Question 1 of 3 · Frames, Machines & Pulleys · Intermediate · About 22 min

Pinned lever with diagonal force link

A rigid horizontal lever $AC$ is pinned at $A=(0,0)$ and carries a $750\,\mathrm{N}$ downward load at $C=(1.6,0)$ metres. At a two-force link pulls on the lever along the direction . Find the link force and pin reactions. Check whether the assumed pull is consistent with equilibrium.

A rigid horizontal lever AC, 1.60 m long, with a pin support at A on the left. Point B is 0.60 m from A. A straight link runs from pin B up and to the left, 3 units left for every 4 units up, ending at a small fixed pin. Beside the link, draw a small right-angled slope triangle with sides marked 3, 4 and 5. A downward force arrow at C. Two dimensions under the lever on separate rows: A to B and A to C. Labels: A; B; C; link; 750 N; 3; 4; 5; 0.60 m; 1.60 m — Schematic, not to scale unless dimensions are given.

Given

$AB=0.6$ m
$AC=1.6$ m
Link direction $(-3/5,+4/5)$

Find

Link force $F_B$
$A_x,A_y$

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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Pinned lever with diagonal force link

Given

Find

Assumptions

Worked solution