Dimensional analysis
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Dimensional Analysis. What is dimensional analysis?!. A way to analyze and solve problems using the units, or dimensions, of the measurements Also known as conversion factors. Problem: How many seconds do students spend at school everyday?. Knowns:

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Dimensional Analysis

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Dimensional analysis

Dimensional Analysis


What is dimensional analysis

What is dimensional analysis?!

  • A way to analyze and solve problems using the units, or dimensions, of the measurements

  • Also known as conversion factors


Problem how many seconds do students spend at school everyday

Problem: How many seconds do students spend at school everyday?

  • Knowns:

    • School starts at 7:25am and ends at 2:05pm, a total of 7.67 hours

    • 1 hour = 60 minutes

    • 1 minutes = 60 seconds

  • Unknown:

    • How many seconds are in a school day?


Solution

Solution:


Practice problems

Practice Problems:

1. How many minutes are there in 1 week?


Practice problems1

Practice Problems

  • How many seconds are there in a year?


Using dimensional analysis to solve problems

Using Dimensional Analysis to Solve Problems

  • You are cooking Thanksgiving dinner. You have a recipe that makes 6 pounds of stuffing. From previous Thanksgivings you noticed that an average person eats 0.452 pounds. How many people can you invite to your Thanksgiving dinner this year?


Practice problems2

Practice Problems

1. An experiment requires that each student use an 8.5-cm length of magnesium ribbon. How many students can do the experiment if there is a 570-cm length of Mg ribbon available?


Practice problem

Practice Problem

2. A 1.00-degree increase on the Celsius scale is equivalent to a 1.80-degree increase on the Fahrenheit scale. If a temperature increases by 48.0 Celsius, what is the corresponding temperature increase on the Fahrenheit scale?


Converting between units

Converting Between Units

  • Suppose that a laboratory experiment requires 7.5 dg of magnesium metal, and 100 students will do the experiment. How many grams of magnesium should your teacher have on hand? Multiplying 100 students by 7.5 dg/student gives you 750 dg. But then you must convert dg to grams.


Practice problems3

Practice Problems

  • Convert the following using dimensional analysis

    • 0.044 km to meters (1000 m = 1 km)

    • 4.6 mg to grams (1000 mg = 1 g)

    • 0.107 g to centigrams (100 centigrams= 1 g)


Multistep unit conversion

Multistep Unit Conversion

What is 0.073 cm in micrometers?

Knowns:

length = 0.073 cm = 7.3 x 10-2

102 = 1 m

1 m = 106 micrometers

Unknowns:

length in micrometers


Practice problem1

Practice Problem

  • The radius of a potassium atom is 0.227 nm. Express this radius in the unit centimeters.


Homework

Homework!!!

  • p.R68 #1abc, 2abc, 3ab, 4abc, 5ac


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