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

두 개 이상의 힘 벡터의 벡터 추가는 결과 힘을 얻기 위해 평행사변형 법칙을 사용하여 수행할 수 있습니다.
두 척의 작은 예인선이 배를 끌고 있다고 생각해 보십시오. F1과 F2의 두 힘은 동시에 함선에 작용합니다.
평행사변형 법칙을 사용하여 알짜 힘을 찾으려면 평행 사변형이 형성되도록 두 힘 벡터에 평행선을 그립니다.
이제 평행사변형의 대각선은 두 개의 예인선으로 인해 배에 가해지는 알짜 힘 FN 을 나타냅니다. 힘 F1 과 F2 의 벡터 합으로 표현됩니다.
이제 다른 예인선의 세 번째 힘이 배에 작용한다고 가정합니다.
FN과 제3의 힘F3를 사용하여 또 다른 평행사변형이 형성됩니다. 이 새로운 평행사변형의 대각선은 세 개의 예인선 모두로 인해 배에 결과적인 힘을 제공합니다.
여기서 배에 가해지는 결과적인 힘은 세 가지 힘 모두의 벡터 합으로 표현됩니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 쪽 18-22</li>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 셀프, BP (2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 쪽 29</li>
</ol>

힘의 벡터 덧셈

물체에 작용하는 여러 힘의 영향을 이해할 때 벡터 덧셈은 매우 중요한 개념입니다. 이 수학적 개념은 둘 이상의 힘이 관련될 때 물체에 작용하는 알짜 힘을 계산하는 데 사용될 수 있습니다.

벡터 추가의 개념을 이해하려면 두 척의 작은 예인선이 선박을 끄는 시나리오를 생각해 보세요. 두 힘, F1과 F2는 선박에서 서로 다른 방향으로 동시에 작용합니다. 평행사변형 법칙은 선박에 작용하는 알짜 힘을 계산하는 데 사용될 수 있습니다.

평행사변형 법칙은 두 벡터를 더하는 기하학적 방법을 제공하므로 벡터 덧셈에 유용합니다. 평행사변형의 인접한 변이 두 벡터를 나타낼 때 두 벡터의 교차점을 통과하는 대각선은 두 벡터의 벡터 합을 나타냅니다. 두 척의 예인선이 선박을 끌고 있는 상황에서 이 법칙을 적용하기 위해 두 힘 벡터에 대한 평행선을 그려 평행사변형을 형성합니다. 그런 다음 두 벡터의 교차점을 통과하는 대각선이 그려집니다. 이 대각선은 두 예인선으로 인해 선박에 작용하는 합력 또는 알짜 힘을 나타냅니다. 이 알짜 힘은 두 힘의 벡터 합으로 표현됩니다.

그러나 세 번째 힘 F3이 도입되면 또 다른 평행사변형이 그려집니다. 이번에는 이전 합력 F1 + F2 가 새 평행사변형의 한 변으로 사용되며, 세 번째 힘 F3을 반대편으로 합니다. 다시 한번, 이 평행사변형의 대각선은 세 개의 예인선 모두로 인해 선박에 작용하는 합력 또는 알짜 힘을 나타냅니다. 선박에 가해지는 이 알짜 힘은 세 가지 힘의 벡터 합으로 표현됩니다. , 즉 F1 + F2 + F3입니다.

벡터 덧셈은 물체에 작용하는 여러 힘의 영향을 이해하는데 매우 중요한 도구입니다. 물리학, 공학, 수학 등 다양한 분야에서 매우 중요합니다. 평행사변형의 법칙과 벡터 덧셈의 개념을 이해함으로써 물체에 작용하는 알짜 힘을 정확하게 계산하고 예측할 수 있습니다.

