Physics: Scalars and Vectors
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Questions and Answers

What is a scalar quantity?

A scalar quantity is a quantity that has magnitude only and has no direction in space.

Give two examples of scalar quantities.

Length and time are examples of scalar quantities.

How are vectors represented?

Vectors are represented by arrows.

What is the resultant of two vector quantities?

<p>The resultant of two vector quantities is the sum or the combined effect of the two vector quantities.</p> Signup and view all the answers

What is the triangle law?

<p>The triangle law states that when two vectors are joined head to tail, the resultant vector is found by drawing the diagonal of the triangle that is formed by the two vectors.</p> Signup and view all the answers

What is the parallelogram law?

<p>The parallelogram law states that when two vectors are joined tail to tail, the resultant vector is found by drawing the diagonal of the parallelogram that is formed by the two vectors.</p> Signup and view all the answers

What is the process called when a single force can be resolved into components which are perpendicular to each other?

<p>The process of resolving a force into components which are perpendicular to each other is called <em>resolution of forces</em>.</p> Signup and view all the answers

How are the magnitudes of the vertical and horizontal components determined in the resolution of forces?

<p>The magnitudes of the vertical and horizontal components can be determined using knowledge of simple trigonometry.</p> Signup and view all the answers

If a vector of magnitude v makes an angle θ with the horizontal, what is the formula for the horizontal component of the vector?

<p>The horizontal component of the vector is <em>x = v Cos θ</em>.</p> Signup and view all the answers

If a vector of magnitude v makes an angle θ with the horizontal, what is the formula for the vertical component of the vector?

<p>The vertical component of the vector is <em>y = v Sin θ</em>.</p> Signup and view all the answers

If a vector of magnitude v makes an angle θ with the horizontal, what is the horizontal component of the vector if v = 15 and * θ = 60°*?

<p>The horizontal component of the vector is <em>x = 15 Cos 60° = 7.5</em>.</p> Signup and view all the answers

If a vector of magnitude v makes an angle θ with the horizontal, what is the vertical component of the vector if v = 15 and * θ = 60°*?

<p>The vertical component of the vector is <em>y = 15 Sin 60° = 12.99</em>.</p> Signup and view all the answers

Flashcards

Scalar Quantity

A quantity with magnitude only and no direction.

Examples of Scalar Quantities

Length, area, volume, time, and mass.

Vector Quantity

A quantity that has both magnitude and direction.

Examples of Vector Quantities

Displacement, velocity, acceleration, and force.

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Vector Diagrams

Diagrams that represent vectors using arrows.

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Resultant Vector

The sum or combined effect of two or more vectors.

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Vectors in Same Direction

Vectors that add directly to create a larger magnitude.

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Vectors in Opposite Directions

Vectors that subtract from each other’s magnitude.

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Tail-to-Tail Method

Joining vectors at their tails to find the resultant.

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Head-to-Tail Method

Joining vectors at their heads to determine resultant.

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Parallelogram Law

A method to find the resultant of two vectors forming a parallelogram.

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Triangle Law of Addition

A method of adding two vectors by forming a triangle.

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Resolution of Forces

Breaking a force into perpendicular components.

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Components of a Vector

Perpendicular parts of a vector that can be analyzed separately.

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Trigonometry in Vectors

Using sine and cosine to resolve vectors into components.

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Magnitude of Components

The lengths of x and y components from a vector.

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Angle with Horizontal

The angle a vector makes relative to the horizontal axis.

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Horizontal Component

The part of a vector that runs parallel to the x-axis.

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Vertical Component

The part of a vector that runs parallel to the y-axis.

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Constant Speed

When an object moves at a steady pace without acceleration.

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Component of Weight on Ramp

The pull of weight parallel to the slanted surface of a ramp.

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Force Required for Motion

Force necessary to maintain movement against resistance.

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Using Pythagoras’ Theorem

Method to calculate the magnitude of resultant vectors.

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Magnitude Calculation

Finding the size of the resultant vector using components.

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Direction Determination

Calculating the angle of the resultant vector.

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Resultant Angle

The angle formed by the resultant vector with respect to a reference direction.

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Force at an Angle

The application of a force that is not straight along one axis.

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Magnitude of Resultant from Forces

The size of the resultant from multiple force vectors' effects.

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Study Notes

Scalars

  • A scalar quantity has only magnitude.
  • It has no direction in space.
  • Examples of scalars include: length, area, volume, time, and mass.

Vectors

  • A vector quantity has both magnitude and direction.
  • Examples of vectors include: displacement, velocity, acceleration, and force.

Vector Diagrams

  • Vector diagrams use arrows to represent vectors.
  • The length of the arrow represents the magnitude.
  • The direction of the arrow represents the direction.

Resultant of Two Vectors

  • The resultant is the combined effect of two vectors.
  • For vectors in the same direction, the resultant's magnitude is the sum of the individual magnitudes.
  • For vectors in opposite directions, the resultant's magnitude is the difference in magnitudes.

The Parallelogram Law

  • When two vectors' tails are joined, complete the parallelogram.
  • The diagonal represents their resultant.

The Triangle Law

  • When two vectors' head and tail are joined together, the resultant is found by completing the triangle.

Resultant of Two Vectors - Problem Example

  • Given two forces of 12 N and 5 N acting on a body at a certain angle.
  • The resultant force's magnitude is calculated using the Pythagorean theorem (√(12² + 5²)=13N).
  • The angle is calculated using the tangent function (tan⁻¹(5/12) ≈ 67°).

Resultant of Three Vectors - Problem Example

  • Given three forces of different magnitudes and angles, first find the resultant of two of them, then combine this with the third to find the final resultant.
  • This involves resolving into components and then recombining them.

Recap

  • Scalar quantities have magnitude only, like mass.
  • Vector quantities have both magnitude and direction, like velocity.
  • Vectors are represented by arrows.
  • The resultant is the sum of two or more vectors.

Resolving a Vector into Perpendicular Components

  • Resolving a vector is the opposite of finding the resultant.
  • Vectors are often resolved into components perpendicular to each other.
  • This creates x and y components.

Resolving Forces

  • A force can be resolved into components parallel and perpendicular to a given direction.
  • Formulae for the components: Fx = F cos θ, Fy = F sin θ

Practical Applications

  • Pulling a table with a 50 N force at a 30° angle is the same as pulling it up with 25 N and horizontally with 43.3 N.
  • Resolution is essential for calculating components in many applications, including forces.

Calculating Perpendicular Components

  • If a vector has magnitude v making an angle θ with the horizontal
  • Its x-component is v * cos θ
  • Its y-component is v * sin θ

Calculating Perpendicular Components - Problem Example

  • A 15 N force acts on a box at a 60° angle.
  • The horizontal component is 7.5 N.
  • The vertical component is 12.99 N.

Component of Weight

  • When an object is on an incline, the component of weight parallel to the incline is used to find the pulling force required to keep it moving at a constant speed.
  • The component parallel to the incline: weight * sin θ
  • The component perpendicular to the incline: weight * cos θ

Summary of Perpendicular Components

  • If a vector has magnitude ‘v’ and makes an angle θ with the horizontal,
  • the horizontal component = v cos θ
  • the vertical component = v sin θ

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Vectors and Scalars PDF

Description

This quiz covers the fundamental concepts of scalars and vectors in physics. Participants will explore the definitions, examples, and methods for adding vector quantities using vector diagrams and laws. Test your understanding of how scalars and vectors differ, along with their graphical representations.

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