Work-Energy Theorem Calculator
Calculate work, kinetic energy, and force using work-energy relationships.
Work-Energy Formulas
Work: W = F·d·cos(θ) [joules]
Kinetic Energy: KE = ½mv² [joules]
Work-Energy Theorem: W = ΔKE = ½m(v²_f - v²_i)
Power: P = W/t [watts]
Work-Energy Applications
| Scenario | Work Type | KE Effect |
|---|---|---|
| Pushing car from rest | Positive | Increases |
| Friction slowing ball | Negative | Decreases |
| Lifting box vertically | Against gravity | No change (gravity perpendicular) |
| Braking to stop | Negative (friction) | Becomes zero |
Frequently Asked Questions
What is the work-energy theorem?
The work-energy theorem states: Work done on object = Change in kinetic energy. W = ΔKE = ½m(v²_f - v²_i). Relates force, displacement, and velocity changes.
How do I calculate work?
Work = Force × Distance × cos(θ), where θ is angle between force and displacement. If force parallel to motion: W = F × d. Work measured in joules (J).
What is kinetic energy?
Energy of motion. KE = ½mv², where m = mass (kg), v = velocity (m/s). Increases with speed squared—doubling speed quadruples kinetic energy.
How does work relate to kinetic energy change?
Work done = final KE - initial KE. Positive work increases speed. Negative work (friction) decreases speed. Zero net work = constant velocity.
What is the relationship between force and work?
Work requires both force AND displacement. A force with no displacement does no work. Work = F × d × cos(θ) for constant force.
What about friction in work calculations?
Friction does negative work (opposes motion). Work against friction = friction force × distance. Reduces kinetic energy, dissipates as heat.
Can work be negative?
Yes. Negative work means force opposes motion, reducing kinetic energy. Friction, air resistance do negative work. Pushing uphill against gravity does negative work.
What is the difference between work and power?
Work: energy transferred by force (joules). Power: rate of work done (watts = joules/second). Power = Work / Time.
How does angle affect work?
Work = F × d × cos(θ). At θ=0° (same direction): full work. At θ=90° (perpendicular): no work. At θ=180° (opposite): negative work.
What is the work-energy theorem used for?
Finding final velocity from force and distance. Finding force needed for desired speed change. Understanding energy transformations in motion.
How does mass affect kinetic energy?
KE is proportional to mass (doubles mass = doubles KE). But velocity has quadratic effect (doubles velocity = 4× KE). Velocity matters more.
What units are used for work and energy?
SI unit: joule (J) = newton·meter (N·m) = kg·m²/s². Also: erg, calorie, foot-pound. Always use consistent units.