Working Calculator

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Work Done Calculator

Calculate the work done on an object by a constant force.

function calculateWorkDone() { var forceMagnitudeInput = document.getElementById("forceMagnitude").value; var displacementDistanceInput = document.getElementById("displacementDistance").value; var angleDegreesInput = document.getElementById("angleDegrees").value; var resultDiv = document.getElementById("workDoneResult"); // Validate inputs if (forceMagnitudeInput === "" || isNaN(forceMagnitudeInput) || parseFloat(forceMagnitudeInput) < 0) { resultDiv.innerHTML = "Please enter a valid non-negative force magnitude."; return; } if (displacementDistanceInput === "" || isNaN(displacementDistanceInput) || parseFloat(displacementDistanceInput) < 0) { resultDiv.innerHTML = "Please enter a valid non-negative displacement distance."; return; } if (angleDegreesInput === "" || isNaN(angleDegreesInput)) { resultDiv.innerHTML = "Please enter a valid angle in degrees."; return; } var force = parseFloat(forceMagnitudeInput); var distance = parseFloat(displacementDistanceInput); var angleDegrees = parseFloat(angleDegreesInput); // 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); resultDiv.innerHTML = "

Calculated Work Done:

" + "" + workDone.toFixed(2) + " Joules (J)"; } .working-calculator-container { background-color: #f9f9f9; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 600px; margin: 20px auto; font-family: Arial, sans-serif; } .working-calculator-container h2 { color: #333; text-align: center; margin-bottom: 20px; } .working-calculator-container p { color: #555; text-align: center; margin-bottom: 15px; } .calculator-input-group { margin-bottom: 15px; } .calculator-input-group label { display: block; margin-bottom: 5px; color: #333; font-weight: bold; } .calculator-input-group input[type="number"] { width: calc(100% – 22px); padding: 10px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; } .working-calculator-container button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; width: 100%; display: block; margin-top: 20px; } .working-calculator-container button:hover { background-color: #0056b3; } .calculator-result { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 4px; text-align: center; color: #155724; } .calculator-result h3 { color: #155724; margin-top: 0; margin-bottom: 10px; } .calculator-result p { font-size: 1.2em; font-weight: bold; margin: 0; }

Understanding Work in Physics

In physics, "work" has a very specific meaning that differs from its everyday usage. It refers to the energy transferred to or from an object by means of a force acting on the object over a displacement. For work to be done, two conditions must be met:

  1. A force must be applied to an object.
  2. The object must undergo a displacement (change in position) in the direction of the force, or at least have a component of its displacement in the direction of the force.

The Formula for Work Done

When a constant force acts on an object, the work done (W) can be calculated using the following formula:

W = F × d × cos(θ)

  • 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 (distance moved), measured in meters (m).
  • θ (theta) is the angle between the direction of the force and the direction of the displacement.

Understanding the Components:

Force (F)

Force is a push or a pull that can cause an object to accelerate. In the context of work, it's the specific force that is causing or attempting to cause the displacement.

Displacement (d)

Displacement is the change in an object's position. It's a vector quantity, meaning it has both magnitude (distance) and direction. For work, we consider the straight-line distance between the initial and final positions.

Angle (θ)

The angle between the force and displacement is crucial. It determines how much of the force is actually contributing to the movement.

  • If θ = 0° (cos(0°) = 1): The force is applied exactly in the direction of displacement. Maximum positive work is done. For example, pushing a box horizontally across a floor.
  • If θ = 90° (cos(90°) = 0): The force is perpendicular to the displacement. No work is done by this force. For example, carrying a briefcase horizontally across a room – the upward force you exert on the briefcase does no work because the displacement is horizontal.
  • If θ = 180° (cos(180°) = -1): The force is applied in the opposite direction of displacement. Negative work is done. This often occurs with friction, which opposes motion.

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 moves an object one meter in the direction of the force (1 J = 1 N·m).

Examples of Work Done:

  • Pushing a shopping cart: If you push a shopping cart with a force of 50 N for a distance of 10 meters in the same direction, the work done is W = 50 N × 10 m × cos(0°) = 500 J.
  • Lifting a weight: If you lift a 2 kg weight (requiring a force of approximately 19.6 N due to gravity) vertically by 1.5 meters, the work done is W = 19.6 N × 1.5 m × cos(0°) = 29.4 J.
  • Pulling a sled at an angle: If you pull a sled with a force of 80 N at an angle of 30° above the horizontal, and the sled moves 20 meters horizontally, the work done is W = 80 N × 20 m × cos(30°) ≈ 1385.64 J.

This calculator helps you quickly determine the work done by a constant force, taking into account the magnitude of the force, the distance of displacement, and the angle between them.

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