Uncertainty questions???
Question
When I am finding an area of a square with an uncertainty it’s obvious I do A=lw then Au=A[(lu/l)+(wu/w)). If I am doing the same with a cube, does the same logic apply? Vu=V[(lu/l)+(wu/w)+(hu/h)]. This is where lu is uncertainty of length, wu is uncertainty of width, and h is uncertainty of height. I’m thinking if the same applies with cube then rectangular prism should be straightforward.
Where I am stuck on is cylinder. Let’s say the radius is 10.0cm and the height is 30cm. How exactly would I find the uncertainty of a cylinder?
in progress
0
General Physics
7 years
1 Answer
1123 views
0
Answer ( 1 )
The error formula comes from using differentials to estimate the error.
For a rectangle:
A=lw
dA = l*dw + w * dl
Factor out the lw
dA = lw(dw/w + dl/l) = A(dw/w + dl/l)
For a rectangular prism:
V = lwh = l(wh)
dV = l * d(wh) + wh*dl
dV = l * (w*dh + h*dw) + wh*dl
dV = lw*dh + lh*dw + wh*dl
Factor out lwh and you are left with
dV = lwh (dh/h + dw/w + dl/l) = dV = V (dh/h + dw/w + dl/l)
For a cube:
V = x^3
dV = 3x^2 dx
dV = V( 3dx/x)
Which is the same formula as the prism when l = w = h.