1. What is the Work Formula?

The work formula (W = F × d × cos(θ)) calculates the amount of energy transferred by a force acting through a distance. Work is measured in joules (J) in the International System of Units.

2. How Does the Calculator Work?

The calculator uses the work formula:

Where:

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

Explanation: The formula accounts for both the magnitude of force and displacement, as well as the direction of the force relative to the displacement.

3. Importance of Work Calculation

Details: Calculating work is fundamental in physics and engineering for understanding energy transfer, mechanical systems, and efficiency of machines.

4. Using the Calculator

Tips: Enter force in newtons (N), distance in meters (m), and angle in degrees. All values must be valid (force > 0, distance > 0, angle between 0-180).

5. Frequently Asked Questions (FAQ)

Q1: What happens when θ = 0°?
A: When force and displacement are in the same direction (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 units for work?
A: The SI unit is joules (J). Other units include foot-pounds (ft·lb) and ergs (erg).

Q4: Can work be negative?
A: Yes, when 90° < θ ≤ 180°, cos(θ) is negative, indicating the force opposes the motion.

Q5: How does this relate to energy?
A: Work represents energy transfer. The work-energy theorem states that the work done equals the change in kinetic energy.