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djlucifer
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9702_s12_qp_52
can someone help me to work out the uncertainty step by step
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Eimmanuel
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(Original post by djlucifer)
9702_s12_qp_52
can someone help me to work out the uncertainty step by step
Can you at least state which question or which part(s) of the question do you need help.
There are a few parts concerning uncertainty.
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djlucifer
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here i needed help in this to work out the unceertainty step by step
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Eimmanuel
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(Original post by djlucifer)
here i needed help in this to work out the unceertainty step by step
There are at least 2 methods of computing it.

Method 1:


uncertainty = ½ × (maximum value – minimum value)

This is a method that will work for A level physics and you should know. I say it will work provided that you do thing correctly.

 \Delta \left(\dfrac{1}{L}\right) = \dfrac{1}{2} \times \left( \dfrac{1}{L - \Delta L} - \dfrac{1}{L + \Delta L} \right)

For example, when L = (54.5 ± 0.5) × 10-2 m,


\Delta \left(\dfrac{1}{L}\right) = \dfrac{1}{2} \times \left( \dfrac{1}{(54.5 - 0.5) \times 10^{-2}} - \dfrac{1}{(54.5 + 0.5) \times 10^{-2}} \right)


 \Delta \left(\dfrac{1}{L}\right) = 0.0168

Method 2:
Assume that you know the following rule:


 c = \dfrac{a}{b}



 \dfrac{\Delta c}{c} = \dfrac{\Delta a}{a} + \dfrac{\Delta b}{b}

Let a = 1 and b = L in  c = \dfrac{a}{b} ,


 \dfrac{\Delta c}{c} = \dfrac{\Delta 1}{1} + \dfrac{\Delta L}{L}


 \dfrac{\Delta c}{c} = 0 + \dfrac{\Delta L}{L}


 \dfrac{\Delta c}{c} = \dfrac{\Delta L}{L}

Note that  c = \dfrac{1}{L} ,


 \Delta c = \dfrac{\Delta L}{L} \times c


 \Delta c = \dfrac{\Delta L}{L} \times \dfrac{1}{L}


 \Delta \left(\dfrac{1}{L}\right) = \dfrac{\Delta L}{L^2}

Using method 2 for when L = (54.5 ± 0.5) × 10-2 m,


 \Delta \left(\dfrac{1}{L}\right) = \dfrac{ 0.5 \times 10^{-2}}{(54.5 \times 10^{-2})^2}


 \Delta \left(\dfrac{1}{L}\right) = 0.0168

I did not round to the correct significant figures for the uncertainty. Rounding to how many significant figures for the uncertainty is something you should know.

Both methods give the same answer for the uncertainty. Note that you can use a more sophisticated method and the uncertainty may be smaller but it is ok.
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djlucifer
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can ypu help me to find out the uncertainty here
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Eimmanuel
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(Original post by djlucifer)
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can ypu help me to find out the uncertainty here
I hope you can show your attempt first. It is ok to be wrong and this is how you learn. I can say students learn more when they make mistakes.
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