Name: two-dimensional forces: free-body analysis
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 29 s
Channel: JoVE

Rozważmy wycieraczkę nachyloną pod kątem 25 stopni do linii podstawowej "s" w układzie dwuwymiarowym. Siła działająca na uchwyt, odchylona do środka wycieraczki, tworzy kąt 20 stopni z linią odniesienia "c", która jest równoległa do linii podstawowej "s".
Jeśli składowa siły wzdłuż osi a wynosi 65 niutonów, należy określić wielkość siły i jej składową wzdłuż osi b.
Tutaj, biorąc pod uwagę alternatywne kąty, coa' wynosi 25 stopni, podczas gdy kąt Foc wynosi 20 stopni. Tak więc kąt utworzony przez wektor siły z osią a jest określany przez dodanie dwóch kątów i jest równy 45 stopniom.
Ponieważ znana jest składowa siły wzdłuż osi a, wielkość siły jest szacowana przez stosunek składowej a siły do cosinusa wynoszącego 45 stopni.
Teraz składowa b siły jest wyrażona jako iloczyn wielkości siły i sinusa 45 stopni. Jest ujemny, ponieważ znajduje się wzdłuż ujemnej osi b.

<ol>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. Strony 29-33</li>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. str. 33 \u2012 35.</li>
</ol>

dwuwymiarowy układ sił: rozwiązywanie problemów

Rozwiązywanie problemów związanych z dwuwymiarowymi układami sił jest istotnym aspektem mechaniki i inżynierii. Poprzez zastosowanie zasad analizy wektorowej i równowagi sił, można określić efekt wielu sił działających na obiekt w przestrzeni dwuwymiarowej.

Pierwszym krokiem w rozwiązywaniu problemu związanego z dwuwymiarowym układem sił jest wykonanie diagramu ciała swobodnego rozważanego obiektu. Ten diagram pomaga zidentyfikować wszystkie siły zewnętrzne działające na obiekt, w tym ich wartości, kierunki i punkty przyłożenia.

Następnie trzeba rozłożyć siły na składowe w kierunkach x i y z użyciem zasad analizy wektorowej. Ten krok pomaga przekształcić dane siły na postać wektorową kartezjańską, umożliwiającą łatwe przedstawienie i analizę. Składowe mogą być rozłożone za pomocą funkcji trygonometrycznych, takich jak sinus i cosinus podanych kątów.

Po rozłożeniu sił na składowe, następnym krokiem jest określenie siły netto w każdym kierunku. Robi się to poprzez dodanie wszystkich sił w danym kierunku. Następnie, za pomocą twierdzenia Pitagorasa i zasad trygonometrii, określa się wynikającą siłę i jej kierunek. Jeśli siła netto jest równa zero, obiekt jest w równowadze i nie przyspiesza. Jeśli siła netto jest różna od zera, obiekt przyspiesza w kierunku tej siły. Zasada równowagi sił stanowi, że suma wszystkich sił zewnętrznych działających na element musi być równa zero zarówno w kierunkach x, jak i y. Pozwala to określić nieznane siły działające na obiekt, takie jak napięcie lub ściskanie w elemencie.

W niektórych przypadkach stosuje się również zasadę równowagi momentu, aby określić efekt sił zewnętrznych na obiekt. Ta zasada mówi, że suma wszystkich momentów zewnętrznych działających na element musi być równa zero. Ten krok pomaga określić wartości i kierunki momentów działających na obiekt.

Dwuwymiarowy układ sił: Rozwiązywanie problemów

Rozwiązywanie problemów związanych z dwuwymiarowymi układami sił jest istotnym aspektem mechaniki i inżynierii. Stosując zasady wektora ...

two-dimensional-force-system-problem-solving

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: Problem Solving

two-dimensional forces: free-body analysis

Two-dimensional force analysis starts with a free-body diagram. A free-body diagram shows the object and every external force acting on it. It includes each force’s size, direction, and point of application.

After the diagram is drawn, each force is broken into x- and y-components. This uses vector analysis and trigonometry, especially sine and cosine. The forces can then be written in Cartesian vector form, which makes them easier to work with.

Next, the components in each direction are added to find the net force in x and y. The resultant force is then found with the Pythagorean theorem and trigonometry. If the net force is zero, the object is in equilibrium and does not accelerate. If the net force is not zero, the object accelerates in the direction of the net force.

Force equilibrium means the sum of external forces is zero in both the x and y directions. This helps solve for unknown forces such as tension or compression in a member. In some problems, moment equilibrium is also used. Moment equilibrium means the sum of external moments is zero, which helps determine the size and direction of moments acting on the object.

Two-Dimensional Forces: Free-Body Analysis

two-dimensional-forces-free-body-analysis

scalar and vectors

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Scalar and vector quantities are two main ways to describe physical quantities in mechanics. Common examples include force, speed, velocity, and work. Some of these are scalars, and others are vectors. A scalar is a quantity that has magnitude only. It does not need direction. Mass, area, and length are examples of scalar quantities. Scalars with the same units can be added or subtracted like ordinary numbers. A class that ends 10 min earlier than 50 min lasts 50 min minus 10 min, which is 40...

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two-dimensional force system

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two-dimensional force system: problem solving

Two-dimensional force analysis starts with a free-body diagram. A free-body diagram shows the object and every external force acting on it. It includes each force’s size, direction, and point of application. After the diagram is drawn, each force is broken into x- and y-components. This uses vector analysis and trigonometry, especially sine and cosine. The forces can then be written in Cartesian vector form, which makes them easier to work with. Next, the components in each direction are...

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key terms and concepts

Learn how to use free-body diagrams, force components, and equilibrium to solve two-dimensional force problems and find resultant forces and moments.

Two-Dimensional Forces: Free-Body Analysis | 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.

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Two-Dimensional Forces: Free-Body Analysis

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