Answer to Question #140072 in Molecular Physics | Thermodynamics for Christine

Question #140072
A porcelain vase weighing 49.0N is supported by a tripod. The legs of the tripod are spaced at 120° apart and are inclined 60° with the horizontal. Find the force exerted by each leg of the tripod.
1
Expert's answer
2020-10-29T07:03:04-0400

The forces T1, T2, T3 exerted by the legs should be able to prevent the vase to fall. Moreover, every force is directed along the leg towards the vase, so "\\vec{T_i}\\,\\, (i=1,2,3)" has the horizontal and the vertical components. Due to the symmetry of system the sum of horizontal components will be equal to 0: the moduli of these components are equal and the components are directed along the medians of the equilateral triangle. Therefore, the sum of "\\vec{T_i}\\,\\, (i=1,2,3)" will be equal to the sum of vertical components, and every vertical component is "|\\vec{T_i}|\\cos(90^\\circ-60^\\circ)" :

"(T_1+T_2+T_3)\\cdot\\cos (90^\\circ - 60^\\circ) - 49.0\\,\\mathrm{N} =0," because the sum of forces exerted on the vase should be 0.

Therefore, "3T\\cos30^\\circ = 49.0\\,\\mathrm{N}," so "T = \\dfrac{49.0\\,\\mathrm{N}}{3\\cdot\\frac{\\sqrt{3}}{2}} \\approx 18.9\\,\\mathrm{N}."


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