Two blocks are weighed on two different balances

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Propagating uncertainty into the quantity you actually want

Problem

Two blocks are weighed on two different balances, so their readings are independent. Block A has mass

m_A = 120.0\,\mathrm{g}

with uncertainty

u(m_A) = 0.30\,\mathrm{g}

(one standard deviation); block B has mass

m_B = 85.0\,\mathrm{g}

with uncertainty

u(m_B) = 0.20\,\mathrm{g}

(one standard deviation). The blocks are stacked and their total mass is

M = m_A + m_B

. ((a)) Using the one-at-a-time method (move

m_A

up by

u(m_A)

with

m_B

held fixed, then move

m_B

up by

u(m_B)

with

m_A

held fixed), show that the sensitivity coefficient of

M

to each input is exactly

1

. ((b)) Hence write

u(M)

in terms of

u(m_A)

and

u(m_B)

, and evaluate

M

with its uncertainty. ((c)) Explain in a sentence or two why

u(M)

is not simply

u(m_A) + u(m_B)

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