Mar. 2006 Measuring Instruments Slide 1

Measuring InstrumentsA Lesson in the “Math + Fun!” Series

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 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

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Weight

Speed

Length Temperature

We Need to Measure Many Different Things

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Temperature Measurement

Materials expand when heated

Idea: Connect a reservoir to a very thin tube to make the expansion more noticeable

100

010203040

60708090

50Put 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 C32 F

100 C212 F

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A Second Way for Measuring TemperatureDifferent 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 shape to convert the shifting motion into rotation

Bimetal strip

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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 a hand-crank flashlight that gives off more light the faster you turn the crank)

But how do you measure electricity?

Goleta

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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

The higher the electrical voltage, the stronger the magnetic pull of the wire coil and the greater the rightward movement of the needle

spring

needle’srest

position

Measuring Electrical Voltage

Mar. 2006 Measuring Instruments Slide 8

Activity 1: Making a Scale with a Rubber Band1. 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 how far 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 its movements 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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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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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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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).

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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.

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

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