1. What is Work Done By Force Equation?

Definition: This equation calculates the work done when a force moves an object over a distance at an angle.

Purpose: It helps physicists, engineers, and students understand energy transfer in mechanical systems.

2. How Does the Equation Work?

The equation uses the formula:

Where:

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

Explanation: Work is only done by the component of force in the direction of movement. The cosine term accounts for the angular relationship.

3. Importance of Work Calculation

Details: Calculating work helps determine energy requirements, efficiency of machines, and understanding physical systems.

4. Using the Calculator

Tips: Enter the force magnitude, displacement distance, and angle between them. Angle of 0° means force and displacement are parallel (maximum work).

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 90°?
A: When force is perpendicular to displacement (90°), cos(90°) = 0, so no work is done.

Q2: What are typical units for each variable?
A: Standard SI units are Newtons (N) for force, meters (m) for distance, and Joules (J) for work.

Q3: Can work be negative?
A: Yes, when 90° < θ ≤ 180°, cos(θ) is negative, indicating force opposes motion.

Q4: How is this different from power?
A: Work measures energy transfer, while power measures the rate of work done (work/time).

Q5: What's a practical example?
A: Pushing a box 10m with 50N force at 30° angle: W = 50 × 10 × cos(30°) ≈ 433 J.