Calculate the balancing force for a lever from load force and distances, or check whether both sides have equal moment in balance.

Balance opposing moments about a pivot using perpendicular moment arms.

Perpendicular distance from pivot to the force’s line of action.

Use a force that produces rotation opposite to the load.

Balanced Force Formula

Select the value to solve, or choose Check moment balance. The following equation balances opposing moments on an ideal lever; distances are perpendicular moment arms. Beam weight, friction and other moments are excluded.

BF = EF × D1 / D2
  • Where BF is the balanced force (N)
  • EF is the force on one side of the pivot point of the beam (N)
  • D1 is the perpendicular distance from the line of action of force EF to the pivot point (m)
  • D2 is the perpendicular distance from the pivot point to the line of action of the balancing force (m)

To calculate balanced force, multiply the effort force by the distance from the force to the pivot, then divide by the distance between the pivot and the balance force.

What is a Balanced Force?

Definition:

Here, balancing force means the force needed to counter the load moment about a pivot. Complete static equilibrium also requires the total force, including the pivot reaction, to be zero.

How to Calculate Balanced Force?

Example Problem:

The following example outlines the steps and information needed to calculate the balancing force.

First, determine the force on one side of the pivot point of the beam. In this example, that force is found to be 10 N.

Next, determine the distance from force EF to the pivot point. For this problem, the distance from force EF to the pivot point is found to be 30m.

Next, determine the distance from the pivot point to the balanced force. In this case, the distance from the pivot point to the balanced force is measured to be 20m

Finally, calculate the balanced force using the formula above:

BF = EF * D1 / D2

BF = 10 * 30 / 20

BF = 15N