Name: force, motion, and mechanical effects
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 25 s
Channel: JoVE

人が箱を引っ張ったり押したりすると、箱は水平方向に動きます。ボックスに加えられる引っ張りや押し込みによってその動きが生じることは、力として知られています。ニュートンで表されるベクトル量です。
物体に作用する力は、外力と内力に分類できます。物体に外部から加えられた力が効果を生み出す場合、それは外力と呼ばれ、体内に存在する反力は内部力として知られています。
伝達性の原理は、身体への力の加える点が変化しても同じ作用線に留まる場合、身体に生じる力は変化しないと述べています。
剛体に作用する 2 つの力について考えます。伝染性の原理によれば、体に作用する力が同じ作用線にある場合、たとえ異なる点で作用していても、体は変化しません。
これらの力は等しく反対であるため、それらの合計はゼロに等しく、体にかかる合力は変化しません。

<ol>
	<li>メリアム、JL、クレイジ、LG、ボルトン、JN(2018)。エンジニアリングメカニクス \u2012 ニュージャージー州スタティックス: John Wiley & Sons.PP - 23から24。</li>
	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:マグロウヒル。85ページ\u2012 86。</li>
</ol>

力の概論

ノズルからタービンまでの水の流れを考えてみましょう。水がタービンに当たると、流れの方向に沿った力を及ぼします。力は物体の運動、形状、あるいは向きを変える衝撃です。力は物体との物理的な接触によって引き起こされることもあります（押すまたは引くなど）、また物理的な接触を必要としない相互作用によって引き起こされることもあります（磁力や重力のような力）。力は大きさと方向を持つベクトル量であり、SI単位系ではニュートン（N）で計測されます。1 kgの質量を持つ物体が加速度1m/s^2で前進する場合、この物体に加わる力は1 Nです。

力学では、外力と内力の2種類の力が考慮される剛体にはたらく力で、外力と内力の効果を引き起こします。外力の効果とは、体重や摩擦力などの外部から加えられた力に対して物体が周囲に及ぼす反作用力を指します。内力の効果は、物体の材料内で発生する内部の力や変形です。外力を受けるブラケットの例を考えてみましょう。この力の外的効果は、基礎とボルトがブラケットに及ぼす反作用力です。ブラケットへの力の内的効果は、ブラケットの材料内で発生する内部応力と変形です。これらの内部力と変形は、ブラケットの材料全体に分布しており、物体の材料特性と形状に依存します。

力の伝達原理は、適用された力の作用点を同じ作用線上で移動させることが効果に与える影響を説明する概念です。この原理によれば、剛体に力が作用し、その力の作用点が変わっても同じ作用線上に留まる場合、物体に作用する合力は変わらないとされています。異なる点から剛体に作用する同じ大きさの力を考えてみましょう。力の伝達原理によれば、物体に作用する力は同じ作用線上にあり、特定の点で作用している単一の力に相当することになります。これらの力の作用点が変化したり、同じ作用線上を移動したりしても、物体に対する合力は同じままです。なぜなら、同じ作用線上で同じ力が作用しているからです。

ノズルからタービンベーンに水が流れるとします。水がタービンベーンに当たると、水は流れに沿って移動する力を発揮します...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Force Vectors

力のベクトル

KEY TERMS AND CONCEPTS

主要用語と概念

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 object with a mass of 1 kg that accelerates at 1 m/s2, the applied force is 1 N.

When a rigid body is under load, mechanics separates the effects into external forces and internal forces. External forces produce the reactive forces that the body exerts on its surroundings. These can include body weight, forces applied by people, and frictional forces. Internal effects are the stresses and deformations that develop inside the material.

A bracket loaded by an external force shows both kinds of effects. The foundation and bolts react to the force on the bracket. At the same time, internal stresses and deformations spread through the bracket material. These internal forces depend on the material properties and the shape of the body.

The principle of transmissibility explains what happens when the point of application of a force moves along the same line of action. If the force stays on that line, the resultant force on a rigid body does not change. Two equal forces on a rigid body can therefore be treated as a single equivalent force when they act along the same line of action.

Force, Motion, and Mechanical Effects

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 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 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,...

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,...

direction cosines of a vector

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

Three-dimensional force systems involve forces acting in three different directions at the same time. These problems are common in physics and engineering. They are used to find the resultant force, which helps predict or analyze how an object or structure will behave. The first step is to resolve each force into scalar components. A scalar component is the amount of force along one axis. Trigonometric functions and vector addition are used to break the force into parts and then combine those...

position vectors

Using Position Vectors to Locate Points

Position vectors are used to locate points in space and show the direction and distance between two points. In math and science, they help describe spatial relationships and make calculations easier. A position vector can connect one point to another point or show a point’s location relative to the origin of coordinates. For a point P(x, y, z) relative to the origin O, the position vector r runs from O to P. In Cartesian vector form, it is written as r = x i + y j + z k. Here, i, j, and k are...

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 force changes motion, shape, and orientation, plus the difference between contact and non-contact forces, internal effects, and transmissibility.

Force, Motion, and Mechanical Effects | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Force, Motion, and Mechanical Effects

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