Answer :
Final answer:
The tension in the tie and the compressive force in the jib can be calculated using the principles of static equilibrium, vector decomposition and trigonometric functions.
Explanation:
This question can be solved by applying the principles of static equilibrium and vector decomposition. Given the information, the crane, jib, and tie form a triangle. We know the angles and we can work out the forces acting on the system.
First, you need to determine the weight of the object which is mass times gravity (W=mg). So, for a 285 kg object, this would be 2793 N.
Next, we decompose the weight into two components, one along the jib and one along the tie. For the jib, it's the compressive force (Fc), while for the tie, it's tension (Tt). Using knowledge of the trigonometric functions sine and cosine, these values can be calculated using the given angles: Fc = Wcos(36.6) and Tt = Wsin(36.6).
Lastly, we subtract the angle between the tie and the post from 180 degrees to find the remaining angle of the triangle. By applying the sine rule, we can calculate the tension in the tie using the known values of the compressive force in the jib and the angles of the triangle.
Please note: To get specific numerical results, you would need to follow these steps using a calculator or a comparable computing device.
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