Calculate the resultant force acting on an object by summing all individual forces.
Enter angle relative to positive x-axis.
Enter angle relative to positive x-axis.
Enter angle relative to positive x-axis.
Net Force: 0.00 N
Understanding and Calculating Net Force
In physics, net force is the vector sum of all individual forces acting on an object. It is the single force that produces the same effect as all the forces combined. Understanding net force is crucial because it's the net force that determines an object's acceleration according to Newton's second law of motion (F_net = ma).
Why Calculate Net Force?
Predicting Motion: Knowing the net force allows physicists and engineers to predict how an object will move (whether it will accelerate, decelerate, or maintain constant velocity).
Analyzing Systems: It's fundamental to analyzing complex systems involving multiple interacting forces, such as in mechanics, structural engineering, and fluid dynamics.
Problem Solving: Many physics problems require calculating the net force to solve for other variables like acceleration, mass, or individual force components.
How to Calculate Net Force
Calculating net force involves breaking down each force into its horizontal (x) and vertical (y) components, summing the components separately, and then combining the resultant x and y components to find the magnitude and direction of the net force.
Steps:
Identify Forces: List all forces acting on the object and their directions.
Resolve Forces into Components: For each force F acting at an angle θ (measured counterclockwise from the positive x-axis):
Horizontal component (F_x) = F * cos(θ)
Vertical component (F_y) = F * sin(θ)
Sum Components:
Calculate the total horizontal force (ΣF_x) by adding all F_x components.
Calculate the total vertical force (ΣF_y) by adding all F_y components.
Calculate Net Force Magnitude: Use the Pythagorean theorem with the summed components:
Net Force (F_net) = sqrt((ΣF_x)^2 + (ΣF_y)^2)
Calculate Net Force Direction: Find the angle (α) of the net force using the arctangent function:
Direction (α) = atan2(ΣF_y, ΣF_x) (using atan2 accounts for all quadrants correctly)
Example Calculation:
Let's calculate the net force for three forces:
Force 1: 50 N at 0°
Force 2: 75 N at 90°
Force 3: 30 N at 180°
Component Calculation:
Force 1:
F1_x = 50 * cos(0°) = 50 * 1 = 50 N
F1_y = 50 * sin(0°) = 50 * 0 = 0 N
Force 2:
F2_x = 75 * cos(90°) = 75 * 0 = 0 N
F2_y = 75 * sin(90°) = 75 * 1 = 75 N
Force 3:
F3_x = 30 * cos(180°) = 30 * (-1) = -30 N
F3_y = 30 * sin(180°) = 30 * 0 = 0 N
Summing Components:
ΣF_x = 50 N + 0 N + (-30 N) = 20 N
ΣF_y = 0 N + 75 N + 0 N = 75 N
Net Force Calculation:
Magnitude: F_net = sqrt((20 N)^2 + (75 N)^2)
F_net = sqrt(400 + 5625) N
F_net = sqrt(6025) N ≈ 77.62 N
Direction: α = atan2(75, 20) ≈ 75.07°
Therefore, the net force acting on the object is approximately 77.62 N at an angle of 75.07° relative to the positive x-axis.
function calculateNetForce() {
var force1 = parseFloat(document.getElementById("force1").value);
var direction1 = parseFloat(document.getElementById("direction1").value);
var force2 = parseFloat(document.getElementById("force2").value);
var direction2 = parseFloat(document.getElementById("direction2").value);
var force3 = parseFloat(document.getElementById("force3").value);
var direction3 = parseFloat(document.getElementById("direction3").value);
var totalFx = 0;
var totalFy = 0;
// Function to convert degrees to radians
function degToRad(degrees) {
return degrees * (Math.PI / 180);
}
// Process Force 1
if (!isNaN(force1) && !isNaN(direction1)) {
var rad1 = degToRad(direction1);
totalFx += force1 * Math.cos(rad1);
totalFy += force1 * Math.sin(rad1);
}
// Process Force 2
if (!isNaN(force2) && !isNaN(direction2)) {
var rad2 = degToRad(direction2);
totalFx += force2 * Math.cos(rad2);
totalFy += force2 * Math.sin(rad2);
}
// Process Force 3
if (!isNaN(force3) && !isNaN(direction3)) {
var rad3 = degToRad(direction3);
totalFx += force3 * Math.cos(rad3);
totalFy += force3 * Math.sin(rad3);
}
// Calculate Net Force Magnitude
var netForceMagnitude = Math.sqrt(Math.pow(totalFx, 2) + Math.pow(totalFy, 2));
// Display the result, formatted to two decimal places
document.getElementById("netForceResult").textContent = netForceMagnitude.toFixed(2);
}
function resetForm() {
document.getElementById("force1").value = "";
document.getElementById("direction1").value = "";
document.getElementById("force2").value = "";
document.getElementById("direction2").value = "";
document.getElementById("force3").value = "";
document.getElementById("direction3").value = "";
document.getElementById("netForceResult").textContent = "0.00";
}