Motion and Energy

Isaac Newton

English mathematician, physicist, and astronomer from 17th-18th centuries who developed the three laws of motion forming the foundation of classical mechanics

Newton's Three Laws of Motion

Law of Inertia (First Law), Law of Acceleration (Second Law), Law of Action and Reaction (Third Law)

Inertia

The tendency of an object to resist changes in its state of motion; objects with greater mass have greater inertia

Newton's First Law (Law of Inertia)

A body at rest will remain at rest and a body in motion will remain in motion unless acted upon by an outside unbalanced force

Is inertia a force?

No, inertia is not a force; it is the tendency or resistance of an object to changes in motion; mass is a measure of inertia

Balanced Forces

Forces acting on an object in such a way that the net force equals zero; result in no change in motion

What happens when balanced forces act on an object at rest?

The object remains at rest because the net force is zero

What happens when balanced forces act on a moving object?

The object continues to move at the same velocity (same speed and direction) because the net force is zero

Example of balanced forces

A book sitting on a table: gravity pulls it down and normal force from table pushes up with equal force; net force is zero so book remains at rest

Unbalanced Forces

Forces acting on an object that do not cancel out, resulting in a net force that is not zero; cause objects to accelerate

What is the result of unbalanced forces?

Unbalanced forces cause an object to accelerate, meaning it changes velocity, direction, or both

Real-world example of unbalanced forces (tug-of-war)

In a tug-of-war, if one team pulls harder than the other, the rope accelerates toward the stronger team because unbalanced forces act on it

Soccer Ball example (First Law)

A soccer ball remains stationary until someone kicks it; the kick applies an unbalanced force causing the ball to move; friction eventually stops it

Tug of War example (First Law)

Both teams pulling with equal force = balanced forces and rope does not move; one team pulling harder = unbalanced forces and rope accelerates toward stronger team

Locomotive example (First Law)

A locomotive at rest remains at rest until the engine provides force to move it; once moving, it continues until brakes apply an unbalanced force to stop it

Seatbelts in Cars example (First Law)

When a car suddenly stops, passengers experience inertia and continue moving forward; seatbelt applies an unbalanced force to stop the passengers' motion

Book Sliding on a Table example (First Law)

Pushing a book applies an unbalanced force causing it to accelerate; stopping the push allows friction to decelerate and stop the book

Throwing a Ball Upward example (First Law)

Throwing applies an unbalanced force causing upward acceleration; once released, gravity applies downward unbalanced force causing deceleration, then acceleration back down

Bug on Windshield example (First Law)

Bug experiences unbalanced force from windshield and stops suddenly; car does not feel much change because car's mass is much greater than bug's mass

Rocket in Space example (First Law)

A rocket with no forces acting on it continues moving at constant velocity forever; must fire engines to apply unbalanced force to change direction or speed

Acceleration

A measurement of how quickly an object is changing speed; also includes changes in direction, not just speed

Is acceleration only about speed changes?

No; acceleration refers to any change in velocity, including changes in speed or changes in direction

Can an object accelerate at constant speed?

Yes, if the object is changing direction; a car driving around a circular track at constant speed is still accelerating because direction is changing

Units of acceleration

Meters per second squared (m/s²)

How is acceleration different from speed?

Speed is how fast an object is moving; acceleration is how quickly the speed is changing or how quickly the direction is changing

Newton's Second Law (Law of Acceleration)

Force equals mass times acceleration (F = ma); defines the quantitative relationship between force, mass, and acceleration

Net Force (Fnet)

The sum total and direction of all forces acting on an object; determines whether the object will accelerate and in what direction

How do you calculate net force?

Add all forces acting on the object taking direction into account; forces in same direction add together; forces in opposite directions subtract from each other

What does net force equals zero mean?

The object will not accelerate; it remains at rest or continues moving at constant velocity

What does net force not equal zero mean?

The object will accelerate in the direction of the net force

Net force calculation example

54 N pushing right and 18 N pushing left: net force = 54 N - 18 N = 36 N directed toward the right

Mass

Measurement of how difficult it is to change an object's velocity; a measure of inertia

How does mass relate to inertia?

Mass and inertia are directly related; greater mass means greater inertia; objects with more mass are harder to accelerate or decelerate

How is mass different from weight?

Mass is a measure of the amount of matter and how difficult it is to change motion; weight is the force of gravity on an object; mass stays same everywhere; weight changes with gravity

If mass increases while force stays same, what happens to acceleration?

