# Determine the length of the weightless arm in equilibrium at the ends of which weights of 2 and 12 kg

Determine the length of the weightless arm in equilibrium at the ends of which weights of 2 and 12 kg are suspended. The distance from the fulcrum to the larger load is 2 cm.

According to the balance rule of the lever:
F1 / F2 = l2 / l1; F1 is the force acting on the shoulder l1 (F1 = m1 * g, m1 = 2 kg, g = 10 m / s ^ 2; F1 = 2 * 10 = 20 N); F2 is the force acting on the shoulder l2 (F2 = m2 * g, m2 = 12 kg, g = 10 m / s ^ 2; F2 = 12 * 10 = 120 N), l2 is the distance from the fulcrum to the larger load (l2 = 2 cm), l1 is the distance from the fulcrum to the smaller load.
Distance from fulcrum to smaller load:
l1 = F2 * l2 / F1 = 120 * 2/20 = 12 cm.
Lever length:
l = l1 + l2 = 12 + 2 = 14 cm.
Answer: The length of the arm is 14 cm.

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