abayatpoor
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Hi everyone,

I was wondering if anybody could help me out on the question attahced (part A) its for the Edexcel board. Any help will be much appreciated ! it
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Kevin De Bruyne
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(Original post by abayatpoor)
Hi everyone,

I was wondering if anybody could help me out on the question attahced (part A) its for the Edexcel board. Any help will be much appreciated ! it
Okay, what is an inverse square relationship? Have you ever seen an example of one before?
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abayatpoor
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(Original post by Kevin De Bruyne)
Okay, what is an inverse square relationship? Have you ever seen an example of one before?

Unfortunately not
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Kevin De Bruyne
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(Original post by abayatpoor)
Unfortunately not
Okay, no problem.

Let's make up an example of something that has an inverse square proportion.

Let's say that there's a ball of flame and you have a thermometer, and you are trying to work out what relationship distance has with the temperature.

If the relationship is inverse squared between temperature and distance, then  T = \frac{k}{d^2} where d is the distance in cm between the flame and thermometer, and T is the temperature reading of the thermometer in Celsius , and k is an unknown constant (a number like 1 or 5 or something).


And you randomly pick 5cm and measure the temperature to be 60 degrees. From this you can work out k if you wanted to but that's not the point, but let's say you now know what K is and you've got the formula above.

Now, when you double your distance, by the inverse square relationship it means that your temperature will be a quarter of the original. This is because when you put in (2*5) as the distance in the formula, and square it, you get 4*(5^2), and as this 4 is on the denominator you can say that the whole thing is (1/4) * the old temperature having doubled the distance, which is why it would read 15 degrees.

If you then doubled it to 20cm from 10cm, again it would be 1/4 of 15 degrees.

So the inverse square relationship is essentially that as one variable increases, the other decreases by the square of the proportion of change.

To break down the terminology...

If y is directly proportional to x then if you change x by +1 y changes by +1.

If Y is directly proportional to the square of x, I.e. Y = kx^2 where k is some constant, then when you change x by +2 then y would change by +4. You don't need to know what k is, just how much x changes by, then the formula tells you how much y will change by.

Then if y is inversely proportional to x, then it's y = (k/x), so when you change x by +3 you change y and it becomes 1/3 times the original amount.

Hence inverse square is...


Sorry about the explanation, best I can do on a mobile without diagrams
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abayatpoor
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(Original post by Kevin De Bruyne)
Okay, no problem.

Let's make up an example of something that has an inverse square proportion.

Let's say that there's a ball of flame and you have a thermometer, and you are trying to work out what relationship distance has with the temperature.

If the relationship is inverse squared between temperature and distance, then  T = \frac{k}{d^2} where d is the distance in cm between the flame and thermometer, and T is the temperature reading of the thermometer in Celsius , and k is an unknown constant (a number like 1 or 5 or something).


And you randomly pick 5cm and measure the temperature to be 60 degrees. From this you can work out k if you wanted to but that's not the point, but let's say you now know what K is and you've got the formula above.

Now, when you double your distance, by the inverse square relationship it means that your temperature will be a quarter of the original. This is because when you put in (2*5) as the distance in the formula, and square it, you get 4*(5^2), and as this 4 is on the denominator you can say that the whole thing is (1/4) * the old temperature having doubled the distance, which is why it would read 15 degrees.

If you then doubled it to 20cm from 10cm, again it would be 1/4 of 15 degrees.

So the inverse square relationship is essentially that as one variable increases, the other decreases by the square of the proportion of change.

To break down the terminology...

If y is directly proportional to x then if you change x by +1 y changes by +1.

If Y is directly proportional to the square of x, I.e. Y = kx^2 where k is some constant, then when you change x by +2 then y would change by +4. You don't need to know what k is, just how much x changes by, then the formula tells you how much y will change by.

Then if y is inversely proportional to x, then it's y = (k/x), so when you change x by +3 you change y and it becomes 1/3 times the original amount.

Hence inverse square is...


Sorry about the explanation, best I can do on a mobile without diagrams
Hahaha no problem I really appreicate your time. So lets put it in context, if the distance from the lamap is 60cm the light intnesity is 2.5? Thank you so much bby the way
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Kevin De Bruyne
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(Original post by abayatpoor)
Hahaha no problem I really appreicate your time. So lets put it in context, if the distance from the lamap is 60cm the light intnesity is 2.5? Thank you so much bby the way
100% correct, well done
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abayatpoor
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#7
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(Original post by Kevin De Bruyne)
100% correct, well done
Oh wow thats amazing ! Thanks so much for your time you helped me alot
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