Work Calculator - Force and Displacement

This physics calculator helps you calculate work done by a force over a distance. Work is a measure of energy transfer when a force acts on an object and causes displacement.

Work Definition

• Work: Energy transferred by a force acting through a distance
• Formula: W = Fd cos(θ) (Work = Force × Distance × cos(angle))
• Scalar: Work is a scalar quantity
• Units: Joules (J) - 1 J = 1 N·m

Work Units

• Joule (J): SI unit of work and energy
• Kilojoule (kJ): 1 kJ = 1000 J
• Calorie (cal): 1 cal = 4.184 J
• Kilocalorie (kcal): 1 kcal = 1000 cal
• BTU: British thermal unit, 1 BTU = 1055.06 J

Work Conditions

• Positive Work: Force and displacement in same direction (0° ≤ θ < 90°)
• Zero Work: Force perpendicular to displacement (θ = 90°)
• Negative Work: Force and displacement in opposite directions (90° < θ ≤ 180°)
• Maximum Work: Force and displacement parallel (θ = 0°)

Applications

• Mechanics: Lifting objects and moving loads
• Engineering: Machine design and efficiency
• Sports: Athletic performance analysis
• Transportation: Vehicle propulsion and braking
• Physics: Energy conservation problems
• Biology: Muscle work and metabolism

Work-Energy Theorem

• Theorem: Net work done = Change in kinetic energy
• Formula: W_net = ΔKE = KE_f - KE_i
• Conservation: Work done = Energy transferred
• Efficiency: Useful work ÷ Total work input

Important Notes

• Work is done only when there is displacement
• Work depends on the angle between force and displacement
• Work can be positive, negative, or zero
• Work is related to energy: W = ΔE
• Work is path-dependent in some cases

Work Examples

• Lifting: Work against gravity (positive)
• Lowering: Work with gravity (negative)
• Pushing: Work in direction of motion (positive)
• Braking: Work against motion (negative)
• Carrying: No work if no vertical displacement

Work Relationships

• Power: P = W/t (Power = Work ÷ Time)
• Energy: W = ΔE (Work = Change in Energy)
• Force: W = Fd (for parallel force and displacement)
• Kinetic Energy: W = ½mv²_f - ½mv²_i

Work in Different Systems

• Mechanical Work: Force × Displacement
• Electrical Work: Voltage × Charge
• Thermal Work: Pressure × Volume change
• Chemical Work: Chemical potential energy change