Newton’s Laws of Motion

Observation #1 An object at rest remains at rest, unless

something makes it move.

Observation #2 A object in motion continues in motion with

constant velocity, unless something makes

it change its velocity.

Constant velocity = constant speed in the

same direction.

Observation #3 An object will not change its velocity unless a

net external force acts on it.

Combining Observations 1 & 2

An object left alone will not change it’s velocity. Something must cause a change in velocity.

A force is something that causes an acceleration or change in velocity

Change in speed

Change in direction

By definition is a push or a pull

Force SI unit of force is the Newton (N)

1 N = 0.225 lb

1 lb. = 4.448 N

A Force is a Vector

It has a magnitude, measured in N or lbs.

It acts in a particular direction.

Can exist during physical contact (tension,

friction, applied force) = Contact Force

Can exist with NO physical contact, called field

forces(gravitational, electric)= Noncontact Force

Newton’s First Law An object in motion remains in motion in a straight line

and at a constant speed (velocity) or an object at rest

remains at rest, unless acted upon by an external

(unbalanced) force.

TWO conditions and one constraint.

Condition #1 – The object CAN move but must be at a CONSTANT SPEED

Condition #2 – The object is at REST

Constraint – As long as the forces are BALANCED. If all the

forces are balanced the SUM of all the forces is ZERO.

The bottom line: There is NO ACCELERATION in this case AND the

object must be at EQILIBRIUM ( All the forces cancel out).

00 Faccel

Inertia

Another way to say Newton’s First Law is to

say the Law of Inertia

Inertia is the tendency of objects to resist

changes in motion.

The amount of inertia an object has is

determined by its mass.

Quantity of matter, also called MASS.

Italian for “LAZY”.

Unit for MASS = kilogram.

Inertial Reference Frame

Newton’s Law require measurements to be

made in a reference frame that is not

accelerating to be valid. (moving at constant

velocity)

This excludes situations where the rotation of

the Earth is noticeable.

Large air currents and ocean currents.

Long range missiles.

Newton’s First Law – Inertia Examples

Types of Forces

Contact Forces- result from physical contact

between two objects.

Field Forces- (Noncontact) force that can exist

between two objects even in the absence of

physical contact. (Action-at-a-Distance Force)

Common Types of Forces:

Gravitational Force

Normal Force

Frictional Force

Tension Force

Common Forces

Force of gravity

(Fg) pulls straight

down.

Friction (Ff) occurs

between two objects

that can slide against

each other.

It opposes motion.

Common Forces

Normal force (FN) is the

support force from a

surface.

It is called “normal”

because it is always

perpendicular to the

surface.

Tension (FT) is the force in

a rope or string.

The tension is the same

in every part of a rope.

Determining the Force of Gravity

The magnitude of the force of gravity on

something is called the weight.

Is how MASS is effected by gravity

Weight = mass x gravity

g = 9.81 N/kg

NOTE: MASS and WEIGHT are NOT the same thing. MASS never changes.

mgW

What is the weight of an 85.3-kg person on earth? What is the weight of same person on Mars (g=3.2 m/s2)?

NW

NWmgW

MARS 96.272)2.3)(3.85(

94.835)8.9)(3.85(

Equilibrium Model

A system moving at a constant speed (velocity)

or at rest MUST be at “EQUILIBRIUM”. Fnet = 0

According to Newton’s First Law, objects in

equilibrium have a net external force equals 0. ,

Δv = 0 , ∑ F = 0

TIPS for solving problems:

• Draw a free body diagram

• Resolve anything into COMPONENTS

• Write equations of equilibrium

• Solve for unknowns

Determining Net External Force

The net external force is the sum of all the

forces acting on the object.

Since forces are vectors, we must use

vector addition to find the sum, or resultant.

Free-body diagrams are useful for

determining the net force acting on an

object.

Free-Body Diagram

Free-body diagrams consider just one object and the forces that act on it.

To draw a free body diagram

Draw a dot to represent the object.

Draw and label vector arrows representing all the forces acting on the object.

All the vectors should be shown as acting at a single point.

A pictorial representation of forces complete with labels.

W1,Fg1 or m1g

•Weight(mg) – Always

drawn from the center,

straight down

•Force Normal(FN) – A

surface force always drawn

perpendicular to a surface.

