Welcome to Physics
Measuring
• CALCULATOR!!!!!
• Homework Policy
• I will provide you with a lab notebook
Measuring
Measuring
MKS system
MKS – Meter-KilogramSecond
Meter
• Originally 1/10,000,000 the
distance from the equator
to either pole
• Distance light travels in
1/299,792,458th of a
second (c is constant
everywhere in the
universe)
Kilogram
• Pt-Ir cylinder at the International Bureau of
Weights and Measures.
• Rest mass of 6.022 X 10
Historical Pt-Ir meter bars
U.S. National Kilogram (NIST)
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Giga (G) = 109
Mega (M) = 106
kilo (k)
= 103
hecto (h) = 102
deka (da) = 101
deci (d) = 10-1
centi (c) = 10-2
milli (m) = 10-3
micro ( ) = 10-6
nano (n) = 10-9
pico (p) = 10-12
Second
• 1/86,400 of a mean
solar day
• Defined in terms of
frequency of radiation
emitted by a cesium
isotope
Cesium Fountain
Clock at NIST
The Metric System
Examples:
1 km = 1 X 103 m
450 km = 450 X 103 m = 4.5 X 105 m
The Metric System
Examples:
600 nm
0.0055 Gs
5677 kg
=?m
=?s
=?g
45 uF = 45 X 10-6 F = 4.5 X 10-5 F
Metric Example One:
The Metric System
Examples:
600 nm
0.0055 Gs
0.000567 kg
How many meters is 55 cm?
10-7
=6X
m
= 5.5 X 106 s
= 5.67 X 10-1 g
Step 1:
Step 2:
Step 3:
Step 4:
55 cm
55 cm X
m
cm
55 cm X 1 X 10-2 m
1 cm
55 cm X 1 X 10-2 m = 0.55 m
1 cm
ALWAYS include this zero
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Metric Example 2:
How many milliters is 0.0250 liters?
Step 1:
Step 2:
Step 3:
Step 4:
0.0250 L
0.0250 L
mL
L
0.0250 L 1 mL
1 X 10-3 L
0.0250 L 1 mL = 25.0 mL
1 X 10-3 L
Metric Example 4
How many milliseconds is 0.0450 hectoseconds?
(Ans: 4500 ms)
Metric Practice Examples
4658 cm =
635 cm =
553 ms =
0.0023 kL =
0.468 cm =
7200 cs =
3498 s
=
0.04658 km
0.635 dam
5.53 ds
2300 mL
4.68 mm
7.2 das
0.9717 hours
Metric Example 3
How many kilograms is 13405 mg?
13405 mg
1 X 10-3 g
1 mg
13405 mg
1 X 10-3 g 1 kg
1 mg
1 X 103 g
1 X 10-3 g 1 kg = 0.013405 kg
1 mg
1 X 103 g
13405 mg
Metric Practice Examples
4658 cm =
635 cm =
553 ms =
0.0023 kL =
0.468 cm =
7200 cs =
3498 s
=
? km
? dam
? ds
? mL
? mm
? das
? hours
Metric Example 5
How many square meters is 685 cm2?
685 cm2 1 X 10-2 m
1 cm
685 cm2 1 X 10-2 m 1 X 10-2 m
1 cm
1 cm
685 cm2 1 X 10-2 m 1 X 10-2 m = 0.0685 m2
1 cm
1 cm
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Metric Example 6
Metric Example 7
How many square decimeters is 0.250 m2?
0.250 m2 1 dm
1X10-1 m
How many cubic centimeters (cm3) is
0.00453 m3?
(Ans: 4520 cm3)
0.250 m2
1 dm
1 dm
-1
1X10 m 1X10-1 m
0.250 m2
1 dm
1 dm = 25.0 dm2
-1
1X10 m 1X10-1 m
Challenge
Problem
The tallest building in
the world is in
Taiwan, Taipei
101. It is 509
meters tall. How
many feet is that?
Metric Example 9
Convert 22 miles/hour to m/s.
This problem will require us to do two things:
convert the distances and convert the time.
22 miles
1 hr
1.61 km 1X103m 1 hr 1 min = 9.8 m/s
1.00 mile
1 km 60 min 60 s
(1 cm = 2.54 inches)
http://en.wikipedia.org/wiki/Image:Taipei_
101_International_Finadncial_Center.jpg
Metric Example 10
Metric Practice Examples
Convert 200 cm/s to miles/hour.
200 cm
1s
1X10-2 m 1 km 1.00 mile 60 s
1 cm
1X103 m 1.61 km 1 min
60 min
1 hr
55 mi/hr
55 mi/hr
65 miles/hr
400 cm/s
 km/hr
 meters/min
 meters/s
 miles/hr
= 4.47 miles/hr
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Metric Practice Examples
55 mi/hr
55 mi/hr
65 miles/hr
400 cm/s
 89 km/hr
 1476 meters/min
 29.1 meters/s
 8.94 miles/hr
Accuracy and Precision
• Accuracy
– how close the average of a set of measurements
is to the true value
– Measured using Percent Error
• Precision
– How close a set of measured values are to one
another
– Measured using Range
Error Analysis
Percent Error – Measure of accuracy
% Error = Experimental – Accepted X 100
Accepted
Accuracy and Precision
Students did trials to measure the density of a
metal. The accepted density is 7.2 g/cm3.
Were they accurate or precise?
Set 1
Set 2
Set 3
7.21 7.25 7.18
6.40 7.90 7.30
6.45 6.52 6.48
Error Analysis: Example 1
A student measures the density of a sample of
copper and determines it to be 8.75 g/mL.
The accepted value is 8.96 g/mL. Calculate
the percent error.
NOTE: The “Experimental” value is always the
average of all your trials in an experiment
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Error Analysis: Example 2
A student measures the melting point of a
sample of beryllium at 667 oC. The accepted
value is 649 oC. Calculate the percent error.
Error Analysis: Range
Range - Measure of precision
Range = highest trial – lowest trial
Example 1
A student measures the melting point of a
sample of beryllium and does four trials. The
trials result in melting points of 667 oC, 645
oC, 670 oC, 655 oC. Calculate the range and
comment on precision.
Error Analysis: Range
Example 2
A student measures the density of a sample of
lead and does four trials. The trials result in
densities of 11.3, 10.5, 11.9, 10.8 g/cm3.
Calculate the range and comment on
precision.
Error Analysis
Example 3
Using the numbers in the previous example,
calculate percent error. The accepted
density of lead is 11.4 g/cm3.
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