The opposite ends of the lever of the first kind in the same direction are acted upon by forces whose

The opposite ends of the lever of the first kind in the same direction are acted upon by forces whose moduli are 5 and 15 N. The length of the lever is 1 m. Where is the fulcrum on the lever if the lever is in equilibrium?

L = 1 m.

F1 = 5 N.

F2 = 15 N.

L1 -?

L2 -?

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

The moment of force M is called the product of the applied force F to the smallest distance from the application of force in the axis of rotation of the lever L: M = F * L.

F1 * L1 = F2 * L2.

The length of the entire lever L is expressed by the formula: L = L1 + L2.

L2 = L – L1.

F1 * L1 = F2 * (L – L1).

F1 * L1 = F2 * L – F2 * L1.

F1 * L1 + F2 * L1 = F2 * L.

L1 = F2 * L / (F1 + F2).

L1 = 15 N * 1 m / (5 N + 15 N) = 0.75 m.

L2 = 1 m – 0.75 m = 0.25 m.

Answer: the fulcrum is at a distance L1 = 0.75 m from the action of the force F1 and at a distance of L2 = 0.25 m from the action of the force F2.