Question #2546b

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Answer 1 · 2017-04-06T08:58:34

See below

The question only makes sense if we take into account the mass of the string.

Reubens

The small element $dx$ will have mass: $dm= M/L dx$ , assuming the string is of uniform density.

The FBD for the small element requires:

$sum mathbf F = m mathbf a$

$implies T + dT - T = dm \ a$

$implies dT = M/L dx \ a$

$implies T = M/L a x + C$

$T(0) = 10 implies C = 10$

$T(L) = 20 implies 20 = M/La L + 10$

$implies T = 10/L x + 10$

Which is simply a linear increase along the string which is what intuitively one would expect.