On a weightless lever, two weights weighing 2.4 kg and 6 kg are balanced. is the ratio of the arms of this lever exactly?

Given:

m1 = 2.4 kilograms – the mass of the first weight on the lever;

m2 = 6 kilograms – the mass of the second weight on the lever;

g = 10 Newton / kilogram – acceleration of gravity.

It is required to determine the ratio of the arms of a given lever.

According to the condition of the problem, the lever is in equilibrium, in addition, the mass of the lever itself is not taken into account. Then, let l1 be the distance from the equilibrium point to the first weight, and l2 – the distance from the equilibrium point to the second weight. Then we have:

F1 * l1 = F2 * l2;

m1 * g * l1 = m2 * g * l2;

m1 * l1 = m2 * l2;

m1 * l1 / l2 = m2;

l1 / l2 = m2 / m1 = 6 / 2.4 = 2.5.

Answer: the ratio of the shoulders of this lever is 2.5