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8/30/13. Today I will measure objects to the correct degree of certainty Warm Up - Describe a real life situation where you might use the scientific method. Don’t use one we’ve done in class!. Measurements and Math. College Prep Physics. Measurements.

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8 30 13
8/30/13

  • Today I will measure objects to the correct degree of certainty

  • Warm Up - Describe a real life situation where you might use the scientific method. Don’t use one we’ve done in class!


Measurements and math

Measurements and Math

College Prep Physics


Measurements
Measurements

  • A measurement consists of a number and a unit.

    • That boy is almost 7 tall.

      Seven what??

      That boy is almost 7 feet tall.


Measurement
Measurement

  • Metric System

    • SI units – base units

      • Length - meter

      • Mass– gram (kilogram)

      • Volume - liter

      • Time – second

      • Temperature – Kelvin


Measurement1
Measurement

  • Metric System

    • Derived units – made up of bases

      • Area → a = l x w

        Meter squared (m2)

      • Volume → v = l x h x w

        meter cubed (m3)

      • Density  D=m/v

        g/mL or g/cm3


Making measurements
Making Measurements

  • Uncertainty in measurement

    • When measuring, estimate the measurement to one place past the last place on the instrument.

    • For example, measuring length


Reliability
Reliability

  • Precision

    • Will give the same number over and over again

  • Accuracy

    • Will be close to the accepted value



Dimensional analysis aka factor label
Dimensional Analysis (AKA Factor Label)

  • Dimensional Analysis – a technique of converting between units using identities.

  • Identities – fractions of two equal values.

1m = 100 cm

1 m .

100 cm

100 cm

1m

or


1 meter = how many micrometers?

1 gram = how many kilograms?

1 liter = how many gigaliters?


Dimensional analysis
Dimensional Analysis

1 m = 100 cm

124 m = ? cm

100 cm

124 m

=12400 cm

x

1

m

  • 1. Start with what you are given

  • 2. Set up your identity. x ------

  • 3. Whatever unit is on top goes on the bottom.

  • 4. Plug in conversion factors

  • 5. Unit cancel!

  • Multiply by top… Divide by bottom.

  • Answer should have same # of sig figs as given


Dimensional analysis1
Dimensional Analysis

1 m = 1 x 109 nm

24000 nm= ? m

1 m

24000 nm

=0.000024 m

x

nm

1 x 109

  • 1. Start with what you are given

  • 2. Set up your identity. x ------

  • 3. Whatever unit is on top goes on the bottom.

  • 4. Plug in conversion factors

  • 5. Unit cancel!

  • Multiply by top… Divide by bottom.

  • Answer should have same # of sig figs as given


Dimensional analysis2
Dimensional Analysis

1 g = 0.001 kg

0.033 kg = ? dg

1 g = 10 dg

We don’t have a direct conversion between kg and dgv.

10 dg

1 g

0.033 kg

330 dg

=

x

x

0.001

kg

1

g


Dimensional analysis3
Dimensional Analysis

1 L = 1000 mL

593 mL = ? cL

1 L = 100 cL

Again, no direct conversion between mL and cL.

1 L

100 cL

593 mL

x

59.3 cL

=

x

1000

mL

1

L


Dimensional analysis4
Dimensional Analysis

  • Complex (derived) units

  • Example – miles/hour

  • Follow the rules to cancel units.

    • Whatever unit is on top, goes on the bottom

    • *If the unit starts on the bottom, it must go on top!!


Dimensional analysis5
Dimensional Analysis

  • If I am traveling at 60.0 m/s, how fast am I going in km/hr?


8 30 131
8/30/13

  • Today I will use dimensional analysis to convert between metric and English systems and to convert complex units

  • Warm Up –

    • How many Gg in 19,500,000 dg?


Dimensional analysis6
Dimensional Analysis

3.2 km = ? mi

1 mi = 1.61 km

1 mi

3.2 km

=1.98757764 mi

=2.0 mi

x

1.61

km

  • 1. Start with what you are given

  • 2. Set up your identity. x ------

  • 3. Whatever unit is on top goes on the bottom.

  • 4. Plug in conversion factors

  • 5. Unit cancel!

  • Multiply by top… Divide by bottom.

  • Answer should have same # of sig figs as given


Dimensional analysis7
Dimensional Analysis

1 ft = 12 in

116 ft= ? cm

1 in = 2.54 cm

We don’t have a direct conversion between ft and cm.

2.54 cm

12 in

116 ft

=3535.68 cm

x

x

1

ft

1

in

=3540 cm


Dimensional analysis8
Dimensional Analysis

A large fish tank can hold 100 gallons of water. How many kL is this?

1 gal = 3.78 L

1 L = 0.001 kL

0.001 kL

3.78 L

100 gal

= 0.378 kL

x

x

1

gal

1

L

= 0.4 kL


Dimensional analysis9
Dimensional Analysis

  • A cake requires 3.0 tablespoons of sugar per gallon of mix. How many tablespoons per quart (tbs/qt) is this?

gal

3.0 tbs

1

x

= 0.75 tbs/qt

gal

4 qt


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