1. What is the Work Done Formula?

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

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

2. How Does the Formula Work?

The formula is:

Where:

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

Explanation: Only the component of force in the direction of motion does work. The cosine factor accounts for the angle between force and displacement.

3. Importance of Work Calculation

Details: Work calculations are fundamental in mechanics, energy analysis, and designing mechanical systems.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 90°?
A: No work is done (cos(90°) = 0) because force is perpendicular to motion.

Q2: What are typical units for each variable?
A: Force in Newtons (N), distance in meters (m), angle in degrees, work in Joules (J).

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

Q4: How does this relate to energy?
A: Work equals energy transferred. 1 Joule = 1 Newton-meter.

Q5: What if the force varies?
A: For variable forces, you need to integrate the force over the distance.