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The nests built by the mallee fowl of Australia can have masses as large as 3.4 × 105 kg. Suppose a nest with this mass is being lifted by a crane. The boom of the crane makes an angle of 45.0° with the ground. If the axis of rotation is the lower end of the boom, the torque produced by the nest has a magnitude of 3.75 × 107 N•m. Treat the boom’s mass as negligible, and calculate the length of the boom.

Respuesta :

Let the length of broom be [tex]l[/tex]

The magnitude of Torque is given by [tex]= Force*length*sin(\theta)[/tex]

Mass of nest [tex]= 3.4[/tex] × [tex]10^{5}[/tex] Kg

Force due to mass of nest =weight of nest = (mass of nest)*g ; where [tex]g = 9.81 m/s^2[/tex]

Magnitude of Torque [tex]= 3.75[/tex] × [tex]10^{7}[/tex] N.m

[tex]\theta = 45 degree[/tex]

Putting these value we get [tex]l=\frac{3.75*10^7}{3.4*10^5*9.81*sin45} = 15.9 m[/tex]

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