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.
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.