The forces of 4H and 20H act on the ends of the lever, the length of the lever is 6о cm, at what distance from the place

The forces of 4H and 20H act on the ends of the lever, the length of the lever is 6о cm, at what distance from the place of application of the greater force is the fulcrum if the lever is in balance.

Equilibrium condition: the sum of the moments of forces relative to the fulcrum is zero. The moment of force that rotates the lever clockwise is considered to be positive. A moment acting in the opposite direction is considered negative.

Let the pivot point be to the left of the load suspension point at 20 N. The distance from the load to the pivot point is x. From the fulcrum to the load 4 N, the distance is 0.6 m – x.

Let’s write down the sum of the moments:

-4 H * (0.6 m – x) + 20 H * x = 0;

-2.4 N * m + 4 H * x + 20 H * x = 0;

24 N * x m = 2.4 N * m;

x = 2.4 N * m / 24 N = 0.1 m.

Answer: 0.1 m (10 cm).