Question 2 of 3 · Frames, Machines & Pulleys · Intermediate · About 22 min

Compound winch drum in static balance

A stationary compound winch drum is supported by a frictionless central bearing $O$ . A $30\,\mathrm{kg}$ load hangs from the right-hand tangent of a small-radius drum ( $r=0.12\,\mathrm{m}$ ), pulling vertically downward. An operator pulls a second rope horizontally leftward at the top of a concentric outer drum ( $R=0.30\,\mathrm{m}$ ). Find the required pull and the bearing reaction components at . The drum weight acts through and is neglected.

Front view of two concentric circular drums on a central bearing O. Outer drum radius 0.30 m, inner drum radius 0.12 m, drawn to that ratio. A rope leaves the very top of the outer drum and runs horizontally to the left, ending in a force arrow pointing left. A second rope leaves the right-hand side of the inner drum and hangs straight down to a rectangular block hanging below the drums. Show radius R as a thin line from O towards the lower left, and radius r as a thin line from O towards the upper right, with neither label crossing a rope. Labels: O; T; 30 kg; R = 0.30 m; r = 0.12 m — Schematic, not to scale unless dimensions are given.

Given

$m=30$ kg
$r=0.12$ m
$R=0.30$ m

Find

Operator force $T$
Bearing reactions $O_x,O_y$

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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Compound winch drum in static balance

Given

Find

Assumptions

Worked solution