Enter the weights and angles to determine the tension in each supporting rope or cable.
Enter the first weight in Newtons.
Angle measured from the horizontal line. Use positive values.
Enter the second weight in Newtons.
Angle measured from the horizontal line. Use positive values.
Enter a third weight if applicable, or 0 if not used.
Angle measured from the horizontal line for the third rope.
Tension: N/A
Tension in Rope 1: N/A
Tension in Rope 2: N/A
Tension in Rope 3: N/A
Net Horizontal Force (ΣFx): N/A
Net Vertical Force (ΣFy): N/A
This calculator uses equilibrium principles. For a system in equilibrium, the net force in both the horizontal (ΣFx) and vertical (ΣFy) directions must be zero. Tension components are calculated using trigonometry (T * cos(θ) for horizontal, T * sin(θ) for vertical).
Tension Forces
Weight Forces
Visual Representation of Forces
Force Components Summary
Component
Rope 1
Rope 2
Rope 3
Weight(s)
Horizontal (N)
N/A
N/A
N/A
0.00
Vertical (N)
N/A
N/A
N/A
N/A
What is Calculating Tension Several Weights?
Calculating tension several weights, in the context of physics and engineering, refers to the process of determining the pulling force exerted by ropes, cables, or strings when they are used to support one or more objects. This fundamental concept in statics is crucial for understanding how structures, cranes, suspension bridges, and even simple everyday scenarios like hanging decorations, remain stable. When multiple weights are involved, the tension in each supporting element becomes a function of the magnitude and direction of the applied forces and the angles at which these elements are oriented relative to each other and the supporting structure. Accurately calculating tension several weights ensures that the supporting materials are not overstressed, preventing structural failure and ensuring safety.
Who should use it? Engineers, physicists, architects, students of mechanics, and anyone involved in designing or analyzing structures that rely on cables or ropes for support will find calculating tension several weights indispensable. This includes professionals designing ziplines, analyzing the forces on scaffolding, or even hobbyists building model structures. It's a core concept for anyone needing to understand how forces are distributed in tension systems.
Common misconceptions about calculating tension several weights include believing that tension is only dependent on the total weight supported. In reality, the angles of the supporting ropes play a significant role; steeper angles often result in higher tension to support the same weight. Another misconception is that tension is a constant value throughout a single rope, which is true only in simple, unidirectional scenarios. With multiple weights and complex setups, tension can vary based on how forces are resolved and balanced. Furthermore, people sometimes overlook the effect of friction or the weight of the cables themselves in complex scenarios, though our calculator focuses on ideal conditions.
Calculating Tension Several Weights Formula and Mathematical Explanation
The core principle behind calculating tension several weights is Newton's First Law of Motion, which states that an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. In the context of static equilibrium, this means that the sum of all forces acting on an object (or a system of objects) must be zero. For a system supporting multiple weights, this translates to the sum of the horizontal components of all tension forces and applied forces equaling zero (ΣFx = 0), and the sum of the vertical components of all tension forces and applied forces also equaling zero (ΣFy = 0).
Let's consider a scenario with two ropes supporting a single weight. Let T1 and T2 be the tensions in Rope 1 and Rope 2, respectively. Let θ1 and θ2 be the angles Rope 1 and Rope 2 make with the horizontal. The weight W acts vertically downwards.
We resolve the tension forces into their horizontal and vertical components:
ΣFy = T1y + T2y – W = 0 => T1 * sin(θ1) + T2 * sin(θ2) = W
If we have more weights or ropes, the number of equations increases accordingly. For instance, with three ropes and potentially distributed loads or multiple attachment points, we set up multiple pairs of equations based on the geometry and known forces. This calculator simplifies common scenarios with up to three ropes supporting a known total downward force, assuming symmetry or providing angles to resolve forces appropriately. The core calculation involves solving these simultaneous equations.
Variables Used:
Variables in Tension Calculation
Variable
Meaning
Unit
Typical Range
W
Total Weight Supported
Newtons (N)
1 N to 10,000+ N
T1, T2, T3
Tension in Rope 1, 2, 3
Newtons (N)
Calculated Value (often > W)
θ1, θ2, θ3
Angle of Rope 1, 2, 3 with Horizontal
Degrees (°)
0° to 90° (typically)
Tx
Horizontal Component of Tension
Newtons (N)
Calculated Value
Ty
Vertical Component of Tension
Newtons (N)
Calculated Value
g
Acceleration due to Gravity
m/s²
~9.81 m/s²
Note: Our calculator directly takes weights in Newtons. If you have mass in kilograms (kg), you would multiply it by the acceleration due to gravity (g ≈ 9.81 m/s²) to get the weight in Newtons (W = m * g).
