Work-Energy Theorem Calculator
Enter mass, initial and final velocity to compute the net work and kinetic-energy change W=½mv²−½mu². m=2 kg, u=3, v=5 → W=16 J; braking u=13.9, v=0 → W=−145 kJ.
Input Data
Results
At a glance:The work-energy theorem states that the net work done on an object by the resultant force equals its change in kinetic energy: W_net=ΔKE=½mv²−½mu². It follows from Newton's second law F=ma: W=∫F·dx=∫ma·dx=½m(v²−u²). Physical meaning: work done by a force is converted into kinetic energy. Positive work (v>u) increases KE; negative work (v<u) decreases it. Conservative forces: work equals minus the potential-energy change (W_c=−ΔPE), so total mechanical energy is conserved; non-conservative forces (friction) dissipate mechanical energy into heat. Applications: (1) braking distance (friction does negative work to bring KE to zero); (2) projectile motion (gravity's work equals the KE change); (3) elevator acceleration (cable tension does work); (4) collision analysis (impulsive force's work = KE loss); (5) mechanical energy conversion (spring, gravitational PE ↔ KE).
Formula
Work-energy theorem: W_net = ΔKE = ½mv² − ½mu²
Kinetic energy: KE = ½mv²
Work: W = F·d·cosθ
Conservative: W_c = −ΔPE
Mechanical energy: E = KE + PE
$$W_{net} = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$$How to Use
- Enter mass m (kg).
- Enter initial speed u (m/s) and final speed v (m/s).
- The tool computes work W, ΔKE and initial/final KE.
Case Studies
Braking distance and projectile motion
Car braking: m=1500 kg, u=13.9 m/s (50 km/h), v=0 → W=−145000 J.
Friction μ=0.7: brake force=0.7×1500×9.8=10290 N, distance=145000/10290≈14 m; at 100 km/h distance ≈56 m (4×).
Projectile up: m=0.5 kg, u=20 m/s vertical, v=0 at apex → W=−100 J (gravity does negative work); height h=100/(0.5×9.8)=20.4 m.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.