Name: resolving forces in a plane
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 20 s
Channel: JoVE

Rozważmy element konstrukcyjny w przestrzeni dwuwymiarowej, w której siła działa pod kątem theta z osią x.
Biorąc pod uwagę, że linia działania siły przechodzi przez początek układu współrzędnych, jej składowe można wyrazić w formie kartezjańskiej. Kierunek wektora siły jest zawsze określony przez tan odwrotność stosunku jego składowych.
Teraz, nawet jeśli linia działania wektora siły nie przechodzi przez początek układu współrzędnych, jego składowe wektorowe mogą być nadal wyrażone w postaci kartezjańskiej. Konwencję znaków tych składowych wektorowych można wybrać w zależności od ich kierunku.
Tutaj siła jest skierowana pod kątem pi minus theta, mierzonym w kierunku przeciwnym do ruchu wskazówek zegara od dodatniej osi y.
Rozważmy teraz strukturę, w której linia działania siły tworzy dowolny kąt alfa minus beta do dodatniej osi x wybranego układu współrzędnych. Składowe siły można rozwiązać za pomocą podobnej analizy.

<ol>
	<li>Meriam, J.L.; Kraige, L.G. i Bolton, J.N. (2020). Mechanika inżynierska \u2012 Statyka. Hoboken, New Jersey: John Wiley. Strona 33</li>
</ol>

dwuwymiarowy system sił

System dwuwymiarowy w inżynierii mechanicznej dotyczy analizy ruchu i sił w płaszczyźnie. Wektor siły dwuwymiarowej można rozłożyć na składowe:

<img alt="Equation 1" src="/files/ftp_upload/14229/14229_Equation_1v2.svg" style="text-align: center; height: 15px;" />

gdzie Fx i Fy to składowe wektorowe F w kierunkach x i y, odpowiednio. Każda z tych składowych wektorowych może być przedstawiona jako skalar (Fx i Fy) pomnożony przez odpowiedni wektor jednostkowy.

Aby określić składowe wektorowe siły w układzie współrzędnych kartezjańskich, należy najpierw określić kąt θ, jaki siła tworzy z dodatnią osią x. Zakładając, że linia działania siły przechodzi przez początek układu, jej składowe mogą być wyrażone w postaci kartezjańskiej przy użyciu podstawowej trygonometrii.

<img alt="Equation 2" src="/files/ftp_upload/14229/14229_Equation_2v3.svg" style="text-align: center; height: 34px;" />

gdzie F oznacza wielkość wektora siły. Kierunek wektora siły jest określony przez odwrotność tangensa stosunku jego składowych.

<img alt="Equation 3" src="/files/ftp_upload/14229/14229_Equation_3v3.svg" style="text-align: center; height: 34px;" />

Jednak w przypadkach, gdy linia działania wektora siły nie przechodzi przez początek, jego składowe wektorowe mogą wciąż być wyrażone w postaci kartezjańskiej przy użyciu tego samego podejścia. Możemy wybrać znak dla każdej składowej w zależności od kierunku wektora siły. Rozwiązując wektor siły na składowe, możemy określić jego wpływ na badaną strukturę.

Zrozumienie dwuwymiarowego systemu sił jest niezbędne dla inżynierów zajmujących się analizą i projektowaniem struktur, które są bezpieczne i wytrzymałe. Ta wiedza zapewnia podstawową wiedzę na temat reakcji struktury na różne siły i pomaga zlokalizować ewentualne słabe punkty konstrukcyjne.

Dwuwymiarowy system sił

System dwuwymiarowy w inżynierii mechanicznej polega na analizie ruchu i sił w płaszczyźnie. Dwuwymiarowy wektor siły można rozwiązać ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Force Vectors

Wektory siły

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

Two-Dimensional Force System

resolving forces in a plane

Resolving forces in a plane is a key part of two-dimensional mechanical analysis. A force vector can be split into x- and y-components, which show how the force acts in each direction. These components are written with the help of unit vectors, one for the x direction and one for the y direction.

To find the components in a Cartesian coordinate system, first identify the angle theta between the force and the positive x-axis. If the line of action passes through the origin, basic trigonometry gives the Cartesian form of the force. The magnitude of the force is F, and the direction can be found from the inverse tangent of the ratio of its components.

The same component method also works when the line of action does not pass through the origin. In that case, the sign of each component is chosen from the direction of the force vector. By breaking a force into parts, engineers can judge its net effect on a structure and look for possible weak points. This skill helps them analyze and design structures that are safe and structurally sound.

Resolving Forces in a Plane

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Resolving forces in a plane is a key part of two-dimensional mechanical analysis. A force vector can be split into x- and y-components, which show how the force acts in each direction. These components are written with the help of unit vectors, one for the x direction and one for the y direction. To find the components in a Cartesian coordinate system, first identify the angle theta between the force and the positive x-axis. If the line of action passes through the origin, basic trigonometry...

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two-dimensional-force-system-problem-solving

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key terms and concepts

Learn how to break a force into x- and y-components, use trigonometry and angle theta, and understand a structure's net force in a plane.

Resolving Forces in a Plane | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Resolving Forces in a Plane

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