pe topic 1.2 newtons law

Vectors and Scalars

Introduction to Vectors and Scalars

  • Physical quantities encountered daily include time, mass, weight, force, and electric charge.

  • These quantities can be divided into two broad groups: vectors and scalars.

Scalars

  • Scalars are physical quantities with only a number value or magnitude.

  • A scalar tells you how much of something there is.

  • Example: A tub of margarine labeled with a mass of 500g. The mass is a scalar quantity.

  • A scalar is fully described by a magnitude only, represented by a single number.

  • Examples of scalar quantities: speed, volume, mass, temperature, power, energy, and time.

  • Magnitude changes

Vectors

  • Vectors are physical quantities with both magnitude and direction.

  • A vector tells you how much of something there is and which direction it is in.

  • Example: A car traveling east on a freeway at 100 km/h. The velocity is a vector.

    • Magnitude: 100 km/h

    • Direction: East

  • A vector is a quantity that has both a magnitude and a direction.

  • Vector quantities are important in the study of motion.

  • Examples of vector quantities: force, velocity, acceleration, displacement, and momentum.

  • Vector quantities change when:

    • Their magnitude changes.

    • Their direction changes.

    • Both magnitude and direction change.

Difference Between Scalars and Vectors

  • A vector quantity has both direction and magnitude, while a scalar has only magnitude.

  • Identify a vector by the presence of an associated direction.

  • Example: Speed is a scalar, while velocity is a vector that specifies both direction and magnitude.

  • Speed is the magnitude of velocity. A car with a velocity of 40 mph east has a speed of 40 mph.

How to Draw a Vector

  • A vector is drawn as an arrow with a head and a tail.

  • The magnitude is often represented by the length of the arrow.

  • The arrow points in the direction of the vector.

How to Write a Vector

  • Vectors are generally written as boldface letters or with an arrow over the top of the letter.

Scalar or Vector Examples

  • "The football player was running 10 miles an hour towards the end zone" - This is a vector representing velocity with magnitude (10 mph) and direction (towards the end zone).

  • "The car accelerated north at a rate of 4 meters per second squared" - This is a vector with both direction and magnitude; acceleration is a vector quantity.

  • "The volume of that box at the west side of the building is 14 cubic feet" - This is a scalar. The location of the box is irrelevant to the volume's direction.

Average Speed Calculation

  • For an object moving in a straight line at a steady speed, average speed can be calculated with the formula:
    Average[space]speed=Distance[space]movedTime[space]takenAverage[space]speed = \frac{Distance[space]moved}{Time[space]taken}

  • Units:

    • Average speed: meters per second (m/s)

    • Distance moved: meters (m)

    • Time taken: seconds (s)

  • Example: A sprinter travels 200m in 24s. Their average speed is 200÷24=8.33m/s200 ÷ 24 = 8.33 m/s

Homework

  • Look up and write out the equation for acceleration and deceleration.

Newton's First Law of Motion

  • An object at rest stays at rest, and an object in motion stays in motion with constant speed and direction, unless acted upon by an external unbalanced force.

  • A body at rest will remain at rest unless an outside force acts on it, and a body in motion at a constant velocity will remain in motion in a straight line unless acted upon by an outside force.

Newton's Second Law of Motion

  • Force equals mass times acceleration: F=maF = ma

  • The rate of change of momentum is directly proportional to the force applied and takes place in the direction of the force.

  • Acceleration: A measurement of how quickly an object is changing speed.

  • The acceleration of an object depends directly upon the net force acting upon the object and inversely upon the mass of the object.

  • As the force acting upon an object increases, the acceleration increases. As the mass of an object increases, the acceleration decreases.

  • When a pitcher throws a baseball, the harder he throws, the more the ball accelerates. The mass of the ball stays the same, but the force increases.

Newton's Third Law of Motion

  • For every action, there is an equal and opposite reaction.

  • When a body exerts force on another body, the second body will exert an equal force on the first body.

  • In every interaction, there is a pair of forces acting on the two interacting objects.

  • The size of the forces on the first object equals the size of the force on the second object.

  • The direction of the force on the first object is opposite to the direction of the force on the second object.

  • Forces always come in pairs - equal and opposite action-reaction force pairs.

Force

  • A force is a push or a pull that acts upon an object as a result of its interaction with another object.

  • Forces result from interactions.

Introduction to Vectors and Scalars

Physical quantities encountered daily include time, mass, weight, force, and electric charge. These quantities can be divided into two broad groups: vectors and scalars.

Scalars

Scalars are physical quantities with only a number value or magnitude. A scalar tells you how much of something there is. For example, a tub of margarine labeled with a mass of 500g specifies the mass, which is a scalar quantity. A scalar is fully described by a magnitude only, represented by a single number.

