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Resultant Force Calculator

Provide the forces and angles of at least two forces to this resultant calculator and calculate the resultant force instantly

# 1

Angle:

Force:

deg

# 2

Angle:

Force:

deg

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The Resultant Force Calculator helps determine the net force acting on an object when multiple forces are applied at different angles. It calculates both the magnitude and direction of the resultant force efficiently.

Understanding Resultant Force

The resultant force is the vector sum of all forces acting on a body. As force is a vector quantity, the resultant has both magnitude and direction, which causes acceleration in the body according to Newton’s second law.

Resultant Force Formula

For two or more forces, the resultant force is calculated as:

\(\vec{R}_f = \vec{F}_1 + \vec{F}_2 + ... + \vec{F}_n\)

To find components along x and y axes:

\(\vec{R}_{fxi} = F_i \cos\theta_i\)
\(\vec{R}_{fyi} = F_i \sin\theta_i\)

Total components:

\(R_{fx} = \sum R_{fxi}\)
\(R_{fy} = \sum R_{fyi}\)

Magnitude and direction of the resultant force:

\(R = \sqrt{R_{fx}^2 + R_{fy}^2}\)
\(\theta = \tan^{-1} \left(\frac{R_{fy}}{R_{fx}}\right)\)

Step-by-Step Calculation

Determine the x and y components of each force.
Sum all x-components to get \(R_{fx}\) and all y-components to get \(R_{fy}\).
Calculate the angle of the resultant: \(\theta = \tan^{-1} \frac{R_{fy}}{R_{fx}}\).
Calculate the magnitude of the resultant: \(R = \sqrt{R_{fx}^2 + R_{fy}^2}\).

Example:

A car is pushed by 15 N at 0° and 10 N at 90°.

\(F_1 = 15 \, \text{N}, \theta_1 = 0°\)
\(F_2 = 10 \, \text{N}, \theta_2 = 90°\)

Step 1: Components

\(R_{fx1} = 15 \cos0° = 15\)
\(R_{fy1} = 15 \sin0° = 0\)
\(R_{fx2} = 10 \cos90° = 0\)
\(R_{fy2} = 10 \sin90° = 10\)

Step 2: Sum Components

\(R_{fx} = 15 + 0 = 15\)
\(R_{fy} = 0 + 10 = 10\)

Step 3: Angle

\(\theta = \tan^{-1}\frac{10}{15} \approx 33.69°\)

Step 4: Magnitude

\(R = \sqrt{15^2 + 10^2} \approx 18.03 \, \text{N}\)

How the Calculator Works

Input the forces and their angles into the calculator, and it automatically computes:

Horizontal component (Fx)
Vertical component (Fy)
Magnitude of resultant force (R)
Direction angle (θ)

Why Calculate Resultant Force?

Calculating the resultant force allows you to treat multiple forces acting on an object as a single equivalent force, simplifying analysis and understanding the net effect.

FAQs

When is net force zero?

Net force is zero when all acting forces balance each other, resulting in either no motion or constant velocity (Newton’s first law).

How is the resultant force between two vectors calculated?

Using the parallelogram law: \(R = \sqrt{A^2 + B^2 + 2AB\cos\theta}\), where A and B are magnitudes and θ is the angle between vectors.

References

From Phyley.com: Resultant Force Guide. From X-Engineer.org: Resultant Force Introduction.

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