Question 2 of 3 · Force Systems & Equilibrium · Intermediate · About 22 min

Wall-mounted service boom

A horizontal service boom $AB$ extends $2.4\,\mathrm{m}$ rightward from pin $A$ . A cable from its tip $B$ runs to a wall anchor $C$ located $1.8\,\mathrm{m}$ vertically above $A$ . A $850\,\mathrm{N}$ tool load acts downward $1.8\,\mathrm{m}$ from $A$ . Neglect boom weight. Find the cable tension and both reactions at $A$ .

A vertical wall on the left with hatching. A horizontal boom runs 2.40 m to the right from pin A on the wall to its tip B. A straight cable runs from B up to anchor C on the wall, exactly 1.80 m above A. A downward force acts on the boom 1.80 m from A, which is 75% of the way along. Vertical dimension of 1.80 m beside the wall. Two horizontal dimensions under the boom on separate rows: A to the load, and A to B. Labels: A; B; C; Cable T; 850 N; 1.80 m (vertical); 1.80 m (horizontal); 2.40 m — Schematic, not to scale unless dimensions are given.

Given

$AB=2.4$ m
$AC=1.8$ m
$P=850$ N at m

Find

Cable tension $T$
$A_x$
$A_y$

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

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Wall-mounted service boom

Given

Find

Assumptions

Worked solution