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What is a force?

Newton’sLaws of Motion

General Overview• Three physical laws that describe

relationships between forces acting on a body and that body’s motion.

• Formulated by Sir Isaac Newton, English scientist and mathematician, in 1687.

• Have stood the “test of time”Only two exceptions:– Very fast objects: explained by Einstein’s

Special Theory of Relativity– Very small objects: explained by Theory of

Quantum Mechanics

The Three Laws• First Law of Motion

– An object will maintain its current state of rest or uniform velocity unless acted upon by an unbalanced force

• Second Law of Motion– The acceleration of an object is directly proportional to

the net force exerted upon it and inversely proportional to its mass

• Third Law of Motion– For every action there is an equal and opposite reaction

WAY TOO MANY UNFAMILIAR TERMS!!!

Press the Easy Button!

• First Law of Motion:inertia

• Second Law of Motion:Fnet = ma

• Third Law of Motion:action-reaction

YOU MIGHT STILL NEED A VOCAB LIST!!!

The Vocab Breakdown

• Force: a push or pull on an object

• Rest: not moving

• Velocity: speed in a given direction

• Acceleration: change in velocity

• Uniform: constant, not changing

The Vocab Breakdown

• Net: overall sum, considering different directions

• Mass: amount of matter in an object

• Directly Proportional: as the independent variable increases, the dependent variable increases

• Inversely Proportional: as the independent variable increases, the dependent variable decreases

So… Newton used the force too?!?

NO!!! NOT THAT KIND OF FORCE!

Types of Forces

• Applied Force (Fapp): force which is applied to an object by another object or by a person

• Tension (Ftens): force which is transmitted through a string, rope, or wire when it is pulled tight by forces acting at each end.

• Normal Force (Fnorm): support force exerted upon an object which is in contact with another stable object. Exerted perpendicular to the surface.

Types of Forces

• Friction (Ffric): force exerted by a surface as an object moves across it or makes an effort to move across it. Opposes the motion of the object.

• Air Resistance (Fair): special type of frictional force which acts upon objects as they travel through the air. Opposes the motion of the object.

• Gravitational Force (Fgrav): force with which the earth, moon, or other massive body attracts an object towards itself. By definition, this is the weight of the object.

Newton’s First Law of Motion• An object will maintain its current state of

rest or uniform velocity unless acted upon by an unbalanced force.

• What it means:In the absence of an unbalanced force…– an object at rest will remain at rest– an object in motion will remain in motion at

the same speed and in the same direction

1st Law Examples: Auto Collisions

1st Law Examples: Auto Collisions

• What is the occupant’s state of motion before the collision?– Constant forward velocity

• What is the occupant’s state of motion after the collision without a seatbelt?– Constant forward velocity

• What does a seatbelt provide?– An unbalanced force on the occupant– It decelerates the driver to rest

1st Law Examples: Whiplash• Suppose you are sitting at a stoplight when

you are rear-ended by another car.

• To an onlooker on the sidewalk, what initially happens to your head?– It stays at rest as the car and your body move

forward.– It was at rest and will remain at rest.– An unbalanced force does not act on it until…– the headrest pushes your head forward.

1st Law Examples:The Tablecloth Parlor Trick

TRY THIS AT HOME... with PAPER plates!!!

• Why does it work?

• If the tablecloth is pulled quickly enough, the frictional force is minimal, so the table setting remains practically at rest as the tablecloth is pulled out from underneath.

Inertia• The First Law is often called the Law of Inertia• Inertia is the tendency of an object to maintain

its state of rest or constant velocity

• Inertia is really a measure of MASS– More mass

Greater tendency to stay at rest or in motion– Less mass

Less tendency to stay at rest or in motion

• Which is easier to move from rest: a pebble or a boulder? Which is easier to stop when moving?

So inertia is just weight?!?• Not quite, young grasshopper!• Mass and weight are not the same thing!

• Mass: amount of matter in an object– Measured in kilograms (kg) in metric system– Measured in slugs in English system– Never changes!

• Weight: force of gravity on an object– Measured in Newtons (N) in metric system– Measured in pounds (lbs) in English system– Changes based on location (altitude & planet)

Calculating Weight

• Weight can be calculated very easily from the mass of the object.

weight = mass x acceleration due to gravity

On Earth, acceleration due to gravity is 9.8 m/s2

weight = mass x 9.8 m/s2

Calculating Weight

• Solved Example: What is the weight of a 50 kg high school student?

weight = mass x 9.8 m/s2 equation

weight = 50 kg x 9.8 m/s2 plug & chug

weight = 490 kgm/s2

weight = 490 N answer

Note: 1 N = 1 kgm/s2

Calculating Weight• Try this one on your own! Show all work!• What is the weight of 4 kg sack of

potatoes?

• Solution:weight = mass x 9.8 m/s2 equation

weight = 4 kg x 9.8 m/s2 plug & chug

weight = 39.2 kgm/s2

weight = 39.2 N answer

Newton’s Second Law of Motion

• The acceleration of an object is directly proportional to the net force exerted upon it and inversely proportional to its mass.

