimeters tall is your friend? Answer 1560 mm

Assessment Questions Question 2 How many hours are there in one week? How many minutes are there in one week? Answer 168 h; 10 080 min.