A lever 10 m long is pivoted at one end and carries a load of 900 kg at the other end. What force should be applied at the midpoint for equilibrium?

To achieve equilibrium in a lever system, the moments (or torques) around the pivot point must be equal on both sides of the pivot. In this scenario, the lever is 10 meters long and has a load of 900 kg at one end. The weight of the load needs to be calculated first. The weight (force due to gravity) can be determined using the equation:

Weight = mass × gravitational acceleration

Using a standard gravitational acceleration of approximately 9.81 m/s², the load can be calculated as:

Weight = 900 kg × 9.81 m/s² = 8829 N

This weight acts at a distance of 10 meters from the pivot. The moment created by this weight about the pivot is calculated by:

Moment = force × distance = 8829 N × 10 m = 88290 N·m

Now, if a force is applied at the midpoint of the lever (which is 5 meters from the pivot), we need to find the force that creates an equal moment to maintain equilibrium. Let the force applied at the midpoint be F. The moment created by this force is:

Moment = F × distance from pivot

In this case, the distance from the pivot to the