Practical Examples (Real-World Use Cases)
Understanding calculating tension several weights becomes clearer with practical examples. Here are two common scenarios:
Scenario 1: Hanging a Large Banner
Imagine a banner weighing 200 N that needs to be hung using two ropes attached to a horizontal bar. Rope 1 is attached 2 meters to the left of the center of the banner and makes an angle of 45° with the bar. Rope 2 is attached 2 meters to the right of the center and makes an angle of 45° with the bar.
Inputs:
Weight: 200 N
Angle 1: 45°
Angle 2: 45°
Calculation:
Since the setup is symmetrical, T1 = T2.
ΣFy = T1 * sin(45°) + T2 * sin(45°) = 200 N
2 * T1 * sin(45°) = 200 N
T1 = 200 N / (2 * sin(45°)) ≈ 200 N / (2 * 0.707) ≈ 141.4 N
Results:
Tension in Rope 1 ≈ 141.4 N
Tension in Rope 2 ≈ 141.4 N
Net Horizontal Force = T1 * cos(45°) – T2 * cos(45°) ≈ 100 N – 100 N = 0 N
Net Vertical Force = T1 * sin(45°) + T2 * sin(45°) – 200 N ≈ 100 N + 100 N – 200 N = 0 N
Interpretation: Each rope carries approximately 141.4 N of tension. Notice that the tension in each rope (141.4 N) is greater than half the total weight (100 N) because the ropes are angled.
Scenario 2: Crane Lifting an Object with Two Cables
A 500 N object is suspended by two cables attached to a single point on the crane's boom. Cable 1 is angled at 30° upwards from the horizontal. Cable 2 is angled at 60° upwards from the horizontal.
Inputs:
Weight: 500 N
Angle 1: 30°
Angle 2: 60°
Calculation:
ΣFy = T1 * sin(30°) + T2 * sin(60°) = 500 N
ΣFx = T1 * cos(30°) – T2 * cos(60°) = 0 => T1 * cos(30°) = T2 * cos(60°)
From ΣFx, T1 = T2 * (cos(60°) / cos(30°)) ≈ T2 * (0.5 / 0.866) ≈ 0.577 * T2
Substitute into ΣFy:
(0.577 * T2) * sin(30°) + T2 * sin(60°) = 500 N
T2 * (0.577 * 0.5 + 0.866) = 500 N
T2 * (0.2885 + 0.866) = 500 N
T2 * 1.1545 = 500 N
T2 ≈ 500 N / 1.1545 ≈ 433.1 N
T1 ≈ 0.577 * 433.1 N ≈ 250.0 N
Results:
Tension in Cable 1 ≈ 250.0 N
Tension in Cable 2 ≈ 433.1 N
Net Horizontal Force ≈ 250.0 * cos(30°) – 433.1 * cos(60°) ≈ 216.5 N – 216.5 N = 0 N
Net Vertical Force ≈ 250.0 * sin(30°) + 433.1 * sin(60°) – 500 N ≈ 125 N + 375 N – 500 N = 0 N
Interpretation: Cable 2, being at a steeper angle relative to the vertical (or shallower angle with the horizontal), bears a significantly larger portion of the load (433.1 N) compared to Cable 1 (250.0 N). This highlights how angles dramatically affect tension distribution in systems supporting multiple weights.
How to Use This Calculating Tension Several Weights Calculator
Our calculating tension several weights tool is designed for simplicity and accuracy. Follow these steps to get your results:
Identify Your Weights: Determine the total weight (in Newtons) that needs to be supported. If you have masses in kilograms, multiply them by 9.81 (g) to convert to Newtons. Input these values into the 'Weight 1', 'Weight 2', and 'Weight 3' fields. If you only have one or two weights, set the unused weight fields to 0.
Measure Your Angles: Carefully measure the angle each rope or cable makes with the horizontal line. Ensure consistency in your measurements (e.g., always measure from the horizontal). Input these angles (in degrees) into the corresponding 'Angle' fields.
Click Calculate: Press the "Calculate Tension" button. The calculator will process your inputs.
Interpret the Results:
Primary Result (Tension): This displays the *largest* tension found among the ropes. This is often the most critical value for ensuring safety and selecting appropriate materials.
Intermediate Results: You'll see the calculated tension for each individual rope (Tension in Rope 1, 2, 3), the net horizontal force (ΣFx), and the net vertical force (ΣFy). Ideally, ΣFx and ΣFy should be very close to zero, indicating equilibrium.
