Uncertainty questions???


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?

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General Physics RvTDLR 6 years 1 Answer 1102 views 0

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Answer ( 1 )

  1. The error formula comes from using differentials to estimate the error.

    For a rectangle:
    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.

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