1. What is the Work Formula?

Definition: The work formula calculates the energy transferred when a force moves an object over a distance at an angle.

Purpose: It helps physicists and engineers determine the mechanical work done in various systems.

2. How Does the Formula Work?

The formula is:

Where:

• \( W \) — Work done (Joules, J)
• \( F \) — Applied force (Newtons, N)
• \( d \) — Displacement distance (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 the angle between them.

3. Importance of Work Calculation

Details: Understanding work helps in designing efficient mechanical systems, calculating energy requirements, and analyzing 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 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: Force in Newtons (N), distance in meters (m), angle in degrees, and work in Joules (J).

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

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

Q5: What's the difference between work and power?
A: Work is energy transfer, while power is the rate of work done (Joules/second = Watts).