With what acceleration should a weight of 45 kg be lowered on a rope so

With what acceleration should a weight of 45 kg be lowered on a rope so that it does not break? The rope withstands a maximum tension of 400N.

Given:

T = 400 Newton – the maximum tension that the rope can withstand;

m = 45 kilograms – the mass of the load, which is lowered on the rope;

g = 9.8 Newton / kilogram – acceleration of gravity.

It is required to determine a (m / s2) – with what maximum acceleration the load can be lowered so that the rope does not break.

Suppose the rope is lowered with maximum acceleration, at which the tensile force is T.

Then, according to Newton’s second law, we obtain the following equality:

T + m * a = F gravity;

T + m * a = m * g;

m * a = m * g – T;

a = (m * g – T) / m = (45 * 9.8 – 400) / 45 =

= (441 – 400) / 45 = 41/45 = 0.9 m / s2 (the result has been rounded to one decimal place).

Answer: the load can be lowered with an acceleration equal to 0.9 m / s2.