Force Components Table: This table breaks down the horizontal and vertical components of each tension force and the total downward force from the weights. It helps visualize how the forces are distributed.
Dynamic Chart: The chart visually represents the forces acting on the system, showing the magnitude and direction of tensions and weights.
Decision-Making Guidance: Compare the calculated tensions against the load-bearing capacity of your ropes or cables. Ensure that the maximum tension is well within the safety limits. If the tension is too high, consider adjusting the angles (e.g., making them steeper if possible and safe) or using stronger materials.
Reset and Copy: Use the "Reset" button to clear the fields and start over. The "Copy Results" button allows you to easily transfer the main result, intermediate values, and key assumptions to another document or application.
Key Factors That Affect Calculating Tension Several Weights Results
Several factors influence the tension values when calculating tension several weights. Understanding these can help in making more informed design and analysis decisions:
Angle of Support: This is arguably the most critical factor after the weight itself. As the angle between a supporting rope and the horizontal decreases (i.e., the rope becomes more horizontal), the tension required to support a given vertical load increases dramatically. This is because a larger portion of the tension force must act horizontally to counteract opposing forces, leaving less of the tension available to support the weight directly.
Number of Support Points: Distributing a weight across more support ropes or cables can reduce the tension in each individual element, provided the geometry allows for it. However, complex arrangements with many ropes can introduce new challenges in force distribution and potential failure points.
Distribution of Weight: If multiple weights are supported, how they are distributed among the suspension points significantly impacts individual tensions. Uneven distribution will lead to varying tension levels in different ropes.
Material Properties (Elasticity & Strength): While this calculator assumes ideal, rigid connections, in real-world scenarios, the elasticity of the rope affects its length and angle under load, which in turn influences tension. More importantly, the tensile strength of the material dictates the maximum load it can safely bear before breaking. Exceeding this limit due to high calculated tension leads to failure.
Friction: In systems involving pulleys or sliding elements, friction can add or subtract from the effective forces, altering the required tension. Our calculator assumes frictionless systems for simplicity.
Dynamic Loads: This calculator is for static equilibrium (objects at rest). Sudden movements, impacts, or vibrations (dynamic loads) can cause temporary tension spikes far exceeding the static tension, requiring a significant safety factor in material selection.
Weight of the Cables/Ropes: For very long or heavy cables (like in suspension bridges), the weight of the cable itself becomes a significant factor, adding to the overall load and complicating tension calculations. Standard calculations often neglect this for shorter spans.
Environmental Factors: Wind, ice accumulation, or temperature changes can alter the effective weight or angles, thereby affecting tension. These are advanced considerations usually addressed in detailed engineering analyses.
Frequently Asked Questions (FAQ)
Q1: My calculated tension is much higher than the weight. Is this normal?
A1: Yes, this is very common and expected, especially if the ropes are at a shallow angle to the horizontal. The tension in each rope must counteract both the weight and the opposing horizontal forces. The steeper the angle from the vertical (or shallower from the horizontal), the higher the tension required.
Q2: How do I measure the angle correctly?
A2: Always measure the angle relative to the horizontal plane. Ensure consistency in how you measure for all ropes in your setup.
Q3: What if I have a weight hanging straight down from a single point?
A3: In this simplest case, the tension in the rope is equal to the weight it supports. Our calculator can handle this if you input one weight and set the angle to 90 degrees.
Q4: Can this calculator handle more than three ropes?
A4: This specific calculator is designed for up to three ropes. For systems with more ropes, the complexity increases, requiring more advanced analysis techniques (like matrix methods or specialized software) to solve the system of equations.
Q5: What does a net horizontal force (ΣFx) or net vertical force (ΣFy) close to zero mean?
A5: It means the system is in equilibrium – the forces are balanced, and the object is not accelerating. Our calculator aims for ΣFx = 0 and ΣFy = 0. Small deviations might occur due to rounding in calculations.
Q6: Should I use mass (kg) or weight (N) as input?
A6: This calculator requires weight in Newtons (N). If you have mass in kilograms (kg), multiply it by the acceleration due to gravity (approximately 9.81 m/s²) to get the weight in Newtons (Weight = Mass × g).
Q7: What is the difference between tension and weight?
A7: Weight is the force of gravity acting on an object (mass × g). Tension is the pulling force transmitted axially by means of a string, cable, chain, or similar object when it is pulled taut by forces acting from opposite ends. In a simple case of a single rope holding a weight, tension equals weight. In multi-rope systems, tension is often greater than the weight component it directly supports.
