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Measuring Instruments
A Lesson in the “Math + Fun!” Series
Mar. 2006
Measuring Instruments
Slide 1
About This Presentation
This presentation is part of the “Math + Fun!” series devised
by 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
Mar. 2006
Edition
Released
First
Mar. 2006
Revised
Measuring Instruments
Revised
Slide 2
We Need to Measure Many Different Things
Length
Temperature
Weight
Speed
Mar. 2006
Measuring Instruments
Slide 3
Temperature Measurement
Materials expand when heated
Idea: Connect a reservoir to
a very thin tube to make the
expansion more noticeable
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
90
80
70
60
50
40
30
20
10
0
100 C
212 F
Mar. 2006
Measuring Instruments
Slide 4
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.
Bimetal strip
Use spiral shape
to convert the
shifting motion
into rotation
Mar. 2006
Measuring Instruments
Slide 5
Measuring Speed
Goleta
How fast the car is moving
is proportional to how fast
the wheels are spinning
But how do you
measure electricity?
Idea: Convert the spinning
motion to electricity (as in a
hand-crank flashlight that
gives off more light the
faster you turn the crank)
Mar. 2006
Measuring Instruments
Slide 6
Measuring Electrical Voltage
When there is no electricity
in the circuit, the spring keeps
the needle at 0
Electricity in the circuit turns
the wire coil into a magnet
that pulls the iron vane
needle’s
rest
position
spring
The higher the electrical
voltage, the stronger the
magnetic pull of the wire coil
and the greater the rightward
movement of the needle
Mar. 2006
Measuring Instruments
Slide 7
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.
Rubber
band
0
0
Paper
clip
2
Paper or
cardboard
strip
2. Hang something of known weight (e.g., 2 oz) from the clip and see how
far the rubber band stretches. Mark the new position of the paper clip.
3. Repeat with different weights, until the scale has been calibrated.
4. Now, use the scale to measure the weight of an object.
Mar. 2006
Measuring Instruments
Slide 8
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 its
movements as you add weights on the paper plate.
0
0
2
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.
Mar. 2006
Measuring Instruments
Slide 9
Selecting Suitable Instruments for Measurement
We use different instruments depending on the size, weight,
speed, temperature, . . . of the object being measured.
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.
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)?
Mar. 2006
Measuring Instruments
Slide 10
Measuring Very Large and Very Small Items
How high are the mountains to the north of us in Santa Barbara?
Micrometers
for measuring
small items
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.
Mar. 2006
Measuring Instruments
How thick is your toenail?
Slide 11
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 the
wheel 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).
Mar. 2006
Measuring Instruments
Slide 12
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 voltage
that it generates. Here is another way to measure rotation speed.
Connect two balls to the end of strings and attach them to the spindle.
Slow spin
Fast spin
The faster the wheel spins, the higher the balls will fly.
Location of the balls can be used to determine the rotation speed.
Mar. 2006
Measuring Instruments
Slide 13
Next Lesson
May 2006
2006
Mar. 2006
Measuring Instruments
Slide 14