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

Yere sabitlenmiş bir kabloya sahip bir direk gibi üç boyutlu statik bir örnek düşünün. Burada, kablo boyunca bir gerilim kuvveti etki ediyor.
Şimdi, kuvveti bir Kartezyen vektör olarak temsil etmek için keyfi bir kökene sahip bir Kartezyen koordinat sistemi düşünün.
PA ve PB, kablonun iki ucu için konum vektörlerini temsil eder. Kuvvet vektörü, P AB konum vektörü ile aynı yönde A noktasındanB'ye yönlendirilir. Birim vektör bu yönü belirtir.
Vektör toplamanın üçgen yasasını uygulayarak, A ve B noktaları boyunca konum vektörü, PA'nın PB'den çıkarılmasıyla elde edilebilir.
İkincisi, büyüklüğü, bileşenlerinin karelerinin toplamının karekökü kullanılarak bulunabilir.
Şimdi, konum vektörünü büyüklüğüne bölmek, AB kablosu boyunca birim vektörü sağlar.
Son olarak, kuvvet vektörünün büyüklüğü ile birim vektörün çarpımı, kuvvet vektörünü Kartezyen formda ifade eder.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği \u2012 Statik ve Dinamik. Hoboken, New Jersey: Pearson Prentice Salonu. sayfa 59</li>
</ol>

bir çizgi boyunca kuvvet vektörü

Çok sıklıkla üç-boyutlu statik problemlerde, bir kuvvetin yönü, etki hattının geçtiği iki nokta tarafından belirtilir. Yere sabitlenmiş bir kablo ile üç-boyutlu bir kutba bakalım.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Kutup tabanında bir Koordinat sistemini dikkate alarak, kablo uç noktaları A ve B olarak gösterilebilir. P_A ve P_B, kablo uçlarının konum vektörlerini temsil eder. Vektör toplama üçgen kuralı kullanılarak, A ve B noktaları arasındaki konum vektörü elde edilir. Bu amaçla, P_A konum vektöründen P_B çıkarılır.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

Konum vektörünün büyüklüğü, bileşenlerinin karelerinin toplamının karekökünden elde edilebilir.

<img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;" />

Kablo üzerinde etki eden gerilme kuvveti, A noktasından B noktasına doğru ve aynı yönde olan P_AB konum vektörü ile belirlenir. Kablo üzerindeki birim vektör, konum vektörünün büyüklüğüne bölünerek değerlendirilir.

Son olarak, kuvvet vektörü, kuvvet vektörünün büyüklüğü ile birim vektörün çarpımı olarak ifade edilebilir. Bu ürün, kutba etki eden üç-boyutlu bir kuvveti temsil eden bir vektör elde eder.

<img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;" />

Son olarak, kuvvet vektörü, kuvvet vektörünün büyüklüğü ile birim vektörün çarpılmasıyla Kartezyen formda ifade edilebilir. Bu çarpım, direğe etki eden kuvveti temsil eden üç boyutlu bir vektör verir.

<img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;" />

Bir çizgi boyunca Kuvvet Vektörü

Oldukça sık olarak, üç boyutlu statik problemlerde, bir kuvvetin yönü, etki çizgisinin geçtiği iki nokta ile belirlenir. Bir düşünün ...

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Force Vectors

Kuvvet Vektörleri

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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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force vector along a line

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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key terms and concepts

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 Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Finding a Cable Force from Two Points

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