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Mar. 2006 Measuring Instruments Slide 1
Measuring Instruments
A Lesson in the Math + Fun! Series
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Mar. 2006 Measuring Instruments Slide 2
About This Presentation
Edition Released Revised Revised
First Mar. 2006
This presentation is part of the Math + Fun! series devisedby Behrooz Parhami, Professor of Computer Engineering at
University of California, Santa Barbara. It was first prepared
for special lessons in mathematics at Goleta Family School
during three school years (2003-06). Math + Fun! material
can be used freely in teaching and other educational settings.Unauthorized uses are strictly prohibited. Behrooz Parhami
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Mar. 2006 Measuring Instruments Slide 3
Weight
Speed
Length Temperature
We Need to Measure Many Different Things
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Mar. 2006 Measuring Instruments Slide 4
Temperature Measurement
Materials expand when heated
Idea: Connect a reservoir to
a very thin tube to make the
expansion more noticeable
100
0
10
20
30
40
60
70
80
90
50
Put tick marks and numbers
next to the tube by exposing
the thermometer to known
temperatures (0 C for melting
ice, 100 C for boiling water)
0 C
32 F
100 C
212 F
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Mar. 2006 Measuring Instruments Slide 5
A Second Way for Measuring Temperature
Different materials expand by
different amounts when heated
Idea: Connect two different
metals together to form a strip.
Different expansions will cause
the strip to bend when heated.
Use spiral shapeto convert the
shifting motion
into rotation
Bimetal strip
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Mar. 2006 Measuring Instruments Slide 6
Measuring Speed
How fast the car is moving
is proportional to how fast
the wheels are spinning
Idea: Convert the spinning
motion to electricity (as in ahand-crank flashlight that
gives off more light the
faster you turn the crank)
But how do you
measure electricity?
Goleta
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Mar. 2006 Measuring Instruments Slide 7
When there is no electricityin the circuit, the spring keeps
the needle at 0
Electricity in the circuit turns
the wire coil into a magnetthat pulls the iron vane
The higher the electrical
voltage, the stronger the
magnetic pull of the wire coil
and the greater the rightward
movement of the needle
spring
needles
restposition
Measuring Electrical Voltage
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Mar. 2006 Measuring Instruments Slide 8
Activity 1: Making a Scale with a Rubber Band
1. Hang a rubber band from the edge of a table or chair, attach a heavy
paper clip to its end, and put it next to a strip of paper or cardboard.
2. Hang something of known weight (e.g., 2 oz) from the clip and see howfar the rubber band stretches. Mark the new position of the paper clip.
0
2
3. Repeat with different weights, until the scale has been calibrated.
0
Rubber
band
Paperclip
Paper or
cardboard
strip
4. Now, use the scale to measure the weight of an object.
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Activity 2: Making a Scale with a Coil Spring
1. Put a large coil spring on a table and place a paper plate on top of it.
Use a small cardboard box next to the spring to observe and record itsmovements as you add weights on the paper plate.
2. Put something of known weight (e.g., 2 lbs) on the plate and see how
far the coil spring compresses. Mark the new position of the plate.
3. Repeat with different weights, until the scale has been calibrated.
4. Now, use the scale to measure the weight of an object.
0 0
2
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Mar. 2006 Measuring Instruments Slide 10
Selecting Suitable Instruments for Measurement
We use different instruments depending on the size, weight,
speed, temperature, . . . of the object being measured.
3. We may use a 50 tape measure or a special laser device
to determine the outside dimensions of a building.
Challenge question A: Suggest quick and easy ways of measuring
the dimensions of your school campus or of a shopping mall.
Challenge question B: What instrument is used to measure small
items (e.g., thickness of a nail or diameter of a copper wire)?
1. We may use a 12 ruler to measure the distance
between two points on a small map.
2. We may use a 10 tape measure to determine the
dimensions of a desk or the size of a room.
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Mar. 2006 Measuring Instruments Slide 11
Measuring Very Large and Very Small Items
Micrometers
for measuring
small items
How thick is your toenail?
How high are the mountains to the north of us in Santa Barbara?
Measure the angle between a level line and a
line that points to the peak. Convert the angle
to a slope (say, 5%) and multiply by distance.
In the same way, we can measure the diameter
of the moon if we know the distance to it.
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Mar. 2006 Measuring Instruments Slide 12
Activity 3: Measuring Distance Using a Wheel
For this activity, you need a wheel (you can make the wheel out of
a large plastic plate or cut it out from sturdy cardboard). Attach thewheel to a stick by putting a nail or thumb tack through its center.
Put a mark on the edge of the wheel
so that you can count its rotations.
Push the wheel across the distance that you want to measure and
count the number of times the mark meets the stick.
Multiply the number of rotations by the perimeter of the wheel to find
the distance. You can avoid this step by making the perimeter equal
to 1 meter (the diameter must be about 31.8 cm).
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Mar. 2006 Measuring Instruments Slide 13
Activity 4: Measuring Rotation Speed
We saw that rotation speed can be measured by using the rotations to
produce electricity. The faster a wheel spins, the higher the voltagethat it generates. Here is another way to measure rotation speed.
Connect two balls to the end of strings and attach them to the spindle.
The faster the wheel spins, the higher the balls will fly.
Slow spin
Fast spin
Location of the balls can be used to determine the rotation speed.
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Next LessonMay 2006
2 0 0 6
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