Solution 5.7b
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(New page: Resolving vertically upwards, <math>T\cos {{30}^{\circ }}+S-mg=0</math> where <math>S</math> is the spring force '''which we assume is upwards'''. This gives <math>S=mg-\ T\cos {{30}...)
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Resolving vertically upwards,
\displaystyle T\cos {{30}^{\circ }}+S-mg=0
where \displaystyle S is the spring force which we assume is upwards.
This gives
\displaystyle S=mg-\ T\cos {{30}^{\circ }}=40\times 9\textrm{.}8-90\times 0\textrm{.}866=314\ \text{N}
As \displaystyle S is positive this means the spring is pushing upwards on the mass and thus the spring is in compression. (If \displaystyle S had been negative the spring would have been pulling downwards on the mass and thus would be in tension).
