Dos niños sostienen una piñata cuyo peso es de 196N, formando un ángulode 140°con ambas cuerdas. Calcular la fuerza aplicada por cada niño

T = 104.2 N

Explanation:

For this exercise we must define a coordinate system, the x axis is horizontal and the y axis is vertical, let's write the equilibrium equations on each axis

X axis

         T₁ₓ-T₂ₓ = 0

         T₁ₓ = T₂ₓ                           (1)

y axis  

          + T_{2y} - W = 0

          T_{1y} + T_{21y} = W      (2)

Let's use trigonometry to find the decomposition of the stresses, they indicate that the angle between the two forces is 140º, but each force has an angle of 70º

           cos 70 = T₁ₓ / T₁

           T₁ₓ = T₁ cos 70

           sin 70 = / T₁

           T_{1y} = T₁ sin 70

for tension 2 we have a similar equation

            T₂ₓ = T₂ cos 70

             T_{2y} = T₂ sin 70

From equation 1

        T₁ cos 70 = T₂ cos 70

        T₁ = T₂

therefore the two children apply the same force

From equation 2

        T sin 70 + T sin 70 = W

        2 T sin 70 = W

        T = W / 2sin 70

        T = 196 / (2 sin 70)

        T = 104.2 N

the two children have the same strength

the ima (higher than 1m) will be greater than the ima with the height of 1m.