Name: scalar vs vector quantities in mechanics
Uploaded: 2023-09-22T11:49:38.000Z
Duration: 1 min 22 s
Channel: JoVE

Różne wielkości fizyczne w mechanice inżynierskiej używane do opisu ruchu obiektu są mierzone za pomocą skalarów lub wektorów.
Skalary to wielkości fizyczne, które są opisywane przez wielkość i reprezentowane przez wartość liczbową z jednostką fizyczną, dodatnią lub ujemną. Długość, prędkość, odległość i czas to tylko niektóre przykłady.
Wektory to wielkości fizyczne, które są opisane strzałką mającą zarówno wielkość, jak i kierunek. Długość strzałki reprezentuje wielkość, a kąt między wektorem a ustaloną osią reprezentuje kierunek jej linii działania.
Są one reprezentowane pogrubionymi literami lub za pomocą strzałki nad literą, podczas gdy ich wielkości są reprezentowane przez kursywę litery. Niektóre przykłady to prędkość, przyspieszenie i siła.
Weźmy na przykład ruchomą windę. Wymiary i masa windy są wielkościami skalarnymi, podczas gdy prędkość i masa windy są wielkościami wektorowymi, ponieważ mają zarówno wielkość, jak i kierunek.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. str. 17</li>
</ol>

skalar i wektory

W mechanice powszechnie używane terminy, takie jak siła, prędkość, prędkość względna i praca, można sklasyfikować jako wielkości skalarne lub wektorowe. Skalar jest wielkością fizyczną, która może być opisana tylko przez swoją wartość, nie wymaga żadnych składników kierunkowych. Przykładami wielkości skalarnych są masa, powierzchnia i długość.

Wielkości skalarnych o tych samych jednostkach fizycznych można dodawać lub odejmować zgodnie z zwykłymi regułami algebry dla liczb. Na przykład, klasa kończąca się 10 minut wcześniej niż 50 minut trwa 50 min - 10 min = 40 min. Podobnie, porcja kukurydzy o wartości 60 kalorii, a następnie porcja donatów o wartości 200 kalorii daje 60 kalorii + 200 kalorii = 260 kalorii energii. Jeśli pomnożymy wielkość skalarną przez liczbę, otrzymamy tę samą wielkość skalarną, ale o większej (lub mniejszej) wartości. Na przykład, jeśli wczorajsze śniadanie miało 200 kalorii energii, a dzisiejsze śniadanie ma czterokrotnie więcej energii niż wczoraj, to dzisiejsze śniadanie ma 4 * 200 kalorii = 800 kalorii energii. Dwie wielkości skalarnych mogą być również pomnożone lub podzielone przez siebie, aby utworzyć pochodną wielkość skalarną. Na przykład, jeśli pociąg pokonuje odległość 120 km w ciągu 1 godziny, jego prędkość wynosi 120 000 m / 3600 s = 33 m / s, gdzie prędkość jest pochodną wielkością skalarną uzyskaną przez podzielenie odległości przez czas.

Z kolei wielkość wektorowa to wielkość fizyczna, która ma zarówno wartość, jak i kierunek. Wektor można przedstawić graficznie za pomocą strzałki. Długość strzałki symbolizuje wartość wektora, a kąt między nią a ustalonym osią określa jego kierunek. Głowa strzałki reprezentuje kierunek, w którym wskazuje wektor. Przykładami wielkości wektorowych są przemieszczenie, prędkość, położenie, siła i moment siły.

Rozważanie udzielanie wskazówek przyjacielowi podczas wędrówki na postój 6 km od namiotu. Najłatwiejszym sposobem będzie określenie, w jakim kierunku dotrzeć do dokładnej lokalizacji; na przykład 6 km na południowy wschód będzie bardziej pomocny. Ta wielkość to przemieszczenie wędrowca.

Dwa wektory są równe, jeśli mają równe wartości i ten sam kierunek. Dwa wektory o identycznych kierunkach są nazywane wektorami równoległymi. Jeśli wektor wskazuje w przeciwnym kierunku, dokładnie 180°, w stosunku do pierwszego wektora, są one nazywane wektorami antyrównoległymi. Dwa wektory z kierunkami prostopadłymi do siebie są nazywane wektorami ortogonalnymi.

Skalar i wektory

W mechanice powszechnie używane terminy, takie jak siła, prędkość, prędkość i praca, można sklasyfikować jako wielkości skalarne lub wektorowe. Skalar to fizyczny ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Force Vectors

Wektory siły

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 min.

Scalars can also be multiplied by a number. If yesterday’s breakfast had 200 calories of energy and today’s breakfast has four times as much, then today’s breakfast has 800 calories of energy. Two scalars can also be multiplied or divided to make another scalar quantity. For example, a train that covers 120 km in 1 h has a speed of 120,000 m/3600 s, or 33 m/s. That speed is a derived scalar quantity.

A vector has both magnitude and direction. Vectors are often shown with arrows. The arrow length shows the magnitude. The angle with a fixed axis shows the line of action, and the arrowhead shows the direction. Displacement, velocity, position, force, and torque are examples of vector quantities.

Direction matters in everyday situations. If a hiking rest point is 6 km from a tent, saying 6 km southeast is more useful than saying only 6 km. That gives the hiker displacement, which is a vector. Two vectors are equal if they have the same magnitude and the same direction. Vectors with the same direction are parallel. Vectors that point exactly 180° apart are antiparallel. Vectors that meet at right angles are orthogonal.

Scalar vs Vector Quantities in Mechanics

scalar and vectors

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...

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cartesian vector notation

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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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position vectors

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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...

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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 scalar and vector quantities differ in mechanics, with clear examples of magnitude, direction, displacement, speed, and force for high school science.

Scalar vs Vector Quantities in Mechanics | 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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Scalar vs Vector Quantities in Mechanics

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