Name: finding a cable force from two points
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 26 s
Channel: JoVE

Rozważmy trójwymiarowy przykład statyczny, taki jak słup z zakotwiczonym w ziemi. W tym przypadku wzdłuż działa siła naciągająca.
Rozważmy teraz kartezjański układ współrzędnych z dowolnym początkiem układu współrzędnych, aby przedstawić siłę jako wektor kartezjański.
PA i PB reprezentują wektory położenia dla dwóch końców. Wektor siły jest skierowany od punktu A do B w tym samym kierunku, co wektor położenia PAB. Wektor jednostkowy określa ten kierunek.
Stosując prawo dodawania wektorów trójkąta, wektor położenia wzdłuż punktów A i B można uzyskać, odejmując PA od PB.
Po drugie, jego wielkość można znaleźć za pomocą pierwiastka kwadratowego z sumy kwadratów jego składowych.
Teraz podzielenie wektora położenia przez jego wielkość daje wektor jednostkowy wzdłuż AB.
Wreszcie iloczyn wielkości wektora siły i wektora jednostkowego wyraża wektor siły w postaci kartezjańskiej.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. Strona 59</li>
</ol>

wektor siły wzdłuż linii

vW trójwymiarowych problemach statyki kierunek siły często jest określony przez dwa punkty, przez które przechodzi jej linia działania. Rozważmy trójwymiarowy statyczny słup, na którym przymocowany jest kabel.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Rozważając układ współrzędnych kartezjańskich o początku w podstawie słupa, końce kabla mogą być oznaczone jako AB. PA i PB reprezentują wektory pozycji dla dwóch końców kabla. Do uzyskania wektora pozycji pomiędzy punktami A i B używana jest zasada trójkąta dodawania wektorów, w tym celu od wektora pozycji PA odejmowany jest wektor pozycji PB.

.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Wielkość wektora pozycji może być obliczona jako pierwiastek kwadratowy z sumy kwadratów jego składowych.

<img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;" />

Siła rozciągająca kabel jest skierowana od punktu A do punktu B, w tym samym kierunku co wektor pozycji PAB. Wektor jednostkowy wzdłuż kabla określa kierunek siły. Jest on obliczany przez podzielenie wektora pozycji przez jego wielkość.

<img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;" />

Wreszcie, wektor siły może być wyrażony w postaci kartezjańskiej przez pomnożenie wielkości wektora siły przez wektor jednostkowy. Ten iloczyn daje trójwymiarowy wektor reprezentujący siłę działającą na słup.

<img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;" />

Wektor siły wzdłuż linii

Dość często w trójwymiarowych problemach statyki kierunek siły jest określony przez dwa punkty, przez które przechodzi jej linia działania. Rozważ ...

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Mechanical Engineering

Inżynieria mechaniczna

Unit 1

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Force Vectors

Wektory siły

KEY TERMS AND CONCEPTS

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Force Vector along a Line

finding a cable force from two points

A cable force can be found from the two points that define its line of action. In three-dimensional statics, this setup often appears with a pole and a cable anchored to the ground. The cable ends are labeled A and B, and their position vectors are written as P_A and P_B.

The position vector from A to B is found using the triangle law of vector addition. First, subtract P_A from P_B to get P_AB. Then find the magnitude of P_AB by taking the square root of the sum of the squares of its components. This gives the length of the vector in Cartesian form.

The tension force in the cable points from A toward B. It has the same direction as the position vector P_AB. To show that direction, divide P_AB by its magnitude to get the unit vector along the cable. A unit vector is a vector with length 1 that gives direction only.

The force vector is written in Cartesian form by multiplying the force magnitude by the unit vector. This product gives a three-dimensional vector for the force acting on the pole. The method connects the geometry of points A and B to the final force vector.

Finding a Cable Force from Two Points

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A cable force can be found from the two points that define its line of action. In three-dimensional statics, this setup often appears with a pole and a cable anchored to the ground. The cable ends are labeled A and B, and their position vectors are written as P_A and P_B. The position vector from A to B is found using the triangle law of vector addition. First, subtract P_A from P_B to get P_AB. Then find the magnitude of P_AB by taking the square root of the sum of the squares of its...

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Learn how to use two position vectors, a unit vector, and force magnitude to express a cable’s tension as a 3D Cartesian force vector.

Finding a Cable Force from Two Points | 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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Finding a Cable Force from Two Points

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