A lever is 3 m long with a load of 8,000 N suspended at 1 m from the pivot. What force is needed at the end to achieve equilibrium?

To determine the force needed at the end of a 3 m long lever to achieve equilibrium, we can apply the principle of moments (or torque). In equilibrium, the clockwise moments about the pivot point must equal the counterclockwise moments.

The load of 8,000 N is suspended 1 m from the pivot. Therefore, the moment created by the load can be calculated as:

Moment from the load = Load × Distance from the pivot = 8,000 N × 1 m = 8,000 Nm.

Next, if we denote the force at the end of the lever as F and the distance from the pivot to the end of the lever (which is 3 m), the moment created by this force would be:

Moment from the force = F × 3 m.

Setting the two moments equal to each other for equilibrium:

8,000 Nm = F × 3 m.

To find F, we rearrange the equation:

F = 8,000 Nm / 3 m = 2,666.667 N.

This calculation shows that the force needed at the end of the lever to achieve equilibrium is indeed 2,666.667 N, confirming that this answer aligns with the principles of levers and