Two workers are holding a thin plate with length $5 \, \text{m}$ and height $2 \, \text{m}$ at rest by supporting the plate in the bottom corners. The workers are standing at rest on a slope of $10^\circ$. Treat these supporting forces as vertical normal forces and calculate their magnitudes and state if both workers are sharing “the job” fairly.

Question

Two workers are holding a thin plate with length $5 \, \text{m}$ and height $2 \, \text{m}$ at rest by supporting the plate in the bottom corners. The workers are standing at rest on a slope of $10^\circ$. Treat these supporting forces as vertical normal forces and calculate their magnitudes and state if both workers are sharing &#8220;the job&#8221; fairly.

Jason · Accepted Answer

$F_1 = mg\left(\dfrac{1}{2} + \dfrac{\tan 10^\circ}{5}\right) \approx 0.535\,mg$ (down-slope worker) and $F_2 = mg\left(\dfrac{1}{2} &#8211; \dfrac{\tan 10^\circ}{5}\right) \approx 0.465\,mg$ (up-slope worker); the job is not shared fairly, because the down-slope worker supports more of the weight.

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