Net Force Calculator
Calculate resultant force from multiple forces using vector addition
Net Force Calculator
Force 1
Magnitude of force 1 in Newtons
Angle with respect to positive x-axis (0° = horizontal right)
Force 2
Magnitude of force 2 in Newtons
Angle with respect to positive x-axis (0° = horizontal right)
Net Force Results
Formula used: F = √(Fx² + Fy²), θ = tan⁻¹(Fy/Fx)
Vector sum: F⃗ = ∑F⃗ᵢ (vector addition of all forces)
Force status: Equilibrium (balanced forces)
Real-world Context
Example Calculation
Two Forces Acting on an Object
Given: Force 1 = 10 N at 0°, Force 2 = 15 N at 90°
Find: Net force magnitude and direction
Solution
Step 1: Find components
F₁ₓ = 10 × cos(0°) = 10 N, F₁ᵧ = 10 × sin(0°) = 0 N
F₂ₓ = 15 × cos(90°) = 0 N, F₂ᵧ = 15 × sin(90°) = 15 N
Step 2: Sum components
Fₓ = 10 + 0 = 10 N, Fᵧ = 0 + 15 = 15 N
Step 3: Calculate magnitude and direction
F = √(10² + 15²) = √325 = 18.03 N
θ = tan⁻¹(15/10) = 56.3°
Result: Net force = 18.03 N at 56.3°
Vector Addition Rules
Break into Components
Fₓ = F cos(θ), Fᵧ = F sin(θ)
Resolve each force into x and y components
Sum Components
Fₓ_total = ΣFₓᵢ, Fᵧ_total = ΣFᵧᵢ
Add all x-components, add all y-components
Calculate Resultant
F = √(Fₓ² + Fᵧ²)
Use Pythagorean theorem for magnitude
Find Direction
θ = tan⁻¹(Fᵧ/Fₓ)
Use inverse tangent for angle
Common Angles
Note: Angles are measured counterclockwise from the positive x-axis (standard mathematical convention).
Understanding Net Force
What is Net Force?
Net force (also called resultant force) is the vector sum of all individual forces acting on an object. It represents the overall effect of all forces and determines the object's acceleration according to Newton's second law (F = ma). When multiple forces act on an object, they can either reinforce each other or cancel each other out.
Vector Nature of Forces
- •Forces are vectors with both magnitude and direction
- •Vector addition follows the parallelogram law
- •Components can be added algebraically
- •Direction matters in force calculations
Net Force Calculations
Step 1: Component Resolution
Fₓ = F cos(θ)
Fᵧ = F sin(θ)
Step 2: Component Summation
Fₓ_net = ΣFₓᵢ
Fᵧ_net = ΣFᵧᵢ
Step 3: Resultant Calculation
F_net = √(Fₓ² + Fᵧ²)
θ = tan⁻¹(Fᵧ/Fₓ)
Special Cases
Equilibrium (Net Force = 0):
- • Object at rest remains at rest
- • Object in motion continues at constant velocity
- • No acceleration occurs
- • All forces balance out perfectly
Unbalanced Forces (Net Force ≠ 0):
- • Object experiences acceleration
- • Acceleration direction = net force direction
- • Magnitude: a = F_net / m
- • Motion changes according to Newton's laws