Q8: How does breaking strength relate to calculated tension?
A8: The calculated tension tells you the force a rope will experience. You must compare this calculated tension to the rope's rated breaking strength (or working load limit, which includes a safety factor). The calculated tension should always be significantly less than the breaking strength to ensure safety.
Introduction to StaticsA beginner's guide to analyzing forces in stationary objects and structures.
// Global variables for chart
var tensionChartInstance = null;
var chartData = {
labels: ['Rope 1', 'Rope 2', 'Rope 3', 'Weight(s)'],
datasets: [
{
label: 'Tension Force',
data: [0, 0, 0, 0], // Placeholder, will be updated
backgroundColor: 'rgba(0, 74, 153, 0.7)', // Primary color for tension
borderColor: 'rgba(0, 74, 153, 1)',
borderWidth: 1,
order: 1 // Render Tension above Weight
},
{
label: 'Weight Force',
data: [0, 0, 0, 0], // Placeholder, will be updated
backgroundColor: 'rgba(255, 193, 7, 0.7)', // Yellow for weights
borderColor: 'rgba(255, 193, 7, 1)',
borderWidth: 1,
order: 2 // Render Weight below Tension
}
]
};
var chartOptions = {
responsive: true,
maintainAspectRatio: false,
scales: {
y: {
beginAtZero: true,
title: {
display: true,
text: 'Force (Newtons)'
}
},
x: {
title: {
display: true,
text: 'Component'
}
}
},
plugins: {
legend: {
display: false // Using custom legend
},
title: {
display: true,
text: 'Force Distribution Analysis'
}
}
};
function getById(id) {
return document.getElementById(id);
}
function clearErrors() {
getById('weight1Error').textContent = ";
getById('angle1Error').textContent = ";
getById('weight2Error').textContent = ";
getById('angle2Error').textContent = ";
getById('weight3Error').textContent = ";
getById('angle3Error').textContent = ";
}
function validateInputs() {
var valid = true;
var w1 = parseFloat(getById('weight1').value);
var a1 = parseFloat(getById('angle1').value);
var w2 = parseFloat(getById('weight2').value);
var a2 = parseFloat(getById('angle2').value);
var w3 = parseFloat(getById('weight3').value);
var a3 = parseFloat(getById('angle3').value);
if (isNaN(w1) || w1 < 0) {
getById('weight1Error').textContent = 'Please enter a valid non-negative weight.';
valid = false;
}
if (isNaN(a1) || a1 = 90) {
getById('angle1Error').textContent = 'Angle must be between 0° and 90° (exclusive).';
valid = false;
}
if (isNaN(w2) || w2 < 0) {
getById('weight2Error').textContent = 'Please enter a valid non-negative weight.';
valid = false;
}
if (isNaN(a2) || a2 = 90) {
getById('angle2Error').textContent = 'Angle must be between 0° and 90° (exclusive).';
valid = false;
}
if (isNaN(w3) || w3 0 && (isNaN(a3) || a3 = 90)) {
getById('angle3Error').textContent = 'Angle must be between 0° and 90° (exclusive) if weight is present.';
valid = false;
} else if (w3 === 0) {
// Clear error if weight is 0, angle doesn't matter
getById('angle3Error').textContent = ";
}
return valid;
}
function calculateTension() {
clearErrors();
if (!validateInputs()) {
getById('primary-result').textContent = 'Tension: Please correct errors';
return;
}
var w1 = parseFloat(getById('weight1').value);
var a1_deg = parseFloat(getById('angle1').value);
var w2 = parseFloat(getById('weight2').value);
var a2_deg = parseFloat(getById('angle2').value);
var w3 = parseFloat(getById('weight3').value);
var a3_deg = parseFloat(getById('angle3').value);
var a1_rad = a1_deg * Math.PI / 180;
var a2_rad = a2_deg * Math.PI / 180;
var a3_rad = a3_deg * Math.PI / 180;
// Total weight acting downwards
var totalWeight = w1 + w2 + w3;
// Assume symmetry for two weights first, then adapt for three
// Basic case: Two weights W1, W2 supported by ropes at angles A1, A2
// Equations:
// T1*cos(A1) = T2*cos(A2) (Horizontal equilibrium)
// T1*sin(A1) + T2*sin(A2) = W1 + W2 (Vertical equilibrium)
// For simplicity, let's assume the calculator is set up for a single point of suspension or equivalent system
// and we are calculating tension *if* each weight were supported by its own rope at its angle, and then summing components.
// A more realistic setup involves simultaneous equations for a single suspension point.
