Physics Newton's law of motion in our real life

When a rope is going up or down through a pulley then the weight of the rope and associated pull is applied on the pulley and the point from where pulley is hanged will take the total load of the line. In a system in equilibrium the tension (T) in the rope will be same on the both the sides though forces may differ on the both the sides depending upon the pull exerted on these sides by the external forces. The weight on the pulley is general equal to 2T and the point from where the pulley is hanged should be able to tolerate it otherwise it will break from there.

As regards the breaking of cable if the resultant force on the cable increases its permissible strength then it will snap from the weakest point. Due to weathering and other manufacturing reasons as well as mechanical reasons like a kink at a place in the rope some weak points are developed. So we can not say that the rope will break from which point. It will generally snap from the weakest point along the rope under the extreme pull.

The chances will be the same for the both sides. A rope will break at the point where it is the weakest point. The weak point may come due to so many reasons. The rope may be behaving manufacturing defect at a particular point. The rope may get strained at a particular point due to some misuse and the weak point may get developed there. The rope may get cut at that point. We can't it will break while going up or going down.
The weight will be on the Pully and the pully hanging point and not the rope. So whatever weight is there on the rope will be transferred to Pully.

While applying the newton's law of motion for the masses m1 and m2 attached to either side of the in elastic string, this can be written down as m1 g - T = m1f where m1 being the mass attached at the end of one side and f denotes the acceleration. Similarly the equation of the other side would be T- m2g = m2f where m2 is another mass attached to the opposite side of the hook, where the mass of the string has supposed to be a weightless mass.
On adding these two equations,we get f = (m1 - m2/ m1 +m2)g, where m1 and m2 are the masses in terms of kg and g being 9.8 NM^2.
Newton calculated this formulae considering the negligible mass of the string where as practically it is not the same for the entire system. In case of pulley, we apply a thick rope made up of either some metal or a thick rope made up of cotton.
During the process of operation, there are certain areas, which may wear out fast due to the inherent defects and a stage reaches in course of operation, where snap will occur at these weak points, leading to failure of the entire system.
Such a phenomena may occur during either side of the journey when m1 goes up or m2 moves down during the journey maintaining the system of equilibrium.
Precautions-
1) Newton considered the string to be applied in course of pulley as weightless but on application of rope of metallic nature such as steel, the mass per unit length of the same would vary.
2) In case of corrosive environment, there is quite possibility of the same being corroded particularly in stainless steel. This might happen due to deficiencies of Chromium, Manganese, Nickel etc. In that situation corrosion would take place at a particular region making the structure weak and ultimately it might detach from that weak point.