Question

After an unfortunate accident occurred at a local warehouse, you were contracted to determine the cause. A jib crane collapsed and injured a worker. An image of this type of crane is shown in the figure.The horizontal steel beam had a mass of 88.50 kg
per meter of length, and the tension in the cable was =11650 N
. The crane was rated for a maximum load of 500 kg
. If =5.580 m
, =0.522 m
, =1.350 m
, and ℎ=2.070 m
, what was the magnitude of L
(the load on the crane) before the collapse? The acceleration due to gravity is =9.810 m/s2

Answer 1

The magnitude of the load L on the crane before the collapse is 3211.81 N

To determine the magnitude of the load on the crane (L), we will need to make use of the equilibrium conditions of the torque.

It is always an ideal process to list out all the parameters given as this will let you understand how you can determine the answer to the question from the given parameters.

From the given information;

• The tension in the cable = 11650 N
• The length (d) = 5.580 m
• The mass of the horizontal steel beam (M) = 88.50 kg/m (d)
• = 88.50 kg/m × 5.580 m
• = 493.83 kg
• Distance (s) = 0.522 m
• x = 1.350 m and h = 2.070 m
• Acceleration due to gravity = 9.81 m/s²

From the question;

the angle at which the crane is positioned can be determined by taking the tangent of the angle θ. i.e.

$\mathbf{tan \ \theta = \dfrac{h}{d-s}}$

$\mathbf{\theta = tan^{-1} \Big ( \dfrac{h}{d-s} \Big )}$

$\mathbf{\theta = tan^{-1} \Big ( \dfrac{2.070 }{5.580 - 0.522} \Big )}$

$\mathbf{\theta =22.26^0}$

Consider the equilibrium conditions of the torques with respect to the magnitude of the load at point P.

∴

$\mathbf{Tsin \theta (d-s) - W_L (d-x) -(Mg) (\dfrac{d}{2}) = 0}$

By making the magnitude of the load $\mathbf{W_L}$ the subject of the formula, we have:

$\mathbf{W_L = \dfrac{Tsin \theta (d-x) -(Mg) (\dfrac{d}{2})}{ (d-s) } }$

$\mathbf{W_L = \dfrac{(11650 )sin (22.26) (5.580-1.350) -(88.50\times 9.81) (\dfrac{5.580}{2})}{ (5.580-0.522) } }$

$\mathbf{W_L = 3211.81 \ N }$

Therefore, we can conclude that the magnitude of the load is 3211.81 N

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