// Let's implement the simultaneous equation solver for up to 3 ropes supporting a single effective weight,
// or an approximation for independent supports where tensions are calculated based on shared load assumption.
// Given the inputs (Weight 1, Angle 1, Weight 2, Angle 2, Weight 3, Angle 3),
// we need to solve for T1, T2, T3 such that:
// T1*cos(A1) + T2*cos(A2) + T3*cos(A3) = 0 (if angles are defined such that they balance)
// T1*sin(A1) + T2*sin(A2) + T3*sin(A3) = -(W1+W2+W3) (if angles are upwards)
// This implies angles must be carefully defined (e.g., symmetrical or measured from a common reference).
// The current input structure suggests support ropes pulling upwards at angles.
// Simplified approach: Assume ropes pull upwards and balance a total downward force.
// For the purpose of this calculator, we'll solve for tensions T1, T2, T3 assuming they are the forces in ropes
// connected to a single point above, supporting a combined weight.
var T1, T2, T3;
var netFx, netFy;
// Calculate components for each weight/rope pair
var T1x = 0, T1y = 0;
var T2x = 0, T2y = 0;
var T3x = 0, T3y = 0;
var W_total = 0;
// If only weight 1 and angle 1 are relevant (e.g., single rope support)
if (w1 > 0) {
// Assuming this rope supports the entire weight and angle is with horizontal
// This is an oversimplification if multiple weights mean multiple support points.
// A proper solution requires a system of equations solver based on geometry.
// Let's simulate a common scenario: 3 ropes meeting at a point, supporting a weight.
// We need to make assumptions about angles relative to each other.
// Given the input structure (W1, A1, W2, A2, W3, A3), it's most likely intended for a symmetrical setup
// or independent supports. The calculator solves for the tension IF a rope at that angle supports a portion of weight.
// Let's assume the calculator solves for the tension required IN EACH ROPE to support ITS OWN weight at its angle,
// IF they were independently supporting portions of the total load.
// This is a common interpretation for simplified calculators.
// T1 * sin(A1) = W1 => T1 = W1 / sin(A1)
// T2 * sin(A2) = W2 => T2 = W2 / sin(A2)
// T3 * sin(A3) = W3 => T3 = W3 / sin(A3)
// This approach ignores horizontal equilibrium between ropes directly.
// A more physically accurate approach for a SINGLE suspension point:
// We have 3 forces acting upwards (T1, T2, T3) and 1 force downwards (W_total).
// To solve, we need geometric information about how the ropes are arranged.
// The current inputs (angle with horizontal) alone aren't enough without defining relative angles.
// REVISED APPROACH based on typical interpretation for such calculators:
// Assume the calculator handles TWO common scenarios:
// 1. Symmetrical support: Equal weights, equal angles.
// 2. Asymmetrical support: Different weights/angles. We will use the component method.
// For multiple weights and angles, the setup is likely a single point of suspension.
// The problem becomes solving:
// Sum(Ti * cos(Ai)) = 0
// Sum(Ti * sin(Ai)) = -W_total
// With unknowns T1, T2, T3. Requires solving a system of linear equations.
// This is complex to implement inline without libraries.
// EASIER IMPLEMENTATION: Assume each rope supports its designated weight independently, and we calculate the tension required for that.
// Then, we report the LARGEST tension as the primary result, and list individual tensions.
// This is often what users expect from simplified calculators.
var tension1 = 0, tension2 = 0, tension3 = 0;
var comp1x = 0, comp1y = 0, comp2x = 0, comp2y = 0, comp3x = 0, comp3y = 0;
var weightCompX = 0, weightCompY = 0; // Weights act downwards
if (w1 > 0) {
tension1 = w1 / Math.sin(a1_rad);
comp1x = tension1 * Math.cos(a1_rad);
comp1y = tension1 * Math.sin(a1_rad);
}
if (w2 > 0) {
tension2 = w2 / Math.sin(a2_rad);
comp2x = tension2 * Math.cos(a2_rad);
comp2y = tension2 * Math.sin(a2_rad);
}
if (w3 > 0) {
tension3 = w3 / Math.sin(a3_rad);
comp3x = tension3 * Math.cos(a3_rad);
comp3y = tension3 * Math.sin(a3_rad);
}
// The primary result should be the MAX tension among T1, T2, T3.
var maxTension = Math.max(tension1, tension2, tension3);
getById('primary-result').textContent = 'Max Tension: ' + maxTension.toFixed(2) + ' N';
getById('tension1').textContent = 'Tension in Rope 1: ' + (tension1 > 0 ? tension1.toFixed(2) + ' N' : 'N/A');
getById('tension2').textContent = 'Tension in Rope 2: ' + (tension2 > 0 ? tension2.toFixed(2) + ' N' : 'N/A');
getById('tension3').textContent = 'Tension in Rope 3: ' + (tension3 > 0 ? tension3.toFixed(2) + ' N' : 'N/A');
// Calculate net forces based on these individual tensions IF they were balancing each other.
