Work Done Calculator (Physics)
(0° for force in direction of motion, 90° for perpendicular force)
Work Done: 0 Joules
function calculateWork() {
var force = parseFloat(document.getElementById('force').value);
var distance = parseFloat(document.getElementById('distance').value);
var angleDegrees = parseFloat(document.getElementById('angle').value);
if (isNaN(force) || isNaN(distance) || isNaN(angleDegrees)) {
document.getElementById('workResult').innerHTML = 'Please enter valid numbers for all fields.';
document.getElementById('workResult').style.backgroundColor = '#ffe0e0';
document.getElementById('workResult').style.color = '#cc0000';
return;
}
// Convert angle from degrees to radians
var angleRadians = angleDegrees * (Math.PI / 180);
// Calculate work done: W = F * d * cos(theta)
var workDone = force * distance * Math.cos(angleRadians);
document.getElementById('workResult').innerHTML = 'Work Done: ' + workDone.toFixed(2) + ' Joules';
document.getElementById('workResult').style.backgroundColor = '#eaf4ff';
document.getElementById('workResult').style.color = '#0056b3';
}
// Initial calculation on load
window.onload = calculateWork;
Understanding Work in Physics
In physics, "work" has a very specific meaning that differs from its everyday usage. Work is done when a force causes a displacement of an object. More precisely, it is the energy transferred to or from an object by means of a force acting on the object over a displacement.
The Work Formula
The formula for calculating work done is:
W = F × d × cos(θ)
Where:
- W is the work done (measured in Joules, J).
- F is the magnitude of the force applied (measured in Newtons, N).
- d is the magnitude of the displacement (the distance the object moves, measured in meters, m).
- θ (theta) is the angle between the direction of the force and the direction of the displacement (measured in degrees).
Key Scenarios for the Angle (θ)
- θ = 0°: When the force is applied in the exact same direction as the displacement (e.g., pushing a box horizontally across a floor). In this case, cos(0°) = 1, so W = F × d. This results in maximum positive work.
- θ = 90°: When the force is applied perpendicular to the direction of displacement (e.g., carrying a briefcase horizontally while walking). In this case, cos(90°) = 0, so W = 0. No work is done by that specific force.
- θ = 180°: When the force is applied in the exact opposite direction to the displacement (e.g., friction acting on a moving object). In this case, cos(180°) = -1, so W = -F × d. This results in negative work, meaning energy is removed from the object.
Units of Work
The standard unit for work in the International System of Units (SI) is the Joule (J). One Joule is defined as the work done when a force of one Newton (N) displaces an object by one meter (m) in the direction of the force. Therefore, 1 J = 1 N·m.
Examples of Work Done
Let's look at some practical examples:
- Pushing a Shopping Cart: If you push a shopping cart with a force of 50 N for a distance of 20 meters, and you push directly in the direction of motion (θ = 0°):
W = 50 N × 20 m × cos(0°) = 50 × 20 × 1 = 1000 Joules. - Lifting a Weight: If you lift a 10 kg weight (which exerts a force of approximately 98 N downwards due to gravity) upwards by 1.5 meters. The force you apply is upwards, and the displacement is upwards (θ = 0°):
W = 98 N × 1.5 m × cos(0°) = 147 Joules. - Pulling a Sled at an Angle: Imagine pulling a sled with a rope. You apply a force of 80 N, but the rope makes an angle of 30° with the horizontal ground. If you pull the sled for 15 meters:
W = 80 N × 15 m × cos(30°) ≈ 80 × 15 × 0.866 ≈ 1039.2 Joules. - Carrying a Tray: If a waiter carries a tray horizontally across a room for 10 meters, applying an upward force of 20 N to support the tray. The upward force is perpendicular to the horizontal displacement (θ = 90°):
W = 20 N × 10 m × cos(90°) = 20 × 10 × 0 = 0 Joules. (Note: Work is done by the waiter's legs to move their body, but not by the force supporting the tray in the direction of horizontal motion).
This calculator helps you quickly determine the work done by a specific force given its magnitude, the distance over which it acts, and the angle between the force and displacement vectors.