물체에 작용하는 여러 힘의 효과를 이해할 때 벡터 덧셈은 이해해야 할 중요한 개념입니다. 이 수학적 개념은 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Force Vectors

힘 벡터

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

Scalar vs Vector Quantities in Mechanics

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...

vector operations

Adding and Multiplying Vectors

Vectors are quantities with both magnitude and direction, and their operations include addition, subtraction, and scalar multiplication. Scalar multiplication means a vector is multiplied by a scalar value, which creates a new vector with a different magnitude. If the scalar is positive, the direction stays the same. If the scalar is negative, the direction reverses. A common example is momentum, which comes from multiplying mass by velocity. In this case, mass is the scalar quantity and...

introduction to force

Force, Motion, and Mechanical Effects

Force changes the motion, shape, or orientation of an object. A flowing stream of water can push on a turbine vane and make it move in the direction of the flow. In mechanics, force is treated as a vector quantity, which means it has both magnitude and direction. It is measured in newtons, or N, in the SI unit system. Forces can act through direct contact or without contact. A push or pull is a contact force. Magnetic and gravitational forces are examples of non-contact interactions. For an...

force classification

Types of Forces in Physics

Forces in physics can be grouped by how they act and where they come from. These groups help describe motion, behavior, and equilibrium in the physical world. They are also useful in physics and engineering. One common way to classify forces is by whether they need contact. Contact forces act only when two objects touch. Frictional force, tension, and normal force are all contact forces that come from surface contact. Forces can also act without physical touch. These are called non-contact...

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,...

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...

two-dimensional force system: problem solving

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...

scalar notation

Vector Components for Force Calculations

Scalar notation helps simplify vector calculations by breaking a vector into separate x and y parts. When vectors are added or subtracted, each component can be handled on its own using scalar notation. This makes force problems easier to solve.

cartesian vector notation

Vector Components in 3D Space

Cartesian vector notation shows how to write vectors in three-dimensional space using x, y, and z components. It gives a clear way to represent direction and size for quantities used in mechanical engineering. The notation uses the unit vectors i, j, and k for the x, y, and z axes. A vector pointing in the direction (3, −4, 5) can be written as A = 3i - 4j + 5k. The unit vectors are i = (1, 0, 0), j = (0, 1, 0), and k = (0, 0, 1). This form is useful for describing displacement, velocity,...

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Vector Orientation with Direction Cosines

Direction cosines describe how a vector is oriented relative to the x, y, and z axes. For a vector A written in Cartesian form with i, j, and k unit vectors, this idea helps connect the vector’s components to its direction in space. The magnitude of vector A is the square root of the sum of the squares of its components. Its direction is described by the coordinate direction angles α, β, and γ with the x, y, and z axes. These angles can be found by projecting vector A onto each axis. The...

three-dimensional force system

Force Components in 3D Space

A three-dimensional force system describes forces acting in x, y, and z directions. In mechanical engineering, this framework helps students and engineers study how objects and structures behave in three-dimensional space. One common example is a force acting on a particle in space. That force can be split into three parts: the x-component, the y-component, and the z-component. Vector mathematics is used to calculate each component, and together they make up the full three-dimensional force...

three-dimensional force system:problem solving

three-dimensional-force-systemproblem-solving

Resolving Forces in 3D Coordinates

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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...

dot product

Using Dot Product to Find Work and Angle

The dot product connects vectors, work, and direction in mathematics and physics. In engineering, it is found by multiplying the magnitudes of two vectors and the cosine of the angle between them. It is shown with a dot symbol between the vectors. A real-world example is a vehicle pulling an object along the ground with a rope. If the rope is angled above the horizontal axis, the work done can be calculated with the dot product of the applied force and the object’s displacement. This makes the...

dot product: problem solving

Using the Dot Product to Solve Vector Questions

The dot product helps solve vector questions by combining vector size and the cosine of the angle between them. It is useful when the angle is measured anti-clockwise and when a problem asks for a vector relationship in component form. A good first step is to identify the question being asked. Then list the given vectors and write them in Cartesian form, also called component form. This makes the data easier to use in a calculation. Next, decide whether the dot product is the right operation.

cross product

Cross Product Direction and Magnitude

The cross product is a vector operation in vector algebra that creates a third vector from two input vectors. Unlike the scalar product, it does not give a single number. The result is a vector perpendicular to both original vectors. The size, or magnitude, of the cross product depends on the magnitudes of both vectors and the sine of the angle between them. A larger angle between the vectors gives a larger cross product magnitude. The direction is found with the right-hand rule. If the...

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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