•Tension(T or FT) – force in

ropes and always drawn

AWAY from object.

•Friction(Ff)- Always drawn

opposing the motion. m2g

T

T

FN

Ff

Free Body Diagrams

mg

FN Ff

Free Body Diagrams

Fa

A 10-kg box is being pulled across the table to

the right at a constant speed with a force of 50N.

a) Calculate the Force of Friction

a) Calculate the Force Normal

mg

FN

Fa Ff

NFF fa 50

NFmg n 98)8.9)(10(

Example

Suppose the same box is now pulled at an angle

of 30 degrees above the horizontal.

a) Calculate the Force of Friction

b) Calculate the Force Normal

mg

FN Fa

Ff 30

NFF

NFF

axf

aax

3.43

3.4330cos50cos

Fax

Fay

NF

FmgF

mgFF

mgF

N

ayN

ayN

N

73

30sin50)8.9)(10(

!

Example

"The acceleration of an object is directly proportional

to the NET FORCE AND inversely proportional to the

mass."

ma

Fa NET

1

Acceleration is directly proportional to the NET

Force.

DIRECTLY = They do the same thing. If the force

increases, the acceleration increases. If the force

decreases, the acceleration decreases.

Acceleration is inversely proportional to the mass.

INVERSELY = They do the opposite.

If the mass decreases, the acceleration will

increase. If the mass increases, the acceleration

will decrease.

Newton’s Second Law )(amF

Newton’s 2nd Law

N.S.L. works based on these

direct and inverse

relationships. As 2 of the

variable change, ONE of them

must remain constant.

If the force is constant, the

acceleration and mass change

as shown above.

F(net)=ma

2F=m(2a)

3F=m(3a)

If we add a second dog pulling with

100N just like the first dog, we

could pull the sled with twice the

acceleration, provided the mass of

the sled was constant.

Putting it all Together

NETFa m

a1

0

Force Total

NET

NET

NETNET

F

FF

maFm

Fa

10 N 3 N

Magnitude of FNET=

Direction =

Acceleration =

7 N

RIGHT

10 kg

0.70 m/s2

1. Draw a free body diagram

2. Break vectors into components if needed

3. Find the NET force by adding and subtracting

forces that are on the same axis as the

acceleration.

4. Set net force equal to “ma” this is called

writing an EQUATION OF MOTION.

NOTE: To avoid negative numbers, always

subtract the smaller forces from the larger one.

Newton’s 2nd Law Tips

Example An elevator with a mass of 2000 kg rises with an

acceleration of 1.0 m/s2. What is the tension in the

supporting cable?

mg

T

T

T

mgmaT

mamgT

maFNET

)8.9)(2000()1)(2000(

Equation of Motion

21,600 N

Example A 50 N applied force drags an 8.16 kg log to the right

across a horizontal surface. What is the acceleration of the log if the force of friction is 40.0 N?

50 N 40 N

mg

Fn a

a

a

a

maFF

maF

fa

NET

16.810

16.84050

1.23 m/s2

Example A sled is being accelerated to the right at a rate of 1.5

m/s2 by a rope at a 33 degree angle above the + x . Calculate the Frictional Force if the mass of the sled is 66 kg and the tension in the rope is 150 N.

mg

FN

Ff

Tcos

Tsin

f

f

f

f

NET

F

F

FmaT

maFT

maF

)5.1)(66(33cos150

cos

cos

26.8 N

Newton’s Third Law “For every action there is an EQUAL and

OPPOSITE reaction.

This law focuses on action/reaction pairs

(forces)

They NEVER cancel out

All you do is SWITCH the wording!

•PERSON on WALL

•WALL on PERSON

Newton’s Third Law This figure shows the force during a

collision between a truck and a train.

You can clearly see the forces are

EQUAL and OPPOSITE. To help you

understand the law better, look at

this situation from the point of view

of Newton’s Second Law.

TrainTrainTruckTruck

TrainTruck

aMAm

FF

There is a balance between the mass and acceleration.

One object usually has a LARGE MASS and a SMALL

ACCELERATION, while the other has a SMALL MASS

(comparatively) and a LARGE ACCELERATION.

