Sum of Forces Calculator Online

The Sum of Forces Calculator calculates the resultant force acting on an object when multiple forces are applied. By breaking down each force into its horizontal and vertical components and then summing these components, the calculator provides a clear picture of the overall force. This is particularly useful in physics and engineering where accurate force analysis is crucial.

Formula of Sum of Forces Calculator

To calculate the sum of forces, follow these steps:

1. Break each force into its horizontal and vertical components using trigonometry: Fₓ = F cos θ , Fᵧ = F sin θ
2. Add all the horizontal components (ΣFₓ) and vertical components (ΣFᵧ) separately:ΣFₓ = Σ (F cos θ) , ΣFᵧ = Σ (F sin θ)
3. The resultant force components are ΣFₓ and ΣFᵧ.
4. Use the Pythagorean theorem to find the magnitude of the resultant force: F = √(ΣFₓ² + ΣFᵧ²)

Common Terms and Conversions

Here is a table of common terms and conversions that might be useful:

Example of Sum of Forces Calculator

Let's consider an example to illustrate the use of the Sum of Forces Calculator. Suppose there are three forces acting on an object:

• Force 1: 50 N at 30°
• Force 2: 70 N at 60°
• Force 3: 40 N at 120°

1. Calculate the horizontal and vertical components for each force:
   • Force 1:F₁ₓ = 50 cos 30° = 43.3 N , F₁ᵧ = 50 sin 30° = 25 N
   • Force 2:F₂ₓ = 70 cos 60° = 35 N , F₂ᵧ = 70 sin 60° = 60.6 N
   • Force 3:F₃ₓ = 40 cos 120° = -20 N , F₃ᵧ = 40 sin 120° = 34.6 N
2. Sum the horizontal and vertical components:
   • ΣFₓ = 43.3 + 35 - 20 = 58.3 N
   • ΣFᵧ = 25 + 60.6 + 34.6 = 120.2 N
3. Calculate the magnitude of the resultant force:
   • F = √(58.3² + 120.2²) = √(3399.69 + 14448.04) = √17847.73 = 133.6 N

Most Common FAQs