1. What is the Work Equation?

The work equation \( W = \int F \cdot dr \) describes the work done by a force (F) along a displacement (dr). In simpler cases with constant force and straight-line motion, this simplifies to \( W = F \cdot d \cdot \cosθ \), where θ is the angle between the force and displacement vectors.

2. How Does the Calculator Work?

The calculator uses the simplified work equation:

Where:

• \( W \) — Work done (Joules)
• \( F \) — Force applied (Newtons)
• \( d \) — Displacement (meters)
• \( θ \) — Angle between force and displacement (degrees)

Explanation: The equation calculates the mechanical work done when a constant force acts on an object causing displacement.

3. Importance of Work Calculation

Details: Calculating work is fundamental in physics and engineering for understanding energy transfer, mechanical systems, and thermodynamic processes.

4. Using the Calculator

Tips: Enter force in Newtons, displacement in meters, and angle in degrees (0° for parallel, 90° for perpendicular). All values must be valid (force > 0, displacement > 0).

5. Frequently Asked Questions (FAQ)

Q1: What are the units of work?
A: The SI unit of work is the Joule (J), equivalent to 1 Newton-meter (N·m).

Q2: When is work considered negative?
A: Work is negative when the force component is opposite to the displacement direction (90° < θ ≤ 180°).

Q3: What's the difference between work and energy?
A: Work is the transfer of energy, measured in the same units. Work done on a system increases its energy.

Q4: What if the force isn't constant?
A: For variable forces, you must use the integral form \( W = \int F \cdot dr \) over the path.

Q5: How does angle affect work?
A: Maximum work occurs when force and displacement are parallel (θ = 0°), zero when perpendicular (θ = 90°).