Physics Chapter on Vectors

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Questions and Answers

Which of the following is NOT a vector quantity?

Force

Velocity

Acceleration

Time (correct)

The magnitude of a vector can be negative.

False (B)

What is the name given to the sum of two or more vectors?

Resultant

A vector diagram is represented by an arrow where the of the arrow represents the magnitude and the _ of the arrow represents the direction.

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The resultant of two forces acting in opposite directions is always the difference between the two forces.

True (A) Signup and view all the answers

The process of breaking down a single force into two or more components is called ______ of forces.

resolution Signup and view all the answers

What is the triangle law of vector addition?

The triangle law of vector addition states that if two vectors are represented by two sides of a triangle taken in order, then their resultant is represented by the third side of the triangle taken in the opposite order. Signup and view all the answers

Match the following terms with their definitions:

Scalar Quantity = A quantity that has both magnitude and direction Vector Quantity = A quantity that only has magnitude Resultant = The sum of two or more vectors Resolution of forces = The process of breaking down a single force into two or more components Components = The individual forces that make up a larger force Signup and view all the answers

Which of the following correctly describes a scalar quantity?

Has magnitude only with no direction (C) Signup and view all the answers

Vectors can only add up to a larger magnitude and never a smaller one.

False (B) Signup and view all the answers

What is the resultant of two vectors acting in the same direction, if one is 7N and the other is 3N?

10N Signup and view all the answers

The process of finding the resultant of two vectors involves completing a ______ when they are joined tail to tail.

parallelogram Signup and view all the answers

Match the following vector quantities with their corresponding definitions:

Displacement = Change in position of an object Velocity = Displacement divided by time Acceleration = Rate of change of velocity Force = Push or pull on an object Signup and view all the answers

Study Notes

Scalars

A scalar quantity only has magnitude.
It has no direction.
Examples include length, area, volume, time, and mass.

Vectors

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

Vector Diagrams

Vector diagrams use arrows to represent vectors.
The length of the arrow corresponds to the vector's magnitude.
The direction of the arrow indicates the vector's direction.

Resultant of Two Vectors

The resultant of two vectors is the combined effect of the vectors.
Vectors in the same direction are added.
Vectors in opposite directions are subtracted.

Parallelogram Law

When vectors' tails are joined, complete the parallelogram.
The resultant vector is the diagonal of the parallelogram.

Triangle Law

When two vectors' head to tails are joined, draw the resultant.
Complete the triangle to find the resultant vector.

Resultant of Two Vectors (Example Problem)

A problem shows two forces acting on a body.
The resultant force's magnitude is calculated using the Pythagorean theorem.
Its direction is calculated using the tangent function.

Resultant of Three Vectors (Example Problem)

Another problem calculates a system of three vectors.
First, calculate the resultant of two 5 N forces.
Combine that resultant with the third (10N) force.

Recap

What is a scalar quantity?
Give two examples of scalar quantities.
What is a vector quantity?
Give two examples of vector quantities.
How are vectors represented?
What is the resultant of two vector quantities?
What is the triangle law?
What is the parallelogram law?

Resolving a Vector into Perpendicular Components

Resolving a vector finds its components at right angles.
This process works in reverse to finding the resultant vector.
Components are typically determined into the x and y-axis.

Resolving a Force into Components

A force can be resolved into components perpendicular to each other.
These components are determined using trigonometry.
The equations for this are presented.

Practical Applications

There's an example of a table being pulled at an angle.
When resolved, the components show the horizontal(x) and vertical(y) forces.
This example shows pulling the table using separate forces in the y and x direction equals the same effect as a single force.

Calculating the Magnitude of Perpendicular Components

Magnitude of the force(v) and the horizontal angle(θ) determine the components.
Calculate the x(horizontal) component and y(vertical) component using x = v Cos θ and y= v Sin θ respectively.

Calculating the Magnitude of Perpendicular Components (Ex. Problem)

A 15N force is at a 60 degree angle from the horizontal.
The horizontal (x) component is found to be 7.5N .
The vertical (y) component is calculated as 12.99N.

2003 HL Section B Q6 (Ramp Problem)

A wheelchair moves up a 10-degree ramp at a constant speed.
The wheelchair weighs 900 N.
Finding the forces parallel and perpendicular to the ramp using Trigonometry.

Summary

If a vector(v) has two components (x and y), the components are calculated at an angle(θ): x = v Cos θ and y = v Sin θ.

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Test your knowledge on vector quantities and their properties with this quiz. Explore topics such as vector addition, the triangle law, and components of forces. Perfect for students studying physics concepts related to forces and motion.