⚡ Classical Mechanics & Work-Energy Conservation
Work-Energy Theorem Calculator ($W_{\text{net}} = \Delta KE$)
Compute mechanical work done ($W = F \cdot d \cos\theta$), change in kinetic energy ($\Delta KE$), final velocity ($v_f$), and average mechanical power output ($P = W/\Delta t$).
🚗 Car 0–100 km/h (578 kJ)
🛑 Emergency Braking (-578 kJ)
⚾ Baseball Pitch (146 J)
🏃 Sprinter Acceleration (4.0 kJ)
Kinetic Parameters
kg
m/s
m/s
meters (m)
seconds (s)
Net Mechanical Work Done (W)
+578.8 kJ
Initial KE ($KE_i$)
0.00 kJ
Final KE ($KE_f$)
578.8 kJ
Average Net Force
8,268.4 N
💡 Theorem Derivation:
$$W = \Delta KE = \frac{1}{2}(1500)(27.78)^2 - 0 = 578.8\text{ kJ}, \quad F = \frac{W}{d} = 8,268.4\text{ N}$$
The Work-Energy Theorem
The fundamental theorem relates force, displacement, and kinetic energy:
$$W_{\text{net}} = \Delta KE = KE_f - KE_i = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2 = F_{\text{net}} \cdot d \cos(\theta)$$
- Positive Work ($W > 0$): Force accelerates the body ($v_f > v_i$), increasing kinetic energy.
- Negative Work ($W < 0$): Force opposes motion (e.g. friction/brakes), dissipating kinetic energy into thermal heat.
- Average Power ($P$): $$P = \frac{W}{\Delta t} = F_{\text{net}} \cdot v_{\text{avg}}$$ (1 Horsepower $\approx 745.7\text{ Watts}$).