Final answer:
To determine the tensions in cables AB and AD, a free-body diagram should be drawn, and the system of equations generated by applying Newton's second law to the x and y components should be solved.
Step-by-step explanation:
Determining Tensions in Multiple Cables
The problem requires finding the tensions in cables AB and AD at point A such that the resultant is vertical, and given that the tension in cable AC is 54N. To solve this, a free-body diagram must be drawn, illustrating all forces acting on point A, including the known tension in cable AC.
Assuming a vertical resultant force and known forces implies that the horizontal components of the tensions in cables AB and AD must cancel each other out. Therefore, if we label the tensions in cables AB and AD as TAB and TAD respectively, and if the angles these cables make with the horizontal are given or can be determined, we can use trigonometric functions to separate the tensions into their horizontal (x) and vertical (y) components. According to the problem's condition, the sum of the y-components of the tensions must equal the weight of the object suspended (if known), and the sum of x-components must be zero because they cancel each other out.
To find the tensions in AB and AD, we would solve the system of equations resulting from applying Newton's second law in both the x and y directions (ΣFx=0 and ΣFy=0).