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The Mass of a One Cent Coin

The Mass of a One Cent Coin. What is the Mass of a One Cent Coin?. The mass of a 1 cent coin. A student placed a 1 cent coin on this balance. The scale gave the mass as zero. Why?. Sensitivity. The mechanical balance is not sensitive enough to measure the mass of a 1 cent coin.

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The Mass of a One Cent Coin

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  1. The Mass of a One Cent Coin The Professional Development Service for Teachers is funded by the Department of Education and Skills under the National Development Plan

  2. What is the Mass of a One Cent Coin? PDST Resources for Leaving Certificate Physics2

  3. The mass of a 1 cent coin • A student placed a 1 cent coin on this balance. • The scale gave the mass as zero. Why? PDST Resources for Leaving Certificate Physics3

  4. Sensitivity • The mechanical balance is not sensitive enough to measure the mass of a 1 cent coin. • How can we solve this problem? PDST Resources for Leaving Certificate Physics4

  5. More coins please! • We found the mass of forty coins to be 90 g. • What is the average mass of each coin? PDST Resources for Leaving Certificate Physics5

  6. Answer • The average mass of each coin is 90 ÷ 40 = 2.5 g PDST Resources for Leaving Certificate Physics6

  7. Question • Would you say that each coin has the same mass? Say why. PDST Resources for Leaving Certificate Physics7

  8. Answer • To see if each coin has the same mass one could try finding the mass of different groups of, say, 20 coins. If the groups have different masses, then the coins are not all the same. PDST Resources for Leaving Certificate Physics8

  9. A worn coin • If we had an extremely accurate balance, we could find the individual mass of different coins. • It would be no surprise if their masses were slightly different, due to different amounts of wear. PDST Resources for Leaving Certificate Physics9

  10. What do you notice in this picture? PDST Resources for Leaving Certificate Physics10

  11. ZERO ERROR • The electronic balance showed a reading of 10 g when nothing was being weighed on it. • This zero error must be subtracted from subsequent readings. PDST Resources for Leaving Certificate Physics11

  12. There are 29 coins on this balance. Find the average mass of each coin. (Don’t forget the 10 g zero error.) Average mass PDST Resources for Leaving Certificate Physics12

  13. Answer • 77.5 – 10 = 67.567.5 ÷ 29 = 2.33 g • The last time we got an average of 2.5 g.How can we tell which scale is more accurate? PDST Resources for Leaving Certificate Physics13

  14. We can test a balance with a known mass, e.g. a 100 g mass. Calibration PDST Resources for Leaving Certificate Physics14

  15. There are 35 coins on this balance. Find the average mass of a one cent coin. Average mass PDST Resources for Leaving Certificate Physics15

  16. Answer • 80÷35 = 2.29 g • We now have three results for the average mass of a one cent coin: 2.5 g, 2.33 g and 2.29 g. • Are one cent coins made with small difference in mass? PDST Resources for Leaving Certificate Physics16

  17. The Standard Mass of a One Cent Coin. • In fact, one cent coins are all minted to exact specifications. The standard mass of a one cent coin is 2.27 g. • Find the percentage error for each of our results: 2.5 g, 2.33 g and 2.29 g. PDST Resources for Leaving Certificate Physics17

  18. Percentage Errors PDST Resources for Leaving Certificate Physics18

  19. Specifications of a One Cent Coin Diameter (mm): 16.25Thickness (mm): 1.67Weight (g): 2.27Shape: RoundColour: RedComposition: Copper covered steelEdge: Smooth (See: http://www.fleur-de-coin.com/eurocoins/coins.asp) PDST Resources for Leaving Certificate Physics19

  20. Question • How would find out how many coins are in this bag. • You’re not allowed to open the bag or count the coins through the plastic. PDST Resources for Leaving Certificate Physics20

  21. A Suggestion • You could find the mass of the bag of coins. • The mass of the plastic is negligible. • If the standard mass of one cent is 2.27 g, and the bag of coins has mass 337 g, how many coins are in the bag? PDST Resources for Leaving Certificate Physics21

  22. Answer This suggests that there are 148 coins in total.The mass of the plastic bag accounts for the 0.49 g. PDST Resources for Leaving Certificate Physics22

  23. Further Questions • The mintage of 1 c coins from 1999 to 2006 was 8,400,000,000 coins. • Find the total mass of this mintage in tonnes. PDST Resources for Leaving Certificate Physics23

  24. ANSWERS PDST Resources for Leaving Certificate Physics24

  25. Question • How could you prove that a 1 c coin is not made from solid copper? PDST Resources for Leaving Certificate Physics25

  26. One Cent Coins Are Not Made From Solid Copper • You can pick up a 1 c coin with a magnet. This couldn’t be done if they were made from solid copper. (Try picking up a copper calorimeter with a magnet.) • You could find the density of a 1 c coin and compare it with the density of copper. PDST Resources for Leaving Certificate Physics26

  27. Question • How much money would you have if you had your mass in 1 c coins? PDST Resources for Leaving Certificate Physics27

  28. Your Mass in One Cent Coins • Suppose you have a mass of 65 kg. Then: PDST Resources for Leaving Certificate Physics28

  29. Trivia • The Greek one cent coin is called a “lepto”. • The elementary particles – electrons, muons, tauons and neutrinos – are called “leptons.” PDST Resources for Leaving Certificate Physics29

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