A thin wire is bent along the parabola in the plane

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Vector calculus and field geometry · Vector calculus and field geometry

Mathematical Methods for Physics, Ch Line, surface and volume integrals

Problem

A thin wire is bent along the parabola

y=x^2

in the plane

z=0

, from

(0,0,0)\ \mathrm{m}

(1,1,0)\ \mathrm{m}

, with

x

and

y

in metres. Its mass per unit length grows along the wire as

\rho_\ell = kx

, with

k = 0.12\ \mathrm{kg\,m^{-2}}

. Find the mass of the wire.

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