Work Done By Force Field Calculator

Work Done Formula:

\[ W = \int F \cdot dr \]

Work Done (W):

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1. What is Work Done By a Force Field?

Definition: Work is the energy transferred when a force acts on an object and displaces it.

Purpose: This calculator computes the work done by a constant force field on an object moving along a straight line.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ W = F \cdot d \cdot \cos\theta \]

Where:

\( W \) — Work done (Joules, J)
\( F \) — Force magnitude (Newtons, N)
\( d \) — Displacement (meters, m)
\( \theta \) — Angle between force and displacement (degrees)

Explanation: Work is calculated as the dot product of force and displacement vectors. When force and displacement are parallel (θ=0°), work is maximized.

3. Importance of Work Calculation

Details: Calculating work helps understand energy transfer in mechanical systems, efficiency of machines, and potential energy changes.

4. Using the Calculator

Tips: Enter the force magnitude in Newtons, displacement in meters, and angle between them in degrees (0° for parallel, 90° for perpendicular).

5. Frequently Asked Questions (FAQ)

Q1: What does negative work mean?
A: Negative work occurs when the force component opposes displacement (90° < θ ≤ 180°), meaning the force is removing energy from the system.

Q2: What's the unit of work?
A: The SI unit is Joule (J), equivalent to 1 N·m. Other units include foot-pound (ft·lb) and calorie (cal).

Q3: When is work zero?
A: Work is zero when either force is zero, displacement is zero, or force is perpendicular to displacement (θ=90°).

Q4: How does this differ from power?
A: Work measures total energy transfer, while power measures the rate of work done (P = W/t).

Q5: Can this calculator handle variable forces?
A: No, this calculator assumes constant force. For variable forces, integration of the force function is needed.