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The Mass of a One Cent Coin

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Presentation on theme: "The Mass of a One Cent Coin"— Presentation transcript:

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 Physics 2

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 Physics 3

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 Physics 4

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 Physics 5

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

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

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 Physics 8

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 Physics 9

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

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 Physics 11

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

13 Answer 77.5 – 10 = ÷ 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 Physics 13

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

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

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 Physics 16

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 Physics 17

18 Percentage Errors PDST Resources for Leaving Certificate Physics 18

19 Specifications of a One Cent Coin
Diameter (mm): Thickness (mm): 1.67 Weight (g): 2.27 Shape: Round Colour: Red Composition: Copper covered steel Edge: Smooth (See: PDST Resources for Leaving Certificate Physics 19

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 Physics 20

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 Physics 21

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 Physics 22

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 Physics 23

24 ANSWERS PDST Resources for Leaving Certificate Physics 24

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

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 Physics 26

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

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

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 Physics 29

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