f38 Measuring Instruments

8/22/2019 f38 Measuring Instruments

1/14

Mar. 2006 Measuring Instruments Slide 1

Measuring Instruments

A Lesson in the Math + Fun! Series


2/14


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


3/14


Weight

Speed

Length Temperature

We Need to Measure Many Different Things


4/14


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


5/14


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


6/14


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
http://www.artifice.com/support/user_guide/accessories/3d_libs/vehicles-sedan.gif


7/14


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


8/14


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.
http://p.office1000.com/mrp/26749BAU.jpghttp://p.office1000.com/mrp/26749BAU.jpg


9/14


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


10/14


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.


11/14


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.


12/14


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).


13/14


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.


14/14


Next LessonMay 2006

2 0 0 6

f38 Measuring Instruments

Documents

Transcript of f38 Measuring Instruments