Chapter 4Chapter 4

NewtonNewton’’s Laws:s Laws:

Explaining MotionExplaining Motion

Theconcepts of

force,mass, and

weight playcritical

roles.

Newton’s Laws of

Motion

A Brief History

!Where do our ideas and theories aboutmotion come from?

!What roles were played by Aristotle,Galileo, and Newton?

!How didNewton’s theorycome about?

!What does ittell us aboutmotion?

!Can we trustour intuition?

Will the chair continue to move whenthe person stops pushing?

Aristotle’s View

"A force is

needed to keep

an object moving.

"Air rushing

around a thrown

object continues

to push the

object forward.

Galileo’s Contribution

"Galileo challenged Aristotle’s ideas thathad been widely accepted for manycenturies.

"He argued that the natural tendency ofa moving object is to continue moving.# No force is needed to keep an object

moving.

# This goes against what we seem toexperience.

Newton’s Contribution

"Newton built on Galileo’swork, expanding it.

"He developed acomprehensive theory ofmotion that replacedAristotle’s ideas.

"Newton’s theory is stillwidely used to explainordinary motions.

Newton’s First and

Second Laws!How do forces affect the motion of an

object?

!What exactly do we mean by force? Isthere a difference between, say, force,energy, momentum, impulse?

!What do Newton’s first and second lawsof motion tell us, and how are theyrelated to one another?

Newton’s First Law of Motion

An object

remains at rest,

or in uniform

motion in a

straight line,

unless it is

compelled to

change by an

externally

imposed force.

Newton’s Second Law of Motion

The acceleration of an

object is directly

proportional to the

magnitude of the imposed

force and inversely

proportional to the mass

of the object.

The acceleration is the

same direction as that of

the imposed force.

Newton’s Second Law of Motion

$Note that a force is proportional to an object’s

acceleration, not its velocity.

$We need some precise definitions of some

commonly used terms:$The mass of an object is a quantity that tells us how much

resistance the object has to a change in its motion.

$This resistance to a change in motion is called inertia.

!

F = ma

units : 1 newton = 1 N = 1 kg "m s2

$It is the total force or net force

that determines an object’s

acceleration.

$If there is more than one

vector acting on an object, the

forces are added together as

vectors, taking into account

their directions.

!

Fstring =10 N (to the right)

ftable = 2 N (to the left)

Fnet =10 N " 2 N

= 8 N (to the right)

a =Fnet

m=

8 N

5 kg

=1.6 m s2 (to the right)

Two equal-magnitude horizontalforces act on a box. Is the object

accelerated horizontally?

a) Yes.b) No.c) You can’t tell from

this diagram.

Since the two forces are equal

in size, and are in opposite

directions, they cancel each

other out and there is no

acceleration.

Is it possible that the box ismoving, since the forces are equalin size but opposite in direction?

a) Yes, it is possible forthe object to be moving.

a) No, it is impossible forthe object to be moving.

Even though there is no

acceleration, it is possible the

object is moving at constant

speed.

Two equal forces act on an objectin the directions shown. If theseare the only forces involved, will

the object be accelerated?a) Yes.b) No.c) It is impossible to determine

from this figure.

The vector sum of the two forces results in a

force directed toward the upper right corner.

The object will be accelerated toward the

upper right corner.

Two forces act in opposite directionson a box. What is the mass of thebox if its acceleration is 4.0 m/s2?a) 5 kgb) 7.5 kgc) 12.5 kgd) 80 kge) 120 kg

The net force is 50 N - 30 N = 20 N,

directed to the right. From F=ma,

the mass is given by:

m = F/a

= (20 N) / (4 m/s2)

= 5 kg.

A 4-kg block is acted on by threehorizontal forces. What is the net

horizontal force acting on the block?a) 10 Nb) 20 Nc) 25 Nd) 30 Ne) 40 N

The net horizontal force is:

5 N + 25 N - 10 N = 20 N

directed to the right.

A 4-kg block is acted on by threehorizontal forces. What is the

horizontal acceleration of the block?a) 10 Nb) 20 Nc) 25 Nd) 30 Ne) 40 N

From F=ma, the acceleration is given by:

a = F/m

= (20 N) / (4 kg)

= 5 m/s2

directed to the right.

Mass and Weight

!What exactly is mass?

! Is there a difference between mass andweight?

! If something is weightless in space,does it still have mass?

Mass, Weight, and Inertia

$A much larger force

is required to produce

the same acceleration

for the larger mass.

$Inertia is an object’s

resistance to a change

in its motion.

$Mass is a measure of

an object’s inertia.

$The units of mass are

kilograms (kg).

Mass, Weight, and Inertia

$An object’s weight is

the gravitational force

acting on the object.

$Weight is a force,

measured in units of

newtons (N).

$In the absence of

gravity, an object has

no weight but still has

the same mass.

Mass, Weight, and Inertia

$Objects of different mass

experience the same

gravitational acceleration on

Earth: g = 9.8 m/s2

$By Newton’s 2nd Law, F = ma,

the weight is W = mg.

$Different gravitational forces

(weights) act on falling objects

of different masses, but the

objects have the same

acceleration.

A ball hangs from a stringattached to the ceiling. What isthe net force acting on the ball?

a) The net force is downward.b) The net force is upward.c) The net force is zero.

Since the ball is hanging from the

ceiling at rest, it is not

accelerating so the net force is

zero. There are two forces acting

on the ball: tension from the string

and force due to gravitation.