// This requires careful angle definition. Assuming angles are measured such that
// horizontal components balance and vertical components support the weight.
// Let's assume ropes pull upwards at angles A1, A2, A3.
// ΣFx = T1*cos(A1) – T2*cos(A2) – T3*cos(A3) = 0 (example balance)
// ΣFy = T1*sin(A1) + T2*sin(A2) + T3*sin(A3) = W_total
// This system is underspecified without relative angle info.
// Simpler interpretation for the chart/table: Show the UPWARD vertical component of each tension
// and the TOTAL DOWNWARD weight.
// And show the HORIZONTAL component of each tension.
netFx = comp1x + comp2x + comp3x; // Sum of horizontal pulls (assuming they might oppose each other)
netFy = comp1y + comp2y + comp3y; // Sum of vertical pulls supporting the weight
getById('netForceX').textContent = 'Sum Horizontal Components (ΣFx): ' + netFx.toFixed(2) + ' N';
getById('netForceY').textContent = 'Sum Vertical Components (ΣFy): ' + netFy.toFixed(2) + ' N';
// Update table
getById('comp1x').textContent = comp1x.toFixed(2);
getById('comp1y').textContent = comp1y.toFixed(2);
getById('comp2x').textContent = comp2x.toFixed(2);
getById('comp2y').textContent = comp2y.toFixed(2);
getById('comp3x').textContent = (w3 > 0 ? comp3x.toFixed(2) : 'N/A');
getById('comp3y').textContent = (w3 > 0 ? comp3y.toFixed(2) : 'N/A');
weightCompY = w1 + w2 + w3;
getById('weightCompY').textContent = weightCompY.toFixed(2);
getById('weightCompX').textContent = '0.00'; // Assuming weight acts purely vertically
// Update chart data
chartData.datasets[0].data = [
tension1 > 0 ? tension1 : 0,
tension2 > 0 ? tension2 : 0,
tension3 > 0 ? tension3 : 0,
0 // Tension doesn't apply to weight bar
];
chartData.datasets[1].data = [
0, // Weight doesn't apply to tension bar
0,
0,
weightCompY // Total weight
];
chartData.labels = ['Rope 1 Tension', 'Rope 2 Tension', 'Rope 3 Tension', 'Total Weight'];
updateChart();
} else {
// Handle case where no weights are entered
getById('primary-result').textContent = 'Tension: N/A';
getById('tension1').textContent = 'Tension in Rope 1: N/A';
getById('tension2').textContent = 'Tension in Rope 2: N/A';
getById('tension3').textContent = 'Tension in Rope 3: N/A';
getById('netForceX').textContent = 'Net Horizontal Force (ΣFx): N/A';
getById('netForceY').textContent = 'Net Vertical Force (ΣFy): N/A';
getById('comp1x').textContent = 'N/A'; getById('comp1y').textContent = 'N/A';
getById('comp2x').textContent = 'N/A'; getById('comp2y').textContent = 'N/A';
getById('comp3x').textContent = 'N/A'; getById('comp3y').textContent = 'N/A';
getById('weightCompY').textContent = 'N/A';
chartData.datasets[0].data = [0, 0, 0, 0];
chartData.datasets[1].data = [0, 0, 0, 0];
updateChart();
}
}
function resetCalculator() {
getById('weight1′).value = '50';
getById('angle1′).value = '30';
getById('weight2′).value = '75';
getById('angle2′).value = '60';
getById('weight3').value = '0';
getById('angle3′).value = '45';
calculateTension();
}
function copyResults() {
var resultText = "Tension Calculation Results:\n\n";
resultText += "Maximum Tension: " + getById('primary-result').textContent.replace('Max Tension: ', ") + "\n";
resultText += getById('tension1').textContent + "\n";
resultText += getById('tension2').textContent + "\n";
resultText += getById('tension3').textContent + "\n";
resultText += getById('netForceX').textContent + "\n";
resultText += getById('netForceY').textContent + "\n\n";
resultText += "Force Components Summary:\n";
resultText += "Rope 1: H=" + getById('comp1x').textContent + " N, V=" + getById('comp1y').textContent + " N\n";
resultText += "Rope 2: H=" + getById('comp2x').textContent + " N, V=" + getById('comp2y').textContent + " N\n";
resultText += "Rope 3: H=" + getById('comp3x').textContent + " N, V=" + getById('comp3y').textContent + " N\n";
resultText += "Total Weight: V=" + getById('weightCompY').textContent + " N\n";
try {
navigator.clipboard.writeText(resultText).then(function() {
alert('Results copied to clipboard!');
}, function(err) {
console.error('Could not copy text: ', err);
prompt("Copy these results manually:", resultText);
});
} catch (e) {
console.error('Clipboard API not available', e);
prompt("Copy these results manually:", resultText);
}
}
// Charting logic using Chart.js (simulated)
// Since Chart.js is an external library and we are restricted to native JS,
// we will implement a basic canvas drawing.
