A trolley of mass passes a photogate with speed

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

A trolley of mass

m = (2.00 \pm 0.02)\,\mathrm{kg}

passes a photogate with speed

v = (3.50 \pm 0.05)\,\mathrm{m\,s^{-1}}

, each uncertainty a standard deviation and the two quantities measured independently. Its kinetic energy is

KE = \tfrac{1}{2}mv^2

. ((a)) Find the contribution of

m

KE

by moving

m

up to

m+u(m)

with

v

fixed, and the contribution of

v

by moving

v

up to

v+u(v)

with

m

fixed. ((b)) Combine these to give

u(KE)

and quote

KE = \overline{KE} \pm u(KE)

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