Newton’s 3rd Law Examples

Action: HAMMER HITS NAIL

Reaction: NAIL HITS HAMMER

Action: Earth pulls on YOU

Reaction: YOU pull on the earth

Newton’s Law of Gravitation

What causes YOU to be pulled down? THE

EARTH….or more specifically…the EARTH’S

MASS. Anything that has MASS has a gravitational

pull towards it.

MmFgWhat the proportionality above is

saying is that for there to be a

FORCE DUE TO GRAVITY on

something there must be at least 2

masses involved, where one is

larger than the other.

Newton’s Law of Gravitation

As you move AWAY from the

earth, your DISTANCE increases

and your FORCE DUE TO

GRAVITY decrease. This is a

special INVERSE relationship

called an Inverse-Square.

2

1

rFg

The “r” stands for SEPARATION

DISTANCE and is the distance between

the CENTERS OF MASS of the 2 objects.

We us the symbol “r” as it symbolizes the

radius. Gravitation is closely related to

circular motion as you will discover later.

N.L.o.G – Putting it all Together

2

21

2

211

2

21

1067.6

Constant nalGravitatio UniversalG

alityproportion ofconstant

r

mmGF

kgNmxG

G

r

mmF

g

g

earth eLEAVING th areyou when thisUse

earth on the areyou when thisUse

2

21

r

mmGF

mgF

g

g

Try this!

earth eLEAVING th areyou when thisUse

earth on the areyou when thisUse

2

21

r

mmGF

mgF

g

g

mxr

kgxM

r

MGg

r

MmGmg

6

24

2

2

1037.6 Earth theof radius

1097.5Earth theof Mass

Let’s set the 2 equations equal to each other since they BOTH

represent your weight or force due to gravity

SOLVE FOR g!

2

26

2411

/81.9)1037.6(

)1097.5)(1067.6(sm

x

xxg

Which has more force?

When the boxer hits the bag, which has more

force, the boxer on the bag or the bag on the

boxer?

Newton’s Third Law

If an object, A, pulls or pushes on an object,

B, then B also pulls or pushes on A. The

force on each object has the same

magnitude, but the forces are oppositely

directed.

Action-Reaction Pairs

Action-Reaction Pairs

A pair of forces

between two objects

is called an action-

reaction pair.

Newton’s Laws Simplified

Force is required to cause an acceleration.

Force = mass x acceleration

All forces come in pairs.

Constant Force Model vs. Equilibrium

Model

Equilibrium

∑F = 0.

Object will be at rest or

move with constant

velocity.

Position vs. time graph-

Constant Force

∑ F = constant.

Object will accelerate in

the direction of the net

force.

Position vs. time graph-

Normal Force Normal Force (FN) if one component of a

force that a surface exerts on an object with

which it is in contact, perpendicular to the

surface

Block on table, block’s weight pushes down on

table, the table pushes back up on block

Follows Newton’s 3rd Law, for every action

there is an opposite reaction

Size of FN indicates how hard two object press

against each other

If object is resting on horizontal surface and no

other forces act, then FN = W

Tension Force

Force often applied by means of cables or

ropes that are used to pull an object (FT)

Tension is often defined as the tendency of a

rope or a cable to be pulled apart

FT of a rope that is pulling an object is the

same size as the force being applied to

the object being pulled

Assume rope is massless, tension can be

transmitted undiminished through rope unless

stated otherwise (then tension would be different

along different areas of the rope)

Frictional Forces

Frictional forces

oppose the applied

force.

They act in the

opposite direction of

the motion

Two Types of Friction

Static

Kinetic

F Applied F Friction

Static Friction

Static friction (Fs) is the frictional force that acts on a static (nonmoving) object.

When an object is not moving, the frictional force will equal the applied force but be in the opposite direction.

Fs= - Fapplied

F Applied FS

Static Friction

There is a maximum amount of static friction, Fs,max .

Once the applied force exceeds Fs,max the object breaks free and begins moving.

F Applied FS

Kinetic Friction

Kinetic friction is the

frictional force on a

moving object.

The force of kinetic

friction is less than

the maximum static

friction.

The net force on a

moving object is

equal to Fapplied - Fk

F Applied FK

Force of Friction

The Force of Friction

is directly related to

the Normal Force.

