Physics Library
 An open source physics library
Encyclopedia | Forums | Docs | Random | Template Test |  
Login
create new user
Username:
Password:
forget your password?
Main Menu
Sections

Meta

Talkback

Downloads

Information
[parent] resultant force example (Example)

Resultant Forces with Vectors

In physics, the resultant force is the single force that represents the combined effect of multiple forces acting on an object. Forces are vector quantities, characterized by both magnitude and direction. To find the resultant force, we add the individual force vectors using vector addition.

Example: Two Forces Acting on an Object

Consider an object subjected to two forces:

  • $\vec{F_1} = 5 \,$   N at $0^\circ$ (along the positive $x$-axis).
  • $\vec{F_2} = 3 \,$   N at $60^\circ$ from the positive $x$-axis.

We aim to find the resultant force $\vec{F_R} = \vec{F_1} + \vec{F_2}$.

Step 1: Resolve Forces into Components

Express each force in terms of its $x$- and $y$-components:

  • For $\vec{F_1}$:

    $\displaystyle F_{1x} = 5 \cos(0^\circ) = 5 \,$   N$\displaystyle , \quad F_{1y} = 5 \sin(0^\circ) = 0 \,$   N$\displaystyle . $
    So, $\vec{F_1} = (5, 0) \,$   N.
  • For $\vec{F_2}$:

    $\displaystyle F_{2x} = 3 \cos(60^\circ) = 3 \cdot 0.5 = 1.5 \,$   N$\displaystyle , \quad F_{2y} = 3 \sin(60^\circ) = 3 \cdot \frac{\sqrt{3}}{2} \approx 2.598 \,$   N$\displaystyle . $
    So, $\vec{F_2} \approx (1.5, 2.598) \,$   N.

Step 2: Sum the Components

The components of the resultant force $\vec{F_R} = (F_{Rx}, F_{Ry})$ are:

$\displaystyle F_{Rx} = F_{1x} + F_{2x} = 5 + 1.5 = 6.5 \,$   N$\displaystyle , $

$\displaystyle F_{Ry} = F_{1y} + F_{2y} = 0 + 2.598 \approx 2.598 \,$   N$\displaystyle . $
Thus, $\vec{F_R} \approx (6.5, 2.598) \,$   N.

Step 3: Calculate Magnitude and Direction

The magnitude of $\vec{F_R}$ is:

$\displaystyle \vert\vec{F_R}\vert = \sqrt{F_{Rx}^2 + F_{Ry}^2} = \sqrt{6.5^2 + 2.598^2} = \sqrt{42.25 + 6.75} \approx \sqrt{49} \approx 7 \,$   N$\displaystyle . $

The direction (angle $\theta$ relative to the positive $x$-axis) is:

$\displaystyle \theta = \tan^{-1}\left(\frac{F_{Ry}}{F_{Rx}}\right) = \tan^{-1}\left(\frac{2.598}{6.5}\right) \approx \tan^{-1}(0.4) \approx 21.8^\circ. $

Thus, the resultant force is approximately $7 \,$   N at $21.8^\circ$ from the positive $x$-axis.

Diagram of Forces

The following diagram illustrates the two forces and their resultant:

\resizebox{\textwidth}{!}{\includegraphics{forces.png}}

This example was generated by Grok, an AI developed by xAI, on June 6, 2025.



"resultant force example" is owned by bloftin.
View style:

This object's parent.

Cross-references: diagram, magnitude, vector, object, resultant force

This is version 11 of resultant force example, born on 2025-05-30, modified 2025-06-02.
Object id is 1008, canonical name is ResultantForceExample.
Accessed 158 times total.

Classification:
Physics Classification: 45.50.Dd (General motion)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:

No messages.

Testing some escape charachters for html category with a generator has an injective cogenerator" now escape ” with "