A man pulls with 150lbs of force on a rope attached to a bui

A man pulls with 150lbs of force on a rope attached to a building at point A from the position shown. What are the horizontal and vertical components of the 1501b force vector? If point A breaks away from the building under a horizontal force of 100lbs, will it remain attached to the building? How much force must the man pull with, (from his current position) to break away the attachment at point A?

Solution

Here,

angle of rope with horizontal is theta

tan(theta) = 30/25

theta = 50.2 degree

horizontal component of vector = 150 * cos(50.2)

horizontal component of vector = 96.02 lb

vertical component of vector = 150 * sin(50.2)

vertical component of vector = 115.24 lb

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as the horizontal force is less than 100 lbs , the point A will remain attached.

let the force needed to break off is FA

FA * cos(50.2) = 100

FA = 156.2 lb

the force that must be acted on the point A is 156.2 lb