Acceleration decreases; since F = ma, if F stays constant and m increases, then a must decrease

Weight

The force of gravity on an object; equal to mass times the acceleration due to gravity (W = mg)

How do you calculate weight?

Weight = mass × acceleration due to gravity; W = mg where g = 9.8 m/s² on Earth

Does weight change on different planets?

Yes, weight changes on different planets because acceleration due to gravity is different; however mass stays the same everywhere

Relationship between mass and weight

Weight = mass × acceleration due to gravity (W = mg); weight is a force caused by gravity acting on mass

Weight calculation example

If object has mass of 10 kg on Earth: W = mg = 10 kg × 9.8 m/s² = 98 N

Force (in context of F = ma)

Force is measured in Newtons (N) = mass (kg) × acceleration (m/s²); or 1 Newton = 1 kg × m/s²

What does F = ma mean?

Force equals mass times acceleration; shows the quantitative relationship between force, mass, and acceleration

If mass doubles while force stays constant, what happens to acceleration?

Acceleration is cut in half; since F = ma, if m doubles and F stays constant, then a is divided by 2

If acceleration doubles while mass stays constant, what happens to force?

Force doubles; since F = ma, if a doubles and m stays constant, then F doubles

Small Force = Small Acceleration meaning

A smaller force applied to an object produces smaller acceleration; with same mass, smaller force results in smaller change in velocity

Large Force = Large Acceleration meaning

A larger force applied to an object produces larger acceleration; with same mass, larger force results in larger change in velocity

What happens when same force applies to two different masses?

Object with smaller mass accelerates more than object with larger mass; because a = F/m, if F is same but m is different, smaller m gives larger a

Different masses and acceleration to Earth

Different masses accelerate to Earth at same rate (9.8 m/s²), but hit ground with different forces; because F = ma, same acceleration with different masses produces different forces

F = ma Problem Example 1

How much force to move 10 kg cart with 3 m/s² acceleration? F = m × a = 10 kg × 3 m/s² = 30 N

F = ma Problem Example 2

4 N force on 0.5 kg toy car, what is acceleration? a = F/m = 4 N / 0.5 kg = 8 m/s²

F = ma Problem Example 3

Object accelerates at 2 m/s² with 50 N force, what is mass? m = F/a = 50 N / 2 m/s² = 25 kg

Equipment Cart with Friction Problem

12 kg cart pushed with 54 N, friction 18 N: net force = 54 N - 18 N = 36 N; acceleration = 36 N / 12 kg = 3 m/s²

Newton's Second Law: Vehicles comparison

Small car experiences larger acceleration than large truck with same force applied because car has less mass; truck requires more force to achieve same acceleration

Newton's Second Law: Falling Objects

All objects fall to Earth at same acceleration (9.8 m/s²) because although weights differ due to different masses, the ratio of force to mass (F/m = a) remains constant

Newton's Second Law: Bikes and Pushing

Push bike with small force = slow acceleration; push twice as hard = twice as much acceleration

Newton's Third Law (Law of Action and Reaction)

For every action there is an equal and opposite reaction; describes the relationship between two forces in an interaction

Action Force

One force in an interaction between two objects

Reaction Force

The equal and opposite force that results from the action force

Do action and reaction forces act on same object?

No; the action force acts on one object and the reaction force acts on the other object in the interaction

Can action and reaction forces cancel each other out?

No, because they act on different objects; forces can only cancel if they act on same object

Are action and reaction forces simultaneous?

Yes, they occur at the same time (simultaneously)

Key characteristics of Newton's Third Law forces

Neither force exists without the other; they are equal in strength; they are opposite in direction; they occur at the same time

How to identify an action-reaction pair

When action is A exerts force on B, the reaction is B exerts force on A; must be equal strength and opposite direction

Tire and Road example (Third Law)

Action: tire pushes road backward; Reaction: road pushes tire forward; equal opposite forces allow car to move forward

Why can car move forward if forces are equal and opposite?

Action force (tire pushing road) and reaction force (road pushing tire) act on different objects; reaction force acts on car pushing it forward while action force on road which doesn't visibly move due to massive mass

Rocket and Gas example (Third Law)

Action: rocket pushes exhaust gases backward; Reaction: gas pushes rocket forward (thrust); rockets in space operate by pushing exhaust and exhaust pushing rocket forward

Gravitational Interaction example (Third Law)

Action: Earth pulls ball downward with gravitational force; Reaction: ball pulls Earth upward with equal gravitational force

Why doesn't Earth accelerate upward when ball falls?

