Forces of 4N and 20N act on the ends of the lever, the length of the lever is 60 cm. At what distance

Forces of 4N and 20N act on the ends of the lever, the length of the lever is 60 cm. At what distance from the place of application of the greater force is the fulcrum, if the lever is in equilibrium?

F1 = 4 N.

F2 = 20 N.

L = 60 cm = 0.6 m.

L2 -?

When the lever is in equilibrium, the moments of forces M that act from different sides of the lever are equal to each other: M1 = M2.

The moment of force M is the product of force F by the smallest distance from the line of action of the force to the point of equilibrium L: M = F * L.

F1 * L1 = F2 * L2.

L = L1 + L2.

L1 = L – L2.

F1 * (L – L2) = F2 * L2.

F1 * L – F1 * L2 = F2 * L2.

L2 = F1 * L / (F1 + F2).

L2 = 4 N * 0.6 m / (4 N + 20 N) = 0.1 m.

Answer: the equilibrium point is at a distance of L2 = 0.1 m from the action of a greater force.