Mostly due to the

fact that BOTH

are surface

forces

Nkkf

Nssf

Nf

FF

FF

FF

friction oft coefficien

alityproportion ofconstant

Note: Friction ONLY depends on the MATERIALS

sliding against each other, NOT on surface area.

The coefficient of

friction is a unit less

constant that is

specific to the

material type and

usually less than

one.

Friction & Newton’s 1st Law If the coefficient of kinetic friction between a 35-kg crate

and the floor is 0.30, what horizontal force is required to

move the crate to the right at a constant speed across the

floor?

mg

Fn

Fa

Ff

(0.30)(35)(9.8)

a f f k N

a k N

N

a k

a

a

F F F F

F F

F mg

F mg

F

F

102.9 N

Friction & Newton’s 2nd Law Suppose the same 35 kg crate was not moving at a

constant speed, but rather accelerating at 0.70 m/s/s.

Calculate the applied force. The coefficient of kinetic

friction is still 0.30.

mg

Fn

Fa

Ff

(35)(0.70) (0.30)(35)(9.8)

NET

a f

a k N

a k

a k

a

a

F ma

F F ma

F F ma

F mg ma

F ma mg

F

F

127.4 N

Inclines

cosmg

sinmg

mg

FN Ff

Tips

•Rotate Axis

•Break weight into components

•Write equations of motion or

equilibrium

•Solve

Friction & Inclines A person pushes a 30-kg shopping cart up a 10 degree

incline with a force of 85 N. Calculate the coefficient of friction if the cart is pushed at a constant speed.

cosmg

mg

Fn Fa

Ff

sinmg

sin

sin cos

cos sin

sin cos

sin

cos

85 (30)(9.8)(sin10)

(30)(9.8)(cos10)

a f f k N

a k N N

a k

a k

ak

k

F F mg F F

F F mg F mg

F mg mg

F mg mg

F mg

mg

0.117

Example

A 5-kg block sits on a 30 degree incline. It is attached to string that is thread over a pulley mounted at the top of the incline. A 7.5-kg block hangs from the string.

a) Calculate the tension in the string if the acceleration of the system is 1.2 m/s/s

b) Calculate the coefficient of kinetic friction.

m1

m1g

m2g

FN T

T Ff

30

30

m2gcos30

m2gsin30

1 1

2 2

2

( sin )

cos

NET

f

N

F ma

m g T m a

T F m g m a

F m g

Example Cont.

1 1

1 1

(7.5)(9.8) (7.5)(1.2)

NETF ma

m g T m a

m g m a T

T

T

64.5 N

2 2

2 2

2 2

2 2

2 22

2 2

2

( sin )

sin

sin

sin

sincos

sin

cos

64.5 (5)(1.2) (5)(9.8)(sin 30)

(5)(9.8)(cos30)

f

f

k N

k N

k N

N

k

k

k

T F m g m a

T F m g m a

T F m g m a

T m a m g F

T m a m gF m g

F

T m a m g

m g

0.80 N

Coefficient of Friction Example

A 24 kg crate, initially at rest, requires a 75 N

force to set it in motion. Once moving, a

force of 53 N is needed to keep it moving with

constant velocity.

Find the coefficient of static friction and the

coefficient of kinetic friction.

Coefficient of Friction Example

n

s

sF

F max,

mgF

mgF

F

n

n

Y

0

0

N 75

0-N 75

0

,

,

MaxS

MAXS

X

F

F

F

Fn

75 N FS,Max

F gravity=mg

32.0

)m/s kg)(9.81 24(

N 75N 752

S

smg

Coefficient of Friction Example

23.0

)m/s kg)(9.81 (24

N 35

0

N 53

2

k

kk

n

n

k

n

kk

mg

F

mgF

mgF

F

F

F

Fn

75 N Fk

F gravity=mg

Air Resistance

The force of air resistance (FR) is a form of friction.

FR depends on velocity.

FR

Fg

Terminal Speed

At some speed, the air resistance will be equal in magnitude to the force of gravity. (FR = -Fg).

Once an object reaches that speed, it will no longer accelerate. It will continue to fall at a constant speed.

FR

Fg