1. What is the Work Done Equation?

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

Purpose: It helps physicists and engineers determine the energy transferred by a force acting on an object.

2. How Does the Equation Work?

The equation is:

Where:

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

Explanation: Work is only done by the component of force in the direction of movement, which is why we use the cosine of the angle.

3. Importance of Work Calculation

Details: Understanding work done is fundamental in physics and engineering for analyzing energy transfer in mechanical systems.

4. Using the Calculator

Tips: Enter the force in Newtons, distance in meters, and angle in degrees (0° for parallel forces, 90° for perpendicular).

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0°?
A: When force and displacement are parallel (θ=0°), cos(0°)=1, so W = F × d (maximum work).

Q2: What happens when θ = 90°?
A: When force is perpendicular to displacement (θ=90°), cos(90°)=0, so no work is done.

Q3: What are typical force values?
A: 1 N ≈ the force of gravity on a small apple (100g). Human pushing forces are typically 50-500 N.

Q4: How is this related to energy?
A: Work done equals energy transferred. 1 Joule = 1 Newton-meter of work.

Q5: What about negative work?
A: When 90° < θ ≤ 180°, cos(θ) is negative, indicating force opposes motion (e.g., friction).