A fulcrum of a lever (which is placed horizontally) is placed 8 meters from a force of 28 Newton and another force of 14 Newton is placed on the opposite side from the fulcrum. Determine the distance between the forces of 14 Newton from the fulcrum in order to achieve equilibrium.
14 N is half of 28 N, so it must be placed twice as far from the fulcrum for equilibrium
8 * 28 = d * 14
the long multiplication method of al-Uglidisi to determine .
To determine the distance between the force of 14 Newton and the fulcrum in order to achieve equilibrium, we can use the principle of moments.
The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
In this case, let's consider the clockwise moments caused by the 28 Newton force and the anticlockwise moments caused by the 14 Newton force. Since the lever is balanced, the sum of these moments should be zero.
We can calculate the moments using the formula:
Moment = Force x Distance
For the 28 Newton force:
Moment(clockwise) = 28 N x 8 m = 224 Nm
For the 14 Newton force:
We'll let the distance between the force of 14 Newton and the fulcrum be x meters.
Moment(anticlockwise) = 14 N x x m = 14x Nm
Since these moments are equal (in opposite directions), we have:
224 Nm = 14x Nm
Solving for x:
x = 224 Nm / 14 N = 16 m
Therefore, the distance between the force of 14 Newton and the fulcrum to achieve equilibrium is 16 meters.