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What is the resultant force when two forces of 10 N are acting in opposite directions?
What is the resultant force when two forces of 10 N are acting in opposite directions?
A scalar quantity, such as mass, requires direction to determine its magnitude.
A scalar quantity, such as mass, requires direction to determine its magnitude.
False
What is the angle of the resultant force when two forces of 10 N are acting at 90° to each other?
What is the angle of the resultant force when two forces of 10 N are acting at 90° to each other?
45°
The ___________ vector is the single vector that produces the same effect in both magnitude and direction as the original set of vectors.
The ___________ vector is the single vector that produces the same effect in both magnitude and direction as the original set of vectors.
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Match the following forces with their resultant:
Match the following forces with their resultant:
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When two forces of 10 N are acting at 30° to each other, what is the magnitude of the resultant force?
When two forces of 10 N are acting at 30° to each other, what is the magnitude of the resultant force?
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Velocity is a vector quantity that includes direction.
Velocity is a vector quantity that includes direction.
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What is the resultant magnitude of the girl's displacement?
What is the resultant magnitude of the girl's displacement?
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The resultant of two forces acting at an angle of 30° to each other has a resultant magnitude of __________ N.
The resultant of two forces acting at an angle of 30° to each other has a resultant magnitude of __________ N.
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The total distance traveled by the girl is 10.00 blocks.
The total distance traveled by the girl is 10.00 blocks.
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What is the direction of the resultant displacement?
What is the direction of the resultant displacement?
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The resultant vector combines multiple vectors using the __________ law of vector addition.
The resultant vector combines multiple vectors using the __________ law of vector addition.
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Match the vector quantities with their descriptions:
Match the vector quantities with their descriptions:
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What would be the next step after determining the angle from the tangent function to find the resultant direction?
What would be the next step after determining the angle from the tangent function to find the resultant direction?
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Calculate the value of R for R² = 25.00.
Calculate the value of R for R² = 25.00.
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What is the formula to find the vertical component Y of a vector F at an angle q?
What is the formula to find the vertical component Y of a vector F at an angle q?
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The horizontal component X of a vector F is found using the sine function.
The horizontal component X of a vector F is found using the sine function.
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When resolving a weight vector W on an inclined plane, what is the component of the weight parallel to the plane called?
When resolving a weight vector W on an inclined plane, what is the component of the weight parallel to the plane called?
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To calculate the size of the horizontal component X of vector F, use the formula X = F ______ q.
To calculate the size of the horizontal component X of vector F, use the formula X = F ______ q.
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Match the following components with their formulas:
Match the following components with their formulas:
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Which function is used to find the size of the vertical component of a vector at an angle?
Which function is used to find the size of the vertical component of a vector at an angle?
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The components Y and X are perpendicular to each other.
The components Y and X are perpendicular to each other.
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What is the formula for the component of weight W that is perpendicular to an inclined plane?
What is the formula for the component of weight W that is perpendicular to an inclined plane?
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The result of combining coplanar vectors is called the ______.
The result of combining coplanar vectors is called the ______.
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In the context of vectors on an inclined plane, what does the component P represent?
In the context of vectors on an inclined plane, what does the component P represent?
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What is the vertical component of the 6N force acting at an angle of 27° to the horizontal?
What is the vertical component of the 6N force acting at an angle of 27° to the horizontal?
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The total horizontal force is 6N.
The total horizontal force is 6N.
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What is the resultant force found using Pythagoras's theorem in the example?
What is the resultant force found using Pythagoras's theorem in the example?
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To find the horizontal component of the 6N force, we use ________.
To find the horizontal component of the 6N force, we use ________.
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Match the types of forces to their corresponding values:
Match the types of forces to their corresponding values:
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What trigonometric function is used to calculate the vertical component of a vector?
What trigonometric function is used to calculate the vertical component of a vector?
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The resultant direction is found using only Pythagoras's theorem.
The resultant direction is found using only Pythagoras's theorem.
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What is the angle of the given force relative to the horizontal?
What is the angle of the given force relative to the horizontal?