Earth is pulled upward by ball with same force that pulls ball downward; however Earth's mass is so much greater than ball's that using a = F/m, Earth's acceleration is imperceptibly small

Swimmer and Water example (Third Law)

Action: swimmer pushes water backward; Reaction: water exerts force on swimmer forward, propelling swimmer forward

Falling Object and Rising Balloon example (Third Law)

Action: air rushes out of balloon in downward direction; Reaction: balloon goes up

Key principle of forces and interactions

When you push on wall, wall pushes on you

Chair and You example

Gravity pulls you down in seat; by Newton's Third Law seat pushes up against you with equal force; forces are balanced so you are not moving

If gravity pulls down and chair pushes up with equal force why aren't you moving?

Because forces are balanced (equal magnitude but opposite direction), resulting in net force of zero; by First Law with zero net force you remain at rest

When you sit in chair, does chair push on you?

Yes, by Newton's Third Law if you push down on chair with force (due to your weight), chair pushes up on you with equal and opposite force

Skateboard and Wall example

When you push on wall while on skateboard, you slide in opposite direction (away from wall) because you push on wall but wall pushes back with equal and opposite force

Why do you slide backward when pushing wall on skateboard?

You push on wall (action) and wall pushes back with equal and opposite force (reaction); on frictionless surface this force accelerates you away from wall

Why does it hurt when you stub your toe?

When toe exerts force on rock, rock exerts equal force back on toe; harder you hit your toe against it, more force rock exerts back and more pain you experience

Punching a Wall example (Third Law)

If you punch wall with strong force, it punches you back with same force; that's why it hurts

Walking example (Third Law)

You push backward on ground (action); ground pushes forward on you (reaction), propelling you forward

Jumping example (Third Law)

You push downward and backward on ground (action); ground pushes upward and forward on you (reaction), launching you into air

Swimming example (Third Law)

Swimmer pushes water backward (action); water pushes swimmer forward (reaction)

Birds Flying example (Third Law)

Bird pushes air downward and backward with wings (action); air pushes bird upward and forward (reaction)

Rocket Propulsion example (Third Law)

Rocket engine expels hot gases downward and backward (action); gases push rocket upward and forward with thrust (reaction)

Throwing a Ball example (Third Law)

Your hand pushes ball forward (action); ball pushes your hand backward (reaction); you feel this as resistance

Car Acceleration example (Third Law)

Car's engine makes tires push backward on road (action); road pushes forward on tires (reaction), accelerating car forward

Nail and Hammer example (Third Law)

Action: hammer pushes nail forward; Reaction: nail pushes hammer backward; hammer and nail exert equal and opposite forces on each other

If acceleration of object is zero, does this mean no forces act on it?

No, it means forces acting on it are balanced and net force is zero; gravity and normal force act on stationary objects

Basketball player dribbling question

Ball falls and bounces up; yes, force is required because it changed direction = acceleration = force required; agent was the floor

If you know acceleration is zero, does this mean no forces act on it?

No, it means forces are balanced; stationary object has no acceleration but is subject to balanced forces (gravity down, normal force up)

Kicking football contradiction

Action force acts on ball causing it to accelerate; reaction force acts on your foot; forces act on different objects so they don't cancel; tell friend you can't cancel force on ball with force on your foot

Earth pulls on moon question

Yes, moon pulls on Earth with same force that Earth pulls on moon; forces are equal just like distances between New York and San Francisco are same either direction; asking which is stronger doesn't make sense

Dribbling basketball and bounce question

When ball bounces it changes direction; change in direction = acceleration; acceleration requires a force; the agent applying force was the floor

Summary: Newton's First Law

A body at rest will remain at rest and a body in motion will remain in motion unless acted upon by an outside unbalanced force

Summary: Newton's Second Law

Force equals mass times acceleration (F = ma); acceleration of object is directly proportional to net force applied and inversely proportional to its mass

Summary: Newton's Third Law

For every action there is an equal and opposite reaction; when two objects interact they exert equal and opposite forces on each other simultaneously

Key Formula: F = ma

F = Force (Newtons), m = mass (kilograms), a = acceleration (meters per second squared)

Key Formula: W = mg

W = Weight (Newtons), m = mass (kilograms), g = acceleration due to gravity (9.8 m/s² on Earth)

Newton Unit Definition

1 Newton = 1 kg × m/s²

Practice Question 1: Force Interaction

A force interaction requires at least a pair of forces

Practice Question 2: Zero Acceleration

When object has zero acceleration, the forces acting on it are balanced and the net force is zero