Two weights of unequal weight hang at the ends of a thread thrown over a weightless block, and the lighter weight

Two weights of unequal weight hang at the ends of a thread thrown over a weightless block, and the lighter weight is 2 meters lower than the heavy one. If we let the weights move under the influence of gravity, then in 2 seconds they will be at the same height. How many times is the mass of a heavy weight greater than that of a light one?

Given:

S = 2 meters – distance traveled by a lighter weight;

t = 2 s – the time during which the lighter weight travels the distance t;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to find how many times the mass of a heavy weight m1 is greater than the mass of a light weight m2.

Since a light weight starts moving without an initial velocity, we find its acceleration:

a = 2 * S / t ^ 2 = 2 * 2/2 ^ 2 = 4/4 = 1 m / s.

This acceleration is imparted to the light weight by the gravity of the heavier weight. According to Newton’s second law:

m1 * g – m2 * g = m2 * a

m1 * g = m2 * a + m2 * g

m1 * g = m2 * (a + g)

m1 / m2 = (a + g) / g = (1 + 10) / 10 = 11/10 = 1.1

Answer: The mass of a heavy kettlebell is 1.1 times greater (10 percent).