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The total vertical force is calculated by adding ________ and ________.
The total vertical force is calculated by adding ________ and ________.
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What method is used to resolve coplanar vectors into their components?
What method is used to resolve coplanar vectors into their components?
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What does the Triangle law of vector addition describe?
What does the Triangle law of vector addition describe?
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According to the Triangle law, the resultant vector always starts at the origin of the first vector.
According to the Triangle law, the resultant vector always starts at the origin of the first vector.
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What is the terminal point in the context of the Triangle law of vector addition?
What is the terminal point in the context of the Triangle law of vector addition?
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The two vectors are drawn such that the terminal point of one vector joins the ______ of the other.
The two vectors are drawn such that the terminal point of one vector joins the ______ of the other.
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Match the following terms with their descriptions:
Match the following terms with their descriptions:
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Which of the following statements is true regarding the Triangle law of vector addition?
Which of the following statements is true regarding the Triangle law of vector addition?
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The resultant vector can be determined without drawing the vectors.
The resultant vector can be determined without drawing the vectors.
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Explain briefly what is meant by 'two vectors trailing each other.'
Explain briefly what is meant by 'two vectors trailing each other.'
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In the Triangle law of vector addition, the resultant vector is represented by the line that joins the ______ of the first vector to the terminal point of the second vector.
In the Triangle law of vector addition, the resultant vector is represented by the line that joins the ______ of the first vector to the terminal point of the second vector.
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What is essential for applying the Triangle law of vector addition?
What is essential for applying the Triangle law of vector addition?
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Study Notes
Scalar and Vector Quantities
- Scalar quantities have only magnitude (size). Examples include temperature, mass, distance, and speed.
- Vector quantities have both magnitude and direction. Examples include displacement, force, velocity, and acceleration.
- A physical quantity is a vector if it has magnitude and direction and obeys vector addition.
- Current is a scalar quantity despite having both magnitude and direction because it doesn't follow vector addition rules.
- Vectors are represented in diagrams by arrows, where the length represents the magnitude and the direction represents the vector's direction.
Defining Vector and Scalar Quantities
- Scalar: a quantity having only magnitude.
- Vector: a quantity having both magnitude and direction.
Sign Convention for Vectors
- Vectors in the same direction are assigned the same sign.
- Vectors in opposite directions have opposite signs.
- In horizontal directions: right is positive, left is negative.
- In vertical directions: up is positive, down is negative.
Adding Vectors
-
Adding vectors in a straight line: Add them algebraically.
- If vectors point in the same direction, add their magnitudes.
- If vectors point in opposite directions, subtract their magnitudes.
-
Adding vectors at an angle: Use the parallelogram or triangle law of vector addition.
- The resultant is the single vector producing the same effect.
Resolving Vectors
- Vector resolution: splitting a single vector into two or more components perpendicular to each other.
- Procedure:
- Draw a sketch of the vector.
- Draw a rectangle with the vector as a diagonal.
- Label the components (usually vertical and horizontal).
- Use trigonometry(Sin, Cos) to determine the size of the components. The angle is relative to the components, so opposite (Sin), or adjacent (Cos)
Combining Coplanar Vectors
- Coplanar vectors: vectors in the same plane.
- To add: resolve them into vertical and horizontal components.
- Resolve each vector into vertical and horizontal components.
- Combine the horizontal components.
- Combine the vertical components.
- Use Pythagorean theorem to find the magnitude of the resultant.
- Use trigonometry to find the direction.
Examples of Vectors
- Horizontal force of 15 N
- Vertical force of 5 N
- Force of 20 N at 30° to the horizontal
Examples of Velocity Vectors
- A velocity of 4 m/s at E 20° S (20° South of East)
- A velocity of 2 m/s due North
- A velocity of 5 m/s at a direction of 40° West of South (S 40° W)
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Description
Explore the fundamental differences between scalar and vector quantities in physics. This quiz covers definitions, examples, and the rules related to scalar and vector quantities. Test your understanding of how these quantities are represented and their significance in physical applications.
