Name: resultant force from tugboats
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 23 s
Channel: JoVE

Сложение векторов двух или более векторов силы может быть выполнено с использованием закона параллелограмма для получения результирующей силы.
Представьте себе судно, которое тянут два небольших буксира. Две силы, F1 и F2, действуют на корабль одновременно.
Чтобы найти результирующую силу с помощью закона параллелограмма, проведите параллельные линии к обоим векторам силы таким образом, чтобы образовался параллелограмм.
Теперь диагональ параллелограмма представляет собой результирующую силу FN на судне, действующую на два буксира. Он выражается как векторная сумма сил F1 и F2 .
Предположим теперь, что на судно действует третья сила с другого буксира.
Формируется еще один параллелограмм с использованием FN и третьей силы F3. Диагональ этого нового параллелограмма дает результирующую силу на судне, действующую на все три буксира.
Здесь результирующая сила, действующая на корабль, выражается как векторная сумма всех трех сил.

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	<li>Хиббелер, Р.К. (2016). Инженерная механика \u2012 Статика и динамика. Хобокен, Нью-Джерси: Пирсон Прентис Холл. С. 18—22</li>
	<li>Бир, Ф..; Джонстон, Э.Р.; Мазурек, Д.Ф; Кромвель,.Д. и Селф, Б.. (2019). Векторная механика для инженеров \u2012 Статика и динамика. Нью-Йорк: Макгроу-Хилл. С. 29</li>
</ol>

Сложение векторов сил

При понимании воздействия нескольких сил на объект, понятие сложения векторов является ключевым. Это математическое понятие может быть использовано для расчёта суммарной силы, действующей на объект, когда задействованы две или более силы.

Для понимания понятия сложения векторов рассмотрим сценарий, в котором корабль тянут два маленьких буксира. Две силы, F1 и F2, действуют одновременно на корабль в разных направлениях. С помощью закона параллелограмма можно рассчитать суммарную силу, действующую на корабль.

Закон параллелограмма полезен при сложении векторов, потому что он предоставляет геометрический метод сложения двух векторов. Он утверждает, что, когда смежные стороны параллелограмма представляют два вектора, диагональ, проходящая через их пересечение, представляет векторную сумму двух векторов. Для применения этого закона в контексте того, как корабль тянут два буксира, параллельные линии к обоим векторам силы рисуются, образуя параллелограмм. Затем проводится диагональная линия через пересечение двух векторов. Эта диагональ представляет собой результирующую или суммарную силу, действующую на корабль из-за двух буксиров. Эта суммарная сила выражается как векторная сумма двух сил.

Однако, если вводится третья сила F3, рисуется ещё один параллелограмм. В этот раз, предыдущая результирующая сила F1 + F2 используется в качестве одной стороны нового параллелограмма, а третья сила F3 - в качестве другой стороны. Опять же, диагональ этого параллелограмма представляет собой результирующую или суммарную силу, действующую на корабль из-за всех трёх буксиров. Эта суммарная сила на корабль выражается как векторная сумма всех трёх сил, а именно F1 + F2 + F3.

Сложение векторов является мощным инструментом для понимания воздействия нескольких сил на объект. Оно является ключевым в различных областях, включая физику, инженерию и математику. Путём понимания закона параллелограмма и понятия сложения векторов можно проводить точные расчёты и предсказывать суммарную силу, действующую на объект.

При понимании эффектов множественных сил, действующих на объект, сложение векторов является важнейшей концепцией для понимания. Это математическое понятие может быть ...

Education

JoVE Core

Mechanical Engineering

Машиностроение

Unit 1

Раздел 1

Force Vectors

Векторы силы

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

Vector Addition of Forces

resultant force from tugboats

Resultant force can be found with vector addition when two or more forces act on the same object. This idea helps explain how multiple pulls combine to create one net force. It is a key tool for understanding motion in physics.

A clear example is a ship pulled by two small tugboats. The forces, F1 and F2, act at the same time but in different directions. The net force on the ship is the vector sum of those two forces.

The parallelogram law gives a geometric way to add vectors. In this method, the two force vectors form adjacent sides of a parallelogram. The diagonal through their intersection shows the resultant, or net force.

To use the law for the tugboat example, parallel lines are drawn to both force vectors to complete the parallelogram. Then a diagonal is drawn across the shape. That diagonal represents the net force acting on the ship from the two tugboats.

A third force, F3, can be added in the same way. A new parallelogram is drawn using the previous resultant, F1 + F2, as one side and F3 as the other. The diagonal of this second parallelogram gives the total resultant force, written as F1 + F2 + F3.

Vector addition is useful in physics, engineering, and mathematics. It helps scientists and engineers calculate and predict the net force on an object. The parallelogram law makes that prediction easier to picture and measure.

Resultant Force from Tugboats

scalar and vectors

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vector addition of forces

Resultant force can be found with vector addition when two or more forces act on the same object. This idea helps explain how multiple pulls combine to create one net force. It is a key tool for understanding motion in physics. A clear example is a ship pulled by two small tugboats. The forces, F1 and F2, act at the same time but in different directions. The net force on the ship is the vector sum of those two forces. The parallelogram law gives a geometric way to add vectors. In this method,...

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three-dimensional force system:problem solving

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Resolving Forces in 3D Coordinates

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dot product

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Cross Product Direction and Magnitude

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key terms and concepts

Learn how vector addition uses the parallelogram law to find the resultant force on a ship pulled by two or three tugboats in physics.

Resultant Force from Tugboats | 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

Resultant Force from Tugboats

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