1. Mar. 2006Measuring InstrumentsSlide 1 Measuring Instruments A Lesson in the “Math + Fun!” Series

2. Mar. 2006Measuring InstrumentsSlide 2 About This Presentation EditionReleasedRevised FirstMar. 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

3. Mar. 2006Measuring InstrumentsSlide 3 Weight Speed Length Temperature We Need to Measure Many Different Things

4. Mar. 2006Measuring InstrumentsSlide 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

5. Mar. 2006Measuring InstrumentsSlide 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 shape to convert the shifting motion into rotation Bimetal strip

6. Mar. 2006Measuring InstrumentsSlide 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 a hand-crank flashlight that gives off more light the faster you turn the crank) But how do you measure electricity? Goleta

7. Mar. 2006Measuring InstrumentsSlide 7 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’s rest position Measuring Electrical Voltage

8. Mar. 2006Measuring InstrumentsSlide 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 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 Paper clip Paper or cardboard strip 4. Now, use the scale to measure the weight of an object.

9. Mar. 2006Measuring InstrumentsSlide 9 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

10. Mar. 2006Measuring InstrumentsSlide 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.

11. Mar. 2006Measuring InstrumentsSlide 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.

12. Mar. 2006Measuring InstrumentsSlide 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 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).

13. Mar. 2006Measuring InstrumentsSlide 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 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.

14. Mar. 2006Measuring InstrumentsSlide 14 Next Lesson May 2006 2 0 0 6