The soldier needs to lift a load weighing 180 kg. To do this, he has a lever 2 m long.

The soldier needs to lift a load weighing 180 kg. To do this, he has a lever 2 m long. A soldier can apply a force of 600 N. to the lever. Determine the maximum possible distance from the fulcrum to the load.

m = 180 kg.

g = 9.8 m / s ^ 2.

L = 2 m.

F1 = 600 N.

x2 -?

Let us write down the equilibrium condition for the lever: M1 = M2, where M1, M2 are the moments of force that act on the lever from both sides.
The moment of force M is determined by the formula: M = F * x, where F is the force, x is the shoulder on which the force acts.
M1 = F1 * x1, M2 = F2 * x2.

F1 * x1 = F2 * x2.

Let’s find the force F2 with which the weight acts on the lever: F2 = m * g.
The distance x1 from the application of the force F1 to the fulcrum will be determined by the formula: x1 = L – x2.
F1 * (L – x2) = m * g * x2;

F1 * L – F1 * x2 = m * g * x2;

F1 * L = F1 * x2 + m * g * x2;

F1 * L = x2 * (F1 + m * g);

x2 = F1 * L / (F1 + m * g);

x2 = 600 N * 2 m / (600 N + 180 kg * 9.8 m / s ^ 2) = 0.5 m.

Answer: the maximum possible distance from the fulcrum to the load x2 = 0.5 m.