The Mass of a One
Cent Coin
T.H.
The Professional Development Service for Teachers is funded by the
Department of Education and Skills under the National Development Plan
What is the Mass of a One Cent Coin?
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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?
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Sensitivity
 The mechanical
balance is not
sensitive enough to
measure the mass of
a 1 cent coin.
 How can we solve
this problem?
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More coins please!
 We found the mass
of forty coins to be
90 g.
 What is the average
mass of each coin?
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Answer
 The average mass of each coin is
90 ÷ 40 = 2.5 g
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Question
 Would you say that each coin has the
same mass?
Say why.
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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.
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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.
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What do you notice in this picture?
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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.
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Average mass
 There are 29
coins on this
balance.
Find the average
mass of each
coin.
(Don’t forget the
10 g zero error.)
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Answer
 77.5 – 10 = 67.5
67.5 ÷ 29 = 2.33 g
 The last time we got an average of 2.5 g.
How can we tell which scale is more
accurate?
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Calibration
 We can test
a balance
with a known
mass, e.g. a
100 g mass.
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Average mass
 There are 35 coins
on this balance.
Find the average
mass of a one cent
coin.
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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?
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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.
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Percentage Errors
 2.5  2.27   100  10.1%
2.27
1
 2.33  2.27   100  2.6%
2.27
1
 2.29  2.27   100  0.88%
2.27
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Specifications of a One Cent Coin
Diameter (mm): 16.25
Thickness (mm): 1.67
Weight (g): 2.27
Shape: Round
Colour: Red
Composition: Copper covered steel
Edge: Smooth
(See: http://www.fleur-decoin.com/eurocoins/coins.asp)
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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.
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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?
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Answer
337  2  27  148  49
This suggests that there are 148 coins in total.
The mass of the plastic bag accounts for the 0.49 g.
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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.
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ANSWERS
8  4 10  2  27
9
 1 906  10 g
10
 1 906  10  1000 kg
10
 1 906  10 kg
7
 1 906  10  1000 t
7
 19,068 tonnes
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Question
 How could you prove that a 1 c coin is
not made from solid copper?
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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.
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Question
 How much money would you have if you
had your mass in 1 c coins?
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Your Mass in One Cent Coins
 Suppose you have a mass of 65 kg.
Then:
65000  2  27  28634 cents
 €286.34
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Trivia
 The Greek one cent
coin is called a “lepto”.
 The elementary
particles – electrons,
muons, tauons and
neutrinos – are called
“leptons.”
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