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

Question

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.

Answer 1

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 $T = \dfrac{49.0\,\mathrm{N}}{3\cdot\frac{\sqrt{3}}{2}} \approx 18.9\,\mathrm{N}.$