They cancel each other.

Two masses connected by a stringare placed on a fixed frictionless

pulley. If m2 is larger than m1, willthe two masses accelerate?

a) Yes.b) No.c) You can’t tell

from this diagram.

The acceleration of the two

masses will be equal and will

cause m2 to fall and m1 to rise.

Newton’s Third Law

! Where do forces come from?

! If we push on an object like a chair, does thechair also push back on us?

! If objects do push back, who experiences thegreater push, us or the chair?

! Does our answer change if we are pushingagainst a wall?

! How does Newton’s third law of motion helpus to define force, and how is it applied?

Newton’s Third Law(“action/reaction”)

For every action(force),

there is an equalbut opposite

reaction(force).

It is important to identify the forces acting on an object.

$The forces acting

on the book are W

(gravitational force

from Earth) and N

(normal force from

table).

$Normal force

refers to the

perpendicular force a

surface exerts on an

object.

It is important to identify the forces acting on an object.

It is also important to identify the action-reaction pairs.

$The reaction force

to the Earth’s

attractive force W on

the book, is an equal

attractive force -W

the book exerts on

the Earth.

It is important to identify the forces acting on an object.

It is also important to identify the action-reaction pairs.

$The reaction force

to the table’s normal

force N exerted

upward on the book,

is an equal force -N

the book exerts

downward on the

table.

An uncompressed spring and the same spring

supporting a book.

The compressed spring exerts an upward force on the

book.

Third-Law Action/Reaction Pair

If the cart pulls back on the mule equal andopposite to the mule’s pull on the cart, how

does the cart over move?

Third-Law Action/Reaction Pair

The car pushes against the road, and the road,in turn, pushes against the car.

Applications of

Newton’s Laws!How can Newton’s laws be applied in

different situations such as pushing achair, sky diving, throwing a ball, andpulling two connected carts across thefloor?

What forces are involved in moving a chair?

$The weight W

(gravitational force

from Earth)

$The upward force N

(normal force from

floor).

$The push P (normal

force from hand of

person)

$The frictional force f

exerted by the floor

Does a sky diver continue to accelerate?

$Air resistance R is a force

directed upward, that opposes

the gravitational force W

$R increases as the sky

diver’s velocity increases

$When R has increased to the

magnitude of W, the net force

is zero so the acceleration is

zero

$The velocity is then at its

maximum value, the terminal

velocity

What happens when a ball is thrown?

Three forces act on a thrown ball:

$The initial push P

$Only acts at the beginning; once the ball leaves the hand, P

is no longer acting on the ball.

$The weight W

$Is a constant (does not change) throughout the trajector

$The air resistance R

$Is always directed against the motion

$Is proportional to the speed

What happens when objects are connected?

Two connected carts being accelerated by a force F applied by

a string:

$Both carts must have the same acceleration a which is equal

to the net horizontal force divided by the total mass

$Each cart will have a net force equal to its mass times the

acceleration

What happens when objects are connected?

The interaction between the two carts illustrates Newton’s third

law:

$m1 exerts a pull of 16 N to the right on m2

$m2 exerts an equal and opposite pull of 16 N to the left on m1

Two blocks with the same mass are connectedby a string and are pulled across a frictionless

surface by a constant force. Will the twoblocks move with constant velocity?

a) Yes, both blocks movewith constant velocity.

b) No, both blocks movewith constant acceleration.

c) The two blocks will havedifferent velocities and/or accelerations.

The front block will accelerate due to the constant

force F. The rear block is also pulled by a

constant force due to the connecting string, so it

will accelerate with the same acceleration as the

front block. The constant force implies a constant

acceleration. Constant acceleration results in

constantly increasing velocity.

Will the tension in the connecting string begreater than, less than, or equal to the

force F?

a) Greater than.b) Less than.c) Equal to.

The tension in the connecting string is less

than F. Both bodies have the same

acceleration. The force F accelerates a total

mass, 2m. The force in the connecting string

accelerates a mass, m, so it is half of F.

Two blocks tied together by a string are beingpulled across the table by a horizontal force.The blocks have frictional forces exerted onthem by the table as shown. What is the netforce acting on the entire two-block system?

a) 16 Nb) 36 Nc) 38 Nd) 44 Ne) 46 N

The net horizontal force is:

30 N - 6 N - 8 N = 16 N

directed to the right.

What is the acceleration of this system?

a) 2.00 m/s2

b) 2.67 m/s2

c) 5.00 m/s2

d) 7.50 m/s2

The total mass is:

2 kg + 4 kg = 6 kg

The acceleration of the system is:

Total force ÷ total mass =

16 N ÷ 6 kg = 2.67 m/s2

directed to the right.

What force is exerted on the 2-kg block bythe connecting string?

a) 16 Nb) 36 Nc) 38 Nd) 44 Ne) 46 N

The net horizontal force on the 2-kg block is:

Fnet = ma = 2 kg x 2.67 m/s2 = 5.3 N

So the force due to the string is:

Fstring = Fnet + 6 N = 11.3 N

directed to the right.

What is the acceleration of the 4-kg block?

a) 16 Nb) 36 Nc) 38 Nd) 44 Ne) 46 N

The net horizontal force on the 4-kg block is:

Fnet = 30 N - 8 N - 11.3 N = 10.7 N

So the acceleration of the 4-kg block is:

a = F ÷ m = 10.7 N ÷ 4 kg = 2.67 m/s2

directed to the right.