Calculate the mechanical advantage or determine unknown forces/distances in a lever system.
Enter values to calculate.
Understanding the Fulcrum Calculator and Lever Principles
The Fulcrum Calculator is a tool designed to simplify calculations related to levers, a fundamental concept in physics. A lever is a rigid bar that pivots around a fixed point called a fulcrum. Levers are used to apply a force at a distance from the fulcrum to overcome a resistance or to move a load. The principle behind levers is the law of moments.
The Law of Moments
In physics, a moment is the turning effect of a force about a pivot point (the fulcrum). The law of moments states that for a lever to be in equilibrium (balanced), the sum of the clockwise moments must equal the sum of the anticlockwise moments.
A moment is calculated by multiplying the force by the perpendicular distance from the fulcrum to the line of action of the force.
Formula: Moment = Force × Distance
For a lever system with two forces (F1 and F2) and their respective distances from the fulcrum (d1 and d2), the equilibrium condition is:
F1 × d1 = F2 × d2
How the Fulcrum Calculator Works
Our Fulcrum Calculator allows you to input any three of these four variables (Force 1, Distance 1, Force 2, Distance 2) and it will calculate the fourth, or it can verify if a system is balanced.
Force 1 (N): The magnitude of the first force applied to the lever, measured in Newtons (N). This could be an effort force or a load force.
Distance from Fulcrum to Force 1 (m): The perpendicular distance from the pivot point (fulcrum) to the point where Force 1 is applied, measured in meters (m).
Force 2 (N): The magnitude of the second force applied to the lever, measured in Newtons (N). This could be the load being moved or the effort applied.
Distance from Fulcrum to Force 2 (m): The perpendicular distance from the pivot point (fulcrum) to the point where Force 2 is applied, measured in meters (m).
Use Cases
The principles of levers and moments are ubiquitous. This calculator can be helpful for:
Physics students learning about rotational dynamics and equilibrium.
Engineers and designers working with simple machines, mechanical advantage, and structural stability.
DIY enthusiasts planning projects involving levers, such as building a see-saw or a simple lifting mechanism.
Understanding how tools like crowbars, wrenches, and wheelbarrows work.
Mechanical Advantage
Levers are often used to gain mechanical advantage, which is the ratio of the output force (force exerted by the lever) to the input force (effort applied). For a lever, mechanical advantage can be calculated as:
Mechanical Advantage (MA) = Force 2 / Force 1 = Distance 1 / Distance 2
If MA > 1, the lever provides a force advantage (less effort needed to lift a heavier load). If MA < 1, the lever provides a speed or distance advantage. If MA = 1, the lever changes the direction of force but not its magnitude.
Example Calculation
Consider a simple see-saw. If a child weighing 200 N sits 3 meters from the fulcrum (d1 = 3m, F1 = 200 N), and another person weighing 100 N (F2 = 100 N) needs to balance the see-saw, how far from the fulcrum should they sit?
Using the formula F1 × d1 = F2 × d2:
200 N × 3 m = 100 N × d2
600 Nm = 100 N × d2
d2 = 600 Nm / 100 N
d2 = 6 meters
The calculator can quickly solve this and many other lever-related problems.
function calculateFulcrum() {
var force1 = parseFloat(document.getElementById("force1").value);
var distance1 = parseFloat(document.getElementById("distance1").value);
var force2 = parseFloat(document.getElementById("force2").value);
var distance2 = parseFloat(document.getElementById("distance2").value);
var resultDiv = document.getElementById("result");
resultDiv.style.backgroundColor = "var(–success-green)"; // Reset color
// Check if all inputs are valid numbers
var inputsValid = !isNaN(force1) && !isNaN(distance1) && !isNaN(force2) && !isNaN(distance2);
if (!inputsValid) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
resultDiv.style.backgroundColor = "#ffc107"; // Warning color
return;
}
var moment1 = force1 * distance1;
var moment2 = force2 * distance2;
var tolerance = 0.01; // Tolerance for floating point comparisons
if (Math.abs(moment1 – moment2) moment2) {
var diff = moment1 – moment2;
// Calculate which value needs to be adjusted to achieve balance
if (!isNaN(force2) && force2 > 0) {
var neededDistance2 = moment1 / force2;
resultDiv.innerHTML = "Clockwise moment is greater. Adjust distance2 to approx. " + neededDistance2.toFixed(2) + " m for balance.";
} else if (!isNaN(distance2) && distance2 > 0) {
var neededForce2 = moment1 / distance2;
resultDiv.innerHTML = "Clockwise moment is greater. Adjust force2 to approx. " + neededForce2.toFixed(2) + " N for balance.";
} else {
resultDiv.innerHTML = "Clockwise moment is greater. Cannot calculate specific adjustment without valid force2 or distance2.";
resultDiv.style.backgroundColor = "#dc3545"; // Error color
}
} else { // moment2 > moment1
var diff = moment2 – moment1;
// Calculate which value needs to be adjusted to achieve balance
if (!isNaN(force1) && force1 > 0) {
var neededDistance1 = moment2 / force1;
resultDiv.innerHTML = "Anticlockwise moment is greater. Adjust distance1 to approx. " + neededDistance1.toFixed(2) + " m for balance.";
} else if (!isNaN(distance1) && distance1 > 0) {
var neededForce1 = moment2 / distance1;
resultDiv.innerHTML = "Anticlockwise moment is greater. Adjust force1 to approx. " + neededForce1.toFixed(2) + " N for balance.";
} else {
resultDiv.innerHTML = "Anticlockwise moment is greater. Cannot calculate specific adjustment without valid force1 or distance1.";
resultDiv.style.backgroundColor = "#dc3545"; // Error color
}
}
}