Math Is Fun Forum

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

two scales problem by Peterkn0

hi

If I had two sets of scales and placed one on top of the other, then placed a one kilo bag of sugar on the top scale, what would each of the scales read? If you cannot imagine a kilo bag of sugar, a 2.2lb bag will do just as well.

If anyone with a degree or other high-flier qualification in maths or physics answers, please include this in the reply, I as have to convince a few people of the correct answer.

Many thanks, Peterkn0

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: two scales problem by Peterkn0

hi Peterkn0

I'm assuming these scales are bathroom type scales graduated in Kg.

Strictly such scales measure force not mass so the scale should really be in Newtons.   But unless you're in space or on the Moon you won't notice the difference so the Kg scale (because it will be proportional to the Newton scale) will do for our purposes.

Oh yes, I've got an 'A' in A level applied maths and also in physics and a degree in maths.  Do you think that will impress your friends enough?

Each scale will show what it is supporting.  So the top scale will show 1 Kg and the lower scale will show (1 + w) Kg where w is the weight in Kg of the top scale.

Hope that helps. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

peterkn0

Member

Registered: 2012-06-03

Posts: 4

Re: two scales problem by Peterkn0

Thank you very much for that Bob, highly illuminating!

In our discussion we had support for every possible outcome, 1kg on the top scale and zero on the bottom, zero on the top scale and 1kg on the bottom, and 0.5kg on both scales.

As you point out, this is a measure of Force and not Mass, so that makes all the difference.

Your credentials are impeccable! Thanks again.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: two scales problem by Peterkn0

You're welcome. 

If some of your friends remain to be convinced, suggest the doubters take part in the following practical experiment.

The most doubtful one lies on the ground.  The next most doubtful lies on top of this, (nothing naughty; this is a pure science experiment).  Then the next doubter climbs on the pile.  Then the next,  and so on until all the doubters have formed a tower of bodies.

Now ask the one on the bottom if that feels like zero weight. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: two scales problem by Peterkn0

He might be very surprised, that bottom guy.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

peterkn0

Member

Registered: 2012-06-03

Posts: 4

Re: two scales problem by Peterkn0

"High o'er the fence leaps Sunny Jim, Force is the food that raises him". My old Physics teacher used to put up an old breakfast cereal  packet with that slogan, and a cartoon drawing of a young lad leaping over a fence. 1902!
I'm glad it still works.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: two scales problem by Peterkn0

hi

Wiki says it's still sold.  And Nestle still list it.  But I cannot find anywhere that actually sells it.

Perhaps just as well as the units for force are not directly applicable to foodstuffs. 

Sunny Jim looks to be a spritely fellow of senior years.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob