The size of an atom is 0.0000000001 m (10^-10 m).
How do people measure the sizes of things that they cannot see?

Record your ideas about this question in your Active Physics log. Be prepared to discuss your responses with your small group and the class.

FOR YOU TO DO

1. Work with a partner. Use a ruler and pencil to outline a square that is 10 cm x 10 cm on a card. Trace a penny as many times as you like within the square. Draw the circles so that they do not touch each other. Make the circles as close to the actual size of the penny as you can.

2. Drop a ball-point pen onto the card so that the point hits within the square. Do not aim the pen.

a) Have your partner record whether you "hit" a circle, or "miss" a circle. If the pen falls outside the square, ignore that drop.

b) Make 50 "countable" drops. Then switch roles with your partner. Continue until 100 drops are recorded.

3. Find the area of all the pennies using this ratio:

a) Show your calculations in your log.

4. Find the area of one penny by dividing the penny area (calculated in step 3) by the number of penny outlines on your card.

a) Record your calculations in your log.

5. Measure the diameter of one penny circle on your card.

a) Record your measurement.

6. Find the area of one penny using this equation: Area = πr², where π= 3.14
and r = the radius of the penny. (The radius is one-half the diameter.)

a) Record your calculations in your log.

7. Compare the results you obtained using indirect measurement and direct measurement.

a) How close are the results you got using the indirect and the direct methods?

b) Which method is more accurate? Explain your answer.

c) Why is it important not to aim the pencil in the indirect measurement?