• as net force increases, acceleration increases(as long as mass is constant)

Example:– Just you pushes a heavy piano. Piano doesn’t speed

up quickly.– Both you and a partner push the piano. Piano speeds

up quicker.

Newton’s Second Law of Motion

• The acceleration of an object is directly proportional to the net force exerted upon it and inversely proportional to its mass.

• as mass increases, acceleration decreases(as long as force is constant)

Example:– You pull an empty wagon with all your force. Wagon

speeds up quickly.– You pull a wagon loaded with bricks with all your

force. Wagon speeds up slowly.

Newton’s Second Law of Motion• The 2nd Law is expressed as an equation:

Fnet = m·a

where:

Fnet is the net force acting on the objectis measured in newtons (N)

m is the mass of the objectis measured in kilograms (kg)

a is the acceleration of the objectis measured in meters per second squared

(m/s2)

What’s a Net Force?• Sum of forces acting in different

directionsLefts vs. Rights Ups vs. Downs

• How do we know if there’s a net force?The object’s MOTION will tell us!!!– At rest: No net force– Moving at constant velocity: No net force– Accelerating: Net force acts

The easiest way to analyze forces and determine the net force is by drawing!!!

Drawing Forces• We need to diagram both the magnitude and

direction of these forces

– Magnitude: size, amount, how much– Direction: which way is the push or pull

• A force ALWAYS needs both magnitude and direction– INCORRECT: a force of 5 N– CORRECT: a force of 5 N to the right

Drawing Forces

• To draw forces, we use arrows

• These arrows are called “force vectors”

• Length of vector: magnitude of force

• Direction of vector: direction of force

F

5 N right

3 N down

10 N left

Free Body Diagrams

• To diagram ALL the forces acting on an object, we use a FREE BODY DIAGRAM

• Box represents the object

• Arrows represent forces

• Arrows drawn outward from box in direction of force

• Arrows are labeled with name of force

Fapp

Free Body Diagrams• To draw correct FBDs, you need to think about

the forces acting on the object.– This is difficult at first.– Practice makes perfect!

• Key to success: determine if there’s a net force• Remember:

– At rest: No net force– Moving at constant velocity: No net force– Accelerating: Net force acts

Net force is always in the direction of the acceleration!

Free Body Diagrams• Example: What does the FBD for a physics book

resting on the desk look like?• Solution:

Is there a net force? No, the book is at rest.Consider all forces and decide which ones act.– Gravity? YES! Gravity always acts & pulls down.– Applied? NO! Nobody is pushing the book.– Tension? NO! There’s no string, rope, etc.– Friction? NO! It isn’t sliding or trying to slide.– Normal? YES! The desk pushes up on the book.

• So… GRAVITY pulls down & NORMAL FORCE pushes up. Together it looks like…

Fgrav

Fnorm

BUT, PRACTICE

MAKES PERFECT…

Determining Net Force from FBDs

• Add forces in same direction

• Subtract forces in opposite directions

• The VECTOR SUM is the NET FORCE

5 N6 N

2 N1 N

(Net Force)(All Forces)

Determining Net Force from FBDs

• Treat horizontal and vertical forces separately.

5 N4 N

3 N

1 N

(Net Force)(All Forces)

2 N

1 N

Trigonometry is needed to determine a single net force from these two!!!

So, what about Fnet = m·a?

• Working with this equation is a synthesis of 2nd Law knowledge:– First, identify forces acting and draw FBD

• If forces are balanced, Fnet = 0

• If forces are unbalanced, express Fnet as either:– A single force– Vector sum (combination) of of two or more forces

– Second, identify given info from problem– Third, Plug & Chug (you may need to rearrange!)– Finally, express your answer in the correct units!!!

2nd Law Example Problem #1

• Using a rope, you pull your kid brother on a sled across the ice with a force of 75 N. If your brother and the sled have a combined mass of 30 kg, what is the resulting acceleration of the sled? (Ignore friction)

2nd Law Example Problem #1• Identify forces:

– Vertically: Gravity & Normal balance out– Horizontally: Tension only!!!– Net Force? Yes!!! Fnet = Ften

• Identify info:– Ften = 75 N m = 30 kg a = ?

• Plug & Chug:Fnet = m·a75 N = (30 kg)·a (need to rearrange!)a = 75 N / 30 kg

• Answer:a = 2.5 m/s2

Fnorm

Ften

Fgrav

2nd Law Example Problem #2

• You pull your kid brother in wagon with a force of 90 N. The resulting acceleration is only 2 m/s2. If your brother and the wagon have a combined mass of 30 kg, what is the force of friction acting on the wagon?

2nd Law Example Problem #2• Identify forces:

– Vertically: Gravity & Normal balance out– Horizontally: Applied & Friction– Net Force? Fnet = Fapp - Ffric

• Identify info:– Fapp = 90 N m = 30 kg a = 2 m/s2 Ffric = ?

• Plug & Chug:Fnet = m·a90 N – Ffric = (30 kg)·(2 m/s2)90 N – Ffric = 60 NFfric = 90 N – 60 NFfric = 30 N

• Answer:Ffric = 30 N

Fnorm

Ften

Fgrav