Embed Size (px)
Citation preview
Investigation 1D
Dimensional Analysis
2 Investigation 1D: Dimensional Analysis
?
• If someone said you were 3 meters tall, how would you respond?
• Do you know what 3 meters (m) really is?
• You probably know 3 feet (ft) is small for a grown human. So how many feet are equal to 3 meters?
3 Investigation 1D: Dimensional Analysis
Much of the world measures in kilograms, kilometers, meters, and centimeters instead of pounds, miles, feet, and inches.
• How do we translate between units?
• You know that 1 min corresponds to 60 seconds. What are other conversion factors and how do we use them?
4 Investigation 1D: Dimensional Analysis
Part 1: How it works
1. Spread out your unit conversion cards so you can see their values.
Grab one card and flip it over.
How is each side different?
5 Investigation 1D: Dimensional Analysis
60 min = 1 hour
3 694 60 11
3 694 1 60
min hour
hour min
1. Spread out your unit conversion cards so you can see their values.
Part 1: How it works
6
2 hours
Investigation 1D: Dimensional Analysis
2. You can arrange the cards to solve any conversion problem. For example, convert 2 hours to seconds:
2 1 1 2hours hours
Multiplying something by 1 gives you that same something in the end!
Part 1: How it works
7
2 hours
Investigation 1D: Dimensional Analysis
2. You can arrange the cards to solve any conversion problem. For example, convert 2 hours to seconds:
2 1 1 2hours hours
Notice how units cancel out
What is the only unit left? Is it above or below the fraction line?
Part 1: How it works
8
2 hours
Investigation 1D: Dimensional Analysis
2. You can arrange the cards to solve any conversion problem. For example, convert 2 hours to seconds:
60 602 7,200
1 1seconds
2 1 1 2hours hours
Part 1: How it works
9 Investigation 1D: Dimensional Analysis
Part 2: Unit conversions to solve
a. How many milligrams (mg) are in 24 grams (g)?
b. How many centimeters (cm) are in 10 inches (in)?
c. Convert 45 inches to centimeters.
d. Which gas is more expensive: $3.95/gallon or $1.25/liter (L)?
e. Convert 23 miles to inches.
f. How many milliliters (mL) are in 1 gallon?
10 Investigation 1D: Dimensional Analysis
Part 2: Unit conversions to solve
g. Which is longer: 100 meters (m) or 1 mile? Convert miles to meters to find out.
h. How many feet per second is 30 miles per hour?
i. Which is more: 1 liters/second (L/s) or 10 gallons/minute?
j. A construction project calls for 250 kg of cement. Your cement supplier sells 60 lbs bags. How many bags do you need?
k. A doctor tells a patient to take 30 mL of a medicine. How many tablespoons of the medicine should the patient take? One tablespoon contains 15 mL.
11 Investigation 1D: Dimensional Analysis
Part 3: Area and volume conversions
When a conversion uses the same unit more than once, such as in area and volume, the conversion factor needs to be applied more than once.
For example, a volume of 2 cubic meters really has units of m x m x m. This is denoted as m3 (meter cubed). That means any length conversion needs to be applied three times.
32 2 2cubic meters m m m m
each length unit is applied 3 times
12 Investigation 1D: Dimensional Analysis
Part 3: Area and volume conversions
Example:
How many cubic centimeters are in one cubic inch?
13 Investigation 1D: Dimensional Analysis
Part 3: Area and volume conversions
3 32.54 2.54 216.93
.541 1
1 1 1
cm cm cmin in in in
in in icm
n
each length conversion is applied 3 times
Example:
How many cubic centimeters are in one cubic inch?
14 Investigation 1D: Dimensional Analysis
Part 3: Area and volume conversions
3 32.54 2.54 216.93
.541 1
1 1 1
cm cm cmin in in in
in in icm
n
Example:
How many cubic centimeters are in one cubic inch?
Make sure that units are
cancelled out correctly.
15 Investigation 1D: Dimensional Analysis
Part 3: Area and volume conversions
a. How many cubic centimeters are in 1 m3? This is the same as the number of milliliters in 1 m3.
b. How many milliliters are in 1 ft3?
c. How many cubic inches are in 1 ft3?
d. One liter is the volume of a cube that is 10 cm on each side. How many milliliters are in 1 L?
e. The displacement of a car engine is measured in cubic inches or in liters. The engine displacement is the volume of space that the pistons of the engine move in one complete rotating cycle. Which is a larger engine: one with a displacement of 4.3 L or one with a displacement of 250 in3?
16 Investigation 1D: Dimensional Analysis
Part 4: Other conversions
a. An experiment is performed in a container that has a pressure of 25 psi. How many atmospheres (atm) is this pressure?
b. A submarine can withstand a maximum pressure of 20 atm. How many pascals (Pa) is that?
c. A car is capable of producing 150 horsepower (hp). How many watts (W) does that correspond to?
d. An electrical generator can produce 1.5 hp. How many 100 W light bulbs can this generator supply?
17 Investigation 1D: Dimensional Analysis
?
• If someone said you were 3 meters tall, how would you respond?
• Do you know what 3 meters (m) really is?
• You probably know 3 feet (ft) is small for a grown human. So how many feet are equal to 3 meters?
