Work-Energy Theorem Calculator
The Work-Energy Theorem states that the net work done on an object equals the change in its kinetic energy: W_net = ΔKE = ½ m(v_f² - v_i²)
kg
Mass of the object in kilograms
m/s
m/s
s
J
J
J
W
N
degrees
Angle between force and displacement vectors
m
N
Energy Visualization
Initial Kinetic Energy
Work Done
Final Kinetic Energy
Start
End
Object motion visualization based on velocity change
Calculation Results
Net Work Done (W_net)
75.00
Joules (J)
Change in Kinetic Energy (ΔKE)
75.00
Joules (J)
Initial Kinetic Energy (KEᵢ)
25.00
Joules (J)
Final Kinetic Energy (KE_f)
100.00
Joules (J)
Average Power (P_avg)
37.50
Watts (W)
Acceleration (a)
2.50
m/s²
Applied Formula
W_net = ΔKE = ½ × m × (v_f² - v_i²)
W = F × d × cos(θ)
P = W / t
W = F × d × cos(θ)
P = W / t
Calculation History
Sample Calculation
Just now
m=2kg, vᵢ=5m/s, v_f=10m/s
W_net = 75.00 J
Additional Tools
Understanding the Work-Energy Theorem
The Work-Energy Theorem is a fundamental principle in physics that relates the work done on an object to its change in kinetic energy. This powerful tool allows physicists and engineers to solve complex motion problems without detailed knowledge of the path taken.
How to Use This Calculator
- Basic Input Tab: Enter mass, initial and final velocities. The calculator will compute work done and energy changes in real-time.
- Advanced Tab: Input energy values directly or calculate them from mass and velocity.
- Force & Distance Tab: Calculate work using force, distance, and angle between them.
- Click "Calculate All Values" to compute all results, or watch as they update automatically as you type.
- Use the visualization to see energy distribution and object motion.
- Save important calculations to history for future reference.
Key Formulas
- Work-Energy Theorem: W_net = ΔKE = KE_f - KE_i
- Kinetic Energy: KE = ½ × m × v²
- Work by constant force: W = F × d × cos(θ)
- Power: P = W / t (average power)
Real-World Applications
The Work-Energy Theorem has practical applications in various fields:
- Engineering: Designing braking systems for vehicles
- Sports Science: Analyzing athlete performance and energy transfer
- Renewable Energy: Calculating work done by wind on turbine blades
- Aerospace: Determining thrust requirements for spacecraft
- Automotive: Estimating fuel efficiency and acceleration capabilities
Tip: For accurate results, ensure you use consistent units (kilograms for mass, meters per second for velocity, newtons for force, meters for distance).