Examples of scalar quantities:

  • Speed: The rate at which an object covers distance, independent of direction.

  • Volume: The amount of three-dimensional space occupied by a substance.

  • Mass: The amount of matter in an object, measured in kilograms or grams.

  • Temperature: A measure of the average kinetic energy of particles in a substance, usually expressed in degrees Celsius or Fahrenheit.

  • Power: The rate at which work is done or energy is transferred, commonly measured in watts.

  • Energy: The capacity to do work, with units such as joules or calories.

  • Time: A measure of the ongoing sequence of events, usually expressed in seconds, minutes, or hours.

Magnitude Changes: Changes in the value of a scalar quantity will directly affect its measurement, for instance, increasing the mass results in a higher scalar value.

Vectors

Vectors are physical quantities with both magnitude and direction. A vector tells you how much of something there is and which direction it is in. For example, a car traveling east on a freeway at 100 km/h indicates both its speed and direction, making velocity a vector.

  • Magnitude: 100 km/h

  • Direction: East

A vector is defined as a quantity that has both a magnitude and a direction, which is crucial in the study of motion. Examples of vector quantities:

  • Force: Any interaction that, when unopposed, will change the motion of an object.

  • Velocity: The speed of an object in a specific direction.

  • Acceleration: The rate at which an object changes its velocity.

  • Displacement: The shortest distance from the initial to the final position of an object, including direction.

  • Momentum: The quantity of motion an object has, depending on its mass and velocity.

Vector quantities change when:

  • Their magnitude changes.

  • Their direction changes.

  • Both magnitude and direction change.

Difference Between Scalars and Vectors

A vector quantity has both direction and magnitude, while a scalar has only magnitude. You can identify a vector by its associated direction. For example, speed is a scalar, while velocity is a vector that specifies both direction and magnitude. In this case, speed represents the magnitude of velocity. A car with a velocity of 40 mph east has a speed of 40 mph but must also indicate the direction to be accurately described.

How to Draw a Vector

A vector is graphically represented as an arrow. The characteristics of arrows that indicate vectors are as follows:

  • Head: Indicates the direction of the vector.

  • Tail: The starting point of the vector.

  • Length: Represents the magnitude of the vector; a longer arrow signifies a greater magnitude.

How to Write a Vector

Vectors are generally written using boldface letters (e.g., v) or with an arrow over the top of the letter (e.g., (
ightarrow v )).

Scalar or Vector Examples

  • "The football player was running 10 miles an hour towards the end zone" - This is a vector representing velocity with magnitude (10 mph) and direction (towards the end zone).

  • "The car accelerated north at a rate of 4 meters per second squared" - This is a vector illustrating acceleration which includes both direction and magnitude.

  • "The volume of that box at the west side of the building is 14 cubic feet" - This is a scalar. The box's location is irrelevant to the volume's direction.

Average Speed Calculation

For an object moving in a straight line at a steady speed, average speed can be calculated with the formula:

Average speed=Distance movedTime takenAverage\, speed = \frac{Distance\, moved}{Time\, taken}

Units:

  • Average speed: meters per second (m/s)

  • Distance moved: meters (m)

  • Time taken: seconds (s)

Example: A sprinter travels 200m in 24s. Their average speed is 200÷24=8.33m/s200 \div 24 = 8.33 m/s

Homework

Look up and write out the equation for acceleration and deceleration.

Newton's First Law of Motion

An object at rest stays at rest, and an object in motion stays in motion with constant speed and direction unless acted upon by an external unbalanced force. This means that a body at rest will remain at rest unless acted upon by an outside force, while a body in motion will maintain its velocity in a straight line unless an external force is applied.

Newton's Second Law of Motion

Force equals mass times acceleration: F=maF = ma. The acceleration of an object is directly proportional to the net force acting upon it and takes place in the direction of the force. Acceleration measures how quickly an object is changing speed.

The acceleration of an object depends directly upon the net force acting upon it and inversely upon the mass of the object. Therefore, as the force acting upon an object increases, the acceleration increases, while an increase in the object’s mass decreases its acceleration.

For example, when a pitcher throws a baseball, the harder he throws (increasing force), the more the ball accelerates. The mass of the ball remains constant, but the force applied increases.

Newton's Third Law of Motion

For every action, there is an equal and opposite reaction. When a body exerts force on another body, the second body will exert an equal force on the first body. In every interaction, there exists a pair of forces acting on two interacting objects. The size of the force on the first object equals the size of the force on the second object, while their directions are opposite to each other. Forces always come in pairs - they consist of equal and opposite action-reaction force pairs.

Force

A force is a push or a pull that acts upon an object as a result of its interaction with another object. Forces are fundamentally interactions that can cause an object to accelerate, decelerate, or change direction. They can also result in deformation of the object depending on the magnitude of the