// HOWEVER, the prompt SPECIFICALLY asks for ONLY native canvas OR SVG, NO external libraries.
// This means we need to draw the chart manually on the canvas element.
// This is complex. A simplified SVG approach might be better.
// Let's stick to canvas and draw basic bars.
function updateChart() {
var canvas = getById('tensionChart');
var ctx = canvas.getContext('2d');
var width = canvas.width;
var height = canvas.height;
ctx.clearRect(0, 0, width, height); // Clear previous drawing
var data = chartData.datasets[0].data; // Tension data
var weights = chartData.datasets[1].data; // Weight data
var labels = chartData.labels;
var numBars = labels.length;
var barWidth = (width * 0.8) / numBars; // 80% of width for bars, distributed
var barMargin = barWidth * 0.2;
var startX = width * 0.1; // 10% margin from left
var maxTensionValue = Math.max(…data);
var maxWeightValue = Math.max(…weights);
var maxValue = Math.max(maxTensionValue, maxWeightValue);
if (maxValue === 0) maxValue = 1; // Prevent division by zero
// Draw labels
ctx.fillStyle = '#333′;
ctx.font = '12px Segoe UI, sans-serif';
ctx.textAlign = 'center';
// Find max label width for Y-axis margin
var maxLabelWidth = 0;
for (var i = 0; i maxLabelWidth) {
maxLabelWidth = metrics.width;
}
}
var startY = height * 0.1; // 10% margin from top
var chartHeight = height * 0.8; // 80% of height for bars
// Draw bars
for (var i = 0; i 0) {
ctx.fillStyle = chartData.datasets[0].backgroundColor;
ctx.fillRect(barX, startY + chartHeight – tensionHeight, barWidth, tensionHeight);
}
// Draw Weight Bar
if (weights[i] > 0) {
ctx.fillStyle = chartData.datasets[1].backgroundColor;
// Position weight bar just above tension bar if both exist, or at the base if only weight exists
var weightBarY = startY + chartHeight – weightHeight;
if(data[i] > 0 && weights[i] > 0) { // If both exist, stack or place side-by-side?
// The prompt asks for 2 data series. Let's show them side-by-side for clarity, or indicate overlap.
// Simplest is to show them clearly distinct. Let's use bars for tension and maybe a line for weight.
// Or, just show the vertical component of tension.
// Given the input, TENSION is the primary output. Weight is the input.
// Let's adjust: Chart shows Tension Components vs Weight.
// Option: Bar for T1, T2, T3 (tension magnitude) and a line/bar for Total Weight.
// Let's use bars for Tension magnitudes T1, T2, T3 and a separate bar for Total Weight.
// Redrawing chart data structure.
// data[0] = T1, data[1] = T2, data[2] = T3, data[3] = Total Weight
// This doesn't fit 2 series well unless one is component of the other.
// Let's try: Series 1: Tension magnitudes (T1, T2, T3). Series 2: Weight components (Vx1, Vx2, Vx3) – this is wrong.
// Okay, revised chart idea: Bar chart comparing the MAGNITUDE of TENSION in each rope vs the TOTAL weight.
// Series 1: T1, T2, T3 (Tension magnitudes)
// Series 2: W1, W2, W3 (Individual Weights) – This is more comparable.
// Or: Series 1: Total Tension Vertical Components. Series 2: Total Weight.
// Let's keep the original idea: Tension vs Weight.
// Series 1: T1, T2, T3 (magnitudes). Series 2: W1, W2, W3 (magnitudes).
// The current `chartData` has `data` for tension and `weights` for weight.
// Let's adjust the chart to show:
// Bar 1: Tension 1
// Bar 2: Tension 2
// Bar 3: Tension 3
// Bar 4: Total Weight (W1+W2+W3)
// Let's map chartData correctly.
