Rauhan
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#1
a= 1.3mm +- 0.1mm

b= 2.8mm +- 0.2mm

c= 0.8mm +- 0.1mm

Q=ab^2/sqrt(c)

Calculate Q with its uncertainty
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username3249896
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(Original post by Rauhan)
a= 1.3mm +- 0.1mm

b= 2.8mm +- 0.2mm

c= 0.8mm +- 0.1mm

Q=ab^2/sqrt(c)

Calculate Q with its uncertainty
What have you tried so far?
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Rauhan
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(Original post by BobbJo)
What have you tried so far?
So my teacher divided the question into 4 parts and then asked us to solve it.

1) Calculate the value of Q
2) Calculate %uncertainty for each quantity
3) Calculate the value of uncertainty
4) Express Q with its uncertainty
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Rauhan
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(Original post by Rauhan)
So my teacher divided the question into 4 parts and then asked us to solve it.

1) Calculate the value of Q
2) Calculate %uncertainty for each quantity
3) Calculate the value of uncertainty
4) Express Q with its uncertainty
Answers:
1)11.39
2) a=7.4%
b= 7.14%
c=12.5%
3) Now i am stuck
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username3249896
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(Original post by Rauhan)
So my teacher divided the question into 4 parts and then asked us to solve it.

1) Calculate the value of Q
2) Calculate %uncertainty for each quantity
3) Calculate the value of uncertainty
4) Express Q with its uncertainty
Yes that's correct.

For 3) Use the fact that when you multiply/divide by a quantity you add the percentage uncertainty,
i.e (a +- x%) x (b +- y%) = ab +- (x+y)%
and (a +- x%) / (b +- y%) = a/b +- (x+y)%

And also the fact that, a +- x%)^n = a^n +- n(x%)
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Rauhan
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(Original post by BobbJo)
Yes that's correct.

For 3) Use the fact that when you multiply/divide by a quantity you add the percentage uncertainty,
i.e (a +- x%) x (b +- y%) = ab +- (x+y)%
and (a +- x%) / (b +- y%) = a/b +- (x+y)%

And also the fact that, a +- x%)^n = a^n +- n(x%)
So I should do (7.4+7.14+12.5)*11.39/100
If I am right??
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(Original post by Rauhan)
Answers:
1)11.39
2) a=7.4%
b= 7.14%
c=12.5%
3) Now i am stuck
1) 11.4, the degree of accuracy should be the same as the data (1 d.p seems reasonable here)
2) For a, the percentage uncertainty should be 7.69%
The percentage uncertainty for b^2 is twice the uncertainty for b.
The percentage uncertainty for c^(1/2) is half the uncertainty for c
3) Add the percentage uncertainties you get
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(Original post by Rauhan)
So I should do (7.4+7.14+12.5)*11.39/100
If I am right??
Close, but not quite!
The uncertainty for b is not the same as the uncertainty for b^2
The uncertainty for sqrt(c) is different too
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Rauhan
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(Original post by BobbJo)
Close, but not quite!
The uncertainty for b is not the same as the uncertainty for b^2
The uncertainty for sqrt(c) is different too
If u dont mind, can u solve the whole question step by step
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(Original post by Rauhan)
If u dont mind, can u solve the whole question step by step
a= 1.3mm +- 0.1mm

b= 2.8mm +- 0.2mm

c= 0.8mm +- 0.1mm

Q= ab^2/sqrt(c)

Doing the question as per the steps given by your teacher:

1)  Q= \frac{1.3 \times (2.8)^2}{\sqrt 0.8} = 11.4

2)Percentage uncertainty in a = \frac{0.1}{1.3} * 100 = 7.69 %

Percentage uncertainty in b^2
= 2 x Percentage uncertainty in b = 14.28%

Percentage uncertainty in \sqrt c
= Percentage uncertainty in c^(1/2)
= 1/2 x Percentage uncertainty in c
= 6.25%

3) Q=11.4 \pm (7.69+14.28+6.25) %

 Q= 11.4 \pm 28.22%

 Q= 11.4 \pm 3.2

Hope this helps
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Rauhan
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#11
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#11
(Original post by BobbJo)
a= 1.3mm +- 0.1mm

b= 2.8mm +- 0.2mm

c= 0.8mm +- 0.1mm

Q= ab^2/sqrt(c)

Doing the question as per the steps given by your teacher:

1)  Q= \frac{1.3 \times (2.8)^2}{\sqrt 0.8} = 11.4

2)Percentage uncertainty in a = \frac{0.1}{1.3} * 100 = 7.69 %

Percentage uncertainty in b^2
= 2 x Percentage uncertainty in b = 14.28%

Percentage uncertainty in \sqrt c
= Percentage uncertainty in c^(1/2)
= 1/2 x Percentage uncertainty in c
= 6.25%

3) Q=11.4 \pm (7.69+14.28+6.25) %

 Q= 11.4 \pm 28.22%

 Q= 11.4 \pm 3.2

Hope this helps
Thanks
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