In a recent article,1 Baum solves two problems in mechanics using involved trigonometric relations. However, those two problems can instead be solved using algebra-based methods that might be more accessible to students as follows.
A uniform prism of density ρ0 is floating in fluid of density ρF (Fig. 1 1). The tip of the bottom is then a distance h below the surface. Find h.
Using the condition of equilibrium (the magnitudes of buoyant force and weight of the object are equal), and the equation of the similarity of the triangles, the solution is identical by Baum,
Baum argues that this approach, based on Archimedes’ principle, does not determine whether the equilibrium is stable or unstable. However, a floating object is...
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