1. What is Work Done in Terms of Force?

Definition: Work is done when a force causes displacement in the direction of the force. It's calculated as the product of force, displacement, and the cosine of the angle between them.

Purpose: This calculation helps in physics and engineering to determine energy transfer when forces act on objects.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: Only the component of force in the direction of displacement does work. The cosine term accounts for angular differences.

3. Importance of Work Calculation

Details: Understanding work helps design efficient mechanical systems, calculate energy requirements, and analyze physical processes.

4. Using the Calculator

Tips: Enter the force magnitude, displacement distance, and angle between them. For force directly along displacement, use 0° angle.

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 happens at 90 degrees?
A: At exactly 90°, cos(90°)=0, so no work is done as the force is perpendicular to displacement.

Q3: How is this different from power?
A: Work measures total energy transfer, while power measures the rate of work done (work/time).

Q4: What are typical Newton values?
A: 1 N ≈ weight of 100g object on Earth. Human forces range from ~10N (light push) to ~1000N (strong athlete).

Q5: Why use radians for cosine calculation?
A: The calculator automatically converts degrees to radians for the cosine function, which is what the PHP cos() function expects.