A lever 15 metres in length is pivoted at one end with a load of 750 N at the opposite end. What force is needed at the midpoint to achieve equilibrium?

To determine the force required at the midpoint of a lever to maintain equilibrium, we can use the principle of moments. The moment is calculated as the product of the force and the distance from the pivot point. In this case, the lever is 15 meters long, and the load of 750 N is applied at the opposite end, which is 15 meters from the pivot.

To achieve equilibrium, the total moment on one side of the pivot must equal the total moment on the other side. The moment created by the load is calculated by multiplying the load (750 N) by its distance from the pivot (15 m). Thus, the moment created by the load is:

Moment from load = 750 N × 15 m = 11,250 Nm.

When a force is applied at the midpoint of the lever (which is 7.5 m from the pivot), we denote that force as F. The moment created by this force is:

Moment from force = F × 7.5 m.

Setting the moments equal to each other to achieve equilibrium gives the equation:

750 N × 15 m = F × 7.5 m.

Substituting the values, we get:

11,250 Nm = F × 7