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Unit Conversion of Measurements

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Unit Conversion of Measurements Derived Unit A derived unit is a combination of the base units such as area (_m2_), volume, pressure, weight, force, and speed. – PowerPoint PPT presentation

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Title: Unit Conversion of Measurements


1
Unit Conversion of Measurements
2
Derived Unit
  • A derived unit is a combination of the base
    units such as area (_m2_), volume, pressure,
    weight, force, and speed.

3
Dimensional Analysis
  • Sometimes the unit in which a quantity was
    measured must be converted to a different unit so
    it can be used in mathematical operations.
  • Suppose you have half a pizza and you want to
    know how many slices you have. Pizza and slices
    cannot be compared because they are different
    units. To compare them, you need a conversion
    factor. If a pizza has 8 slices, then 1 pizza 8
    slices. This can be rewritten in the following
    ways.

4
Dimensional Analysis
  • If a pizza has 8 slices, then 1 pizza 8 slices.
    This can be rewritten in the following ways.
  • These are conversion factors. Notice that both
    fractions are equal to 1. This means that if you
    multiply them by another value, the value will
    not change.

5
Dimensional Analysis
  • You can use a conversion factor to convert the
    amount of pizza into the number of slices. There
    are four slices in half a pizza.
  • Notice that the conversion factor was chosen so
    that the new unit, slices, appears in the answer
    and the original unit, pizza, cancels.

6
Simple Conversions
  • How many meters are in 54 cm?

7
Determine the possible conversion factors
  • The two units in this problem are m and cm. We
    know that 1 m 100 cm. So,

8
Decide which conversion factor will give the
desired unit for the answer
  • The answer needs to be in m. To get m we need to
    use the conversion factor that has m in the
    numerator and divides by cm (to cancel cm in the
    original value).

9
Multiply the original value by the conversion
factor.
10
A roll of copper wire contains 15 m of wire.
What is the length of the wire incentimeters?
  • possible conversion factors
  • 1 m/ 100 cm or 100cm/ 1m
  • 2. conversion factor used
  • 100 cm / 1m
  • 3. multiply original value
  • 15 m x 100cm/ 1m 1 500 cm

11
Practice Lets convert the following
  1. 1. 550 mm ____.550______m
  2. 3.5 s ___3500_________ ms
  3. 1.6 kg _____1600_______g
  4. 2500 mg __.002500_______kg

12
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13
Density and Specific Gravity
Would the density of a person by the same on the
surface of the earth and on the surface of the
moon?

14
  • Density the amount of matter in an object per
    unit volume
  • As the temperature of a material increases, the
    density tends to decrease.
  • In the lab, the density of an irregularly shaped
    object is found by water displacement

15
Density
  • D m/v
  • m mass (in grams)
  • V volume (in cm3, ml or if a gas L)
  • D density (g/cm3 , solid,
  • g/ml liquid,
  • g/L, gas)
  • A student finds a shiny piece of metal she thinks
    is aluminum. In the lab, she determines that the
    metal has a volume of 245 cm3 and a mass of 612
    g. Is the metal aluminum?

16
Solving the Problem by Density
d 612g/245 cm3 d 2.5 g/cm3
  • D m/v

Density of Al 2.70 g/cm3 Density of the metal
2.50g/cm3
m
d
v
NO the metal is not Aluminum
17
PROBLEM
  • A plastic ball with a volume of 19.7 cm3 has a
    mass of 15.8 g. Would the ball float or sink in
    a container of gasoline? (density of gas
    0.66-0.69g/cm3)
  • A piece of iron has a mass of 2.25 g. What is its
    volume?

18
Specific Gravity
  • Specific gravity a ratio of the density of a
    substance to the density of another substance
    (usually water) at the same temperature
  • Density of water at 4ºC 1.0g/cm3
  • Gravity density of substance (Specific
    g/cm3)
  • density of water
    (g/cm3)

19
Specific Gravity
  • Specific gravity has no units b/c they cancel
    out
  • At 4ºC what can you say about the density of an
    object and its specific gravity?
  • Specific gravity is measured using a hydrometer

20
Three Temperature Scales
  • Fahrenheit
  • Celsius
  • Kelvin
  • Based on the freezing boiling point of alcohol
  • Based on the freezing boiling point of water
  • Based on absolute zero (temperature at which
    there is no molecular motion

21
Temperature Conversions
  • K C 273
  • C K - 273

Example A gas has a temp. of 90 C. What is
the Kelvin temperature?
Temperature scale Boiling point of water Freezing point of water Absolute zero
Fahrenheit 212 32 - 459
Celsius 100 0 - 273
Kelvin 373 273 0
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