4 Unit A2 2: Applied Mathematics (A-level only)
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Question 102
In this question use g=9.8g = 9.8g=9.8 m s−2^{-2}−2.
A uniform carbon-fibre beam XY XY\,XY has length 5.6 m and mass 0.6 kg.
A sensor of weight λ \lambda\,λ newtons is fixed to the beam at XXX, and a counterweight of weight 4λ 4\lambda\,4λ newtons is fixed to the beam at YYY.
The beam is held in horizontal equilibrium by a single vertical cable attached to the beam at a point d d\,d metres from YYY.
Show that d=5.6λ+1.68g5λ+0.6g\displaystyle d = \frac{5.6\lambda + 1.68g}{5\lambda + 0.6g}d=5λ+0.6g5.6λ+1.68g.