Work Energy Theorem Calculator
work-energy theorem calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Work Energy Theorem Calculator
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Formula: W = ΔKE = ½mv₂² - ½mv₁²
Worked example — 1000 J
Formula
W = ΔKE = ½mv₂² - ½mv₁²
The net work done on an object equals its change in kinetic energy.
Worked Examples
Example 1: Accelerating object
Problem:10 kg, v₁=5 m/s, v₂=15 m/s
Solution:W=½(10)(225-25)=1000 J
Result:1000 J
Frequently Asked Questions
What is the work-energy theorem?
The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv₂² − ½mv₁². This means any net force that accelerates an object transfers energy to it, while a decelerating force removes energy.
How do you calculate net work using the work-energy theorem?
Compute KE₁ = ½mv₁² and KE₂ = ½mv₂², then W = KE₂ − KE₁. Example: a 10 kg object accelerates from 5 m/s to 15 m/s. KE₁ = 0.5×10×25 = 125 J, KE₂ = 0.5×10×225 = 1125 J, so W = 1125 − 125 = 1000 J.
What units are used in work-energy calculations?
Mass m is in kilograms (kg), velocities v₁ and v₂ in metres per second (m/s). Kinetic energy KE = ½mv² is in Joules (J). Work W is also in Joules (J). One Joule equals one Newton-metre (1 J = 1 N·m = 1 kg·m²/s²).
What does negative work mean in the work-energy theorem?
Negative work (W < 0) means the net force opposes the motion, reducing kinetic energy. For example, friction does negative work: a 5 kg box sliding on a rough surface from 10 m/s to rest loses KE = ½×5×100 = 250 J, so friction did −250 J of work on the box.
How does energy conservation work in physics?
The law of conservation of energy states that energy cannot be created or destroyed, only transformed. In a closed system, total energy remains constant. For example, a falling object converts potential energy (mgh) to kinetic energy (0.5mv^2). At any point, KE + PE = total mechanical energy.
Background & Theory
Why Skip Straight to Kinetic Energy?
The work-energy theorem is a shortcut: instead of tracking the exact force profile an object experiences over a distance (which can be messy for varying forces like air resistance or a crumpling car body), you only need the mass and the speed before and after. The net work done by ALL forces combined equals the change in kinetic energy — full stop, regardless of how complicated the underlying force history was.
| Scenario | Sign of net work | What it means |
|---|---|---|
| Car accelerating from a stoplight | Positive | Engine adds kinetic energy |
| Car braking to a stop | Negative | Brakes/friction remove kinetic energy, converting it to heat |
| Crumple zone absorbing a crash | Large negative | Deformation work dissipates kinetic energy over a longer stopping distance, lowering peak force |
| Satellite in stable circular orbit | Zero | Gravity acts perpendicular to velocity, so it does no work and speed stays constant |
This is exactly why crumple zones work: spreading a crash's negative work over a longer collapse distance reduces the average braking force for the same total change in kinetic energy (W = F x d, so a bigger d for the same W means a smaller F).
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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