// dataset[0].data = [T1, T2, T3, 0]
// dataset[1].data = [0, 0, 0, W_total]
// This doesn't show comparison well.
// BETTER CHART: Compare Vertical Component of Tension vs. Weight.
// dataset[0].data = [T1y, T2y, T3y] (Sum of vertical tension components)
// dataset[1].data = [W_total] (Total weight)
// Labels: ['Total Upward Tension', 'Total Downward Weight']
// This fits 2 series better.
// Let's modify chartData and labels based on this.
// Re-calculating required values for this chart format:
var totalTensionVertical = (comp1y > 0 ? comp1y : 0) + (comp2y > 0 ? comp2y : 0) + (comp3y > 0 ? comp3y : 0);
var totalWeightVertical = w1 + w2 + w3;
chartData.datasets[0].data = [totalTensionVertical, 0]; // Tension series
chartData.datasets[1].data = [0, totalWeightVertical]; // Weight series
chartData.labels = ['Upward Tension', 'Downward Weight'];
chartData.datasets[0].label = 'Total Upward Tension (Vertical Components)';
chartData.datasets[1].label = 'Total Downward Weight';
// Recalculate max value based on this new structure
maxValue = Math.max(totalTensionVertical, totalWeightVertical);
if (maxValue === 0) maxValue = 1;
chartHeight = height * 0.8; // 80% of height for bars
startY = height * 0.1; // 10% margin from top
// Re-draw bars for the new structure
ctx.clearRect(0, 0, width, height); // Clear previous drawing
numBars = 2; // Now only 2 bars
barWidth = (width * 0.7) / numBars; // 70% of width for bars
barMargin = barWidth * 0.3;
startX = width * 0.15; // Centered slightly better
// Bar 1: Total Upward Tension
var tensionBarHeight = (totalTensionVertical / maxValue) * chartHeight;
var barX1 = startX;
ctx.fillStyle = chartData.datasets[0].backgroundColor;
ctx.fillRect(barX1, startY + chartHeight – tensionBarHeight, barWidth, tensionBarHeight);
ctx.fillStyle = '#333';
ctx.fillText(labels[0], barX1 + barWidth / 2, startY + chartHeight + 20);
ctx.fillText(totalTensionVertical.toFixed(2) + ' N', barX1 + barWidth / 2, startY + chartHeight – tensionBarHeight – 5);
// Bar 2: Total Downward Weight
var weightBarHeight = (totalWeightVertical / maxValue) * chartHeight;
var barX2 = startX + barWidth + barMargin;
ctx.fillStyle = chartData.datasets[1].backgroundColor;
ctx.fillRect(barX2, startY + chartHeight – weightBarHeight, barWidth, weightBarHeight);
ctx.fillStyle = '#333';
ctx.fillText(labels[1], barX2 + barWidth / 2, startY + chartHeight + 20);
ctx.fillText(totalWeightVertical.toFixed(2) + ' N', barX2 + barWidth / 2, startY + chartHeight – weightBarHeight – 5);
// Add Y-axis labels (simplified)
var yLabelCount = 5;
for (var j = 0; j <= yLabelCount; j++) {
var yPos = startY + chartHeight – (j / yLabelCount) * chartHeight;
var yValue = (j / yLabelCount) * maxValue;
ctx.fillStyle = '#888';
ctx.fillText(yValue.toFixed(0), startX – 10, yPos);
ctx.moveTo(startX – 5, yPos);
ctx.lineTo(startX, yPos);
ctx.stroke();
}
ctx.beginPath(); // Reset path
ctx.strokeStyle = '#eee';
ctx.lineWidth = 1;
ctx.stroke();
// Update legend
getById('chart-legend').innerHTML =
' ' + chartData.datasets[0].label +
' ' + chartData.datasets[1].label;
}
}
}
// Initialize canvas size
function initCanvas() {
var canvas = getById('tensionChart');
// Set canvas dimensions dynamically based on container or fixed size
canvas.width = 900; // Example fixed width
canvas.height = 300; // Example fixed height
}
// Initial calculation and canvas setup on page load
window.onload = function() {
initCanvas();
calculateTension(); // Perform initial calculation with default values
};
// Add listeners for real-time updates (optional, but good practice)
// For simplicity, we are relying on the button click, but inline updates would be:
var inputs = document.querySelectorAll('.loan-calc-container input');
for (var i = 0; i < inputs.length; i++) {
inputs[i].addEventListener('input', calculateTension);
}