6.2(+_ 0.2) - 4.1 (+_ 0.1 ) + ?
[6.2( +_ 0.2) - 4.1(+_ 0.1)] : 9.43(+_0.05)
find absolut uncertainty and relative uncertainty.
PLEASE HELP:I solved them and got the exact absolute uncertainty like the answer key, but I didn't get right answer of relative unsertainty, my answer for both case 9.5 %, but the answer key is 11% for both , why?
this is my solution :
for problem 1:
relative uncertainty = [sqr(0.2^2 + 0.1^2)/2.1] *100 am I wrong?
Please help, thank you in advance.
You calculated wrong.
relatuncert= sqrt(.04+.01)/2.1=sqrt(.05)/2.1= .106 rouned to two sig figures will be 11 percent.
To find the absolute uncertainty, you correctly calculated it by taking the square root of the sum of the squares of the individual uncertainties:
Absolute uncertainty = √(0.2^2 + 0.1^2) = 0.223
However, to find the relative uncertainty, you made a slight mistake in your calculation. The formula to calculate relative uncertainty is:
Relative uncertainty = (Absolute uncertainty / Mean value) * 100
Let's calculate it step by step:
First, calculate the mean value using the given formula:
Mean value = [6.2 (+_ 0.2) - 4.1 (+_ 0.1)] / 2 = 1.05
Next, substitute the values into the formula for relative uncertainty:
Relative uncertainty = (0.223 / 1.05) * 100 ≈ 21.2%
So, your answer for the relative uncertainty should be approximately 21.2%, not 9.5% as you calculated. The answer key that states 11% could potentially be incorrect or have a different method for calculating the relative uncertainty. It's important to refer to your course material or consult with your teacher to confirm the correct answer or method.