Question

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.

Answer 1

Let the length of broom be
`l`

The magnitude of Torque is given by
`= Force*length*sin(\theta)`

Mass of nest
`= 3.4` ×
`10^(5)` Kg

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

Magnitude of Torque
`= 3.75` ×
`10^(7)` N.m

`\theta = 45 degree`

Putting these value we get
`l=(3.75*10^7)/(3.4*10^5*9.81*sin45) = 15.9 m`