A uniform lamina $$\(A E C F\)$$ is formed by removing two identical triangles $$\(B C E\)$$ and $$\(C D F\)$$ from a square lamina $$\(A B C D\)$$. The square has side $$\(3 a\)$$ and $$\(E B=D F=h\)$$ (see diagram). The lamina $$\(A E C F\)$$ is placed vertically on its edge $$\(A E\)$$ on a horizontal plane. Find, in terms of $$\(a\)$$, the set of values of $$\(h\)$$ for which the lamina remains in equilibrium.
Exam No：9231_w21_qp_31 Year：2021 Question No：4(b)
Answer:
For equilibrium, \(\bar{x} \leqslant 3 a-h\)
\(27 a^{2}-12 a h+h^{2} \leqslant 6(3 a-h)^{2}\)
\(
27 a^{2}-24 a h+5 h^{2} \geq 0
\)
\(h \leqslant \frac{9}{5} a\)
\(27 a^{2}-12 a h+h^{2} \leqslant 6(3 a-h)^{2}\)
\(
27 a^{2}-24 a h+5 h^{2} \geq 0
\)
\(h \leqslant \frac{9}{5} a\)
Knowledge points:
3.2.5 use the principle that if a rigid body is in equilibrium under the action of coplanar forces then the
Solution:
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