Best Answer:
OK. First of all we assume no friction in the pulley at the end of the jib. So the tension (T) in the cable is the same on both sides of the pulley and is equal to the maximum load.

What we are looking for is the bending load on (A). In other words the force acting at right angles to (A)

There are two forces here acting here.

i) The component of (T) down and to the right due to the cable between the pulley and the load = T.cos(45)

ii) The component of (T) up and to the left due to the cable between the pulley and the winch = T.cos(80)

So the net bending force is the difference between the two

= T.cos(45) - T.cos(80)

= T(cos(45) - cos(80) ) {Saves a bit of looking up if you know that cos(80) = sin(10) }

= T( 0.707 - 0.174 )

= T * 0.533

But you are told that the maximum bending force = 40000 lbs

40000 = 0.533T

T = 40000 /0.533

T = 75047 lbs ≈ 75 klbs

As we said earlier T = load

EDIT:

If you are ever unsure whether it is sin() or cos(), ask yourself what happens if you do a "thought experiment" where you change the angle to 90° or 0°

Here if the angle was 90° instead of 80°, the cable would be pulling with a tension (T) along the bar (A) so the component of (T) at right angles to the bar would be zero.

At 90°, sin(90°) = 1 and cos(90°) = 0.

So T.sin(90°) = T and and T.cos(90°) = 0 So if you know that the answer IS zero, it must be cos()

In the same way, if the angle was 0° the whole of (T) would be pulling at right angles to (A)

At 0°, sin(0°) = 0 and cos(0°) = 1 So again, to get the right answer, (T), it must be cos()

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