Chapter 4 Forces and the

Laws of Motion

Aristotle’s view on motion

Two types of Motion•Natural motion – either straight up or down

•Violent motion – was imposed motion, result of a force.

Force•A push or a pull exerted on some object.

Galileo’s view dispelled Aristotle’s • A force is not necessary

to keep an object moving.

• Introduced ‘friction’,

Friction• Force between materials

that are moving past one another.

• Force that opposes motion.

The cause of an acceleration, or the

change in an object’s speed.

Newton (N)• SI/Metric unit of

force.• Is the amount of force

that, when acting on a 1 kg mass, produces an acceleration of 1 m/s2.

A ‘dyne’ is the measurement of force when using

grams and centimeters.

WeightIs the measure of the

magnitude of the gravitational force

exerted on an object.

Conversion Factor1 N = 0.225 lb

1 lb = 4.448 N

Figure out what your weight is in

Newton’s.

190 lb 4.448 N 1 lb

845.12 N

Forces can act through:

1. Contact

2. At a distance

Contact Forces•A force that arises from the physical contact of two objects.

•Ex: Throwing a ball or pulling a sled.

Field ForcesA force that can exist between objects, even in the absence of physical contact between the objects.

•Ex: force of gravity or attraction/repulsion of electrical charges.

•The effect of a force depends upon the magnitude of the force and the direction of the force.

•Therefore, a force is a vector.

Force Diagram• Is a diagram, in which, all

forces acting on an object are represented by vector arrows.

• Sometimes these are called ‘free-body diagrams”.

Look at figures 4 – 3 & 4 – 4 on pages 126 – 128 .

Section 4 – 2: Newton’s First

Law

An object at rest remains at rest, and an object in motion will continue in motion with a constant velocity (in a straight

line),

unless the object experiences a net

external force.

Inertia

Is the tendency of an object to maintain its

state of motion.

Galileo said that every material object has a resistance to the change of its state of motion.

Newton’s first law is sometimes called the

‘Law of Inertia’Meaning that in the absence

of force a body will preserve its state of motion.

What is “mass”?

•The amount of matter an object contains.

•Mass measures the inertia of an object.

• All objects made of matter have inertia - that is, they resist accelerations (Newton’s First Law), but some objects resist more than others.

Mass is not Volume.• Mass is a scalar quantity.

• SI unit of mass is the kilogram (kg).

Mass is not Weight• Mass is a property of an object

that measures how much it resists accelerating.

• An object is difficult to accelerate because it has mass

Net External Force (Fnet)

Is the total force resulting from a combination of external forces on an

object; sometimes called the ‘resultant force’.

The downward force due to gravity is the

object/body’s weight.The upward force is due

to the force exerted by the contact surface on

the object.

Ex 1: A man is pulling on his dog with a force of 70 N directed at an angle of

30 degrees to the horizontal. Find the x and y components of the force.

Force diagram

70 N

Force diagram

70 N

x

y

X component: since we have a right triangle and know the angle and the hypotenuse. We will use the cosine trig function.

adjcos = -----

hypFx = hyp cos

Fx = 70 cos 30

Fx = 60.6 N

y component: since we have a right triangle and know the angle and the hypotenuse. We will use the sine trig function.

oppsin = -----

hypFy = hyp sin

Fy = 70 sin 30

Fy = 35 N

Ex 2: A crate is pulled to the right with a force of 82 N, to the left with a force

115 N, upward with a force of 565 N, and

downward with a force of 236 N.

Force Diagram

565 N

82 N

236 N

115 N

A) Find the net external force in the x direction.Remember: right is (+) and left is (-)

x = 82 N + (- 115 N) x = - 33 N

B) Find the net external force in the y direction.Remember: up is (+) and down (-)

y = 565 N + (- 236 N) y = 329 N

C) Find magnitude and direction of the

Fnet on the crate.

Fnet329 N

- 33 N

Use the Pythagorean Theorem to find Fnet

and the inverse tangent function to find the direction.

22a c b

22a c b22

netF yx

22a c b22

netF yx 22

net 329)33(F

22a c b22

netF yx 22

net 329)33(F

NFnet 7.330

adj

opptan

adj

opptan

adj

opp1tan

33

329tan 1

33

329tan 1

3.84

Since we are on the negative x-axis, this

is the same as an angle of 95.7o from the positive x-axis.

In your notes do problems 3 & 4

on HPg 133.

Mass is a measurement of inertia.

Ex: A golf ball and a basketball, if the same Fnet acts on both, the golf ball will accelerate more.

EquilibriumThe state in which there is no change in the body’s motion.

Equilibrium Means "Zero Acceleration"

Forces in balance:  

Equilibrium

An object is in equilibrium when the vector sum of

the forces acting on it is equal to zero.

Is the object moving?

Yes, but at constant velocity.

Section 4-3: Newton’s Second and Third Laws

Force is proportional to mass and acceleration

Think about pushing a stalled car. If you try to push it by yourself, you can move it, but not very fast.

However, if a couple of friends help, then it is much easier to move and you can

make it move faster quicker.

Newton’s 2nd LawThe acceleration of an object

is directly proportional to the Net External Force

(Fnet) acting on the object and inversely proportional

to the object’s mass.

From this law we get:

m

Fa net

Normally it is written as:

maF

a = F / m

a = F / m

2a = 2 F / m

a = F / m

2a = 2 F / m

a = 2 F / 2m

a = F / m

a = F / m

a/2 = F /2m

a = F / m

a/2 = F /2m

a/3 = F / 3m

Note: remember that it is the Fnet that cause the

object to move.

Note:

2

kg 1 N 1s

m

Ex 3: Nathan applies a force of 20 N, causing the book to accelerate at a rate of 1.25 m/s2. What is the mass of

the book?

G: a = 1.25 m/s2, Fnet = 20 N

U: m = ?

E: Fnet = ma or m = Fnet/a

S: m = 20 N / 1.25 m/s2

S: m = 16 kg

Ex 4: The Fnet on the propeller of a 3.2 kg

model airplane is 7.0 N forward. What is the acceleration of the

airplane?

G: Fnet = 7.0 N, m = 3.2 kg

U: a = ?

E: Fnet= ma or a = Fnet/m

S: a = 7.0 N / 3.2 kg

S: a = 2.2 m/s2 forward

Remember the from Ch. 2

t

xvavg

Remember the from Ch. 2

2if

avg

vv

t

xv

Remember the from Ch. 2

t

vva if

2if

avg

vv

t

xv

Ex 5: A 2 kg otter starts from rest at the top of a

muddy incline 0.85 m long and slides down to the

bottom in 0.5 sec. What is the net external force?

G: x = .85 m, t = 0.5s vi = 0 m/s, m = 2 kg

U: Fnet = ?We need to find the acceleration, but we need final speed first.

We need to find the average speed first, than use that to find the final

speed.

t

xvavg

sec5.0

85.0 mvavg

sec5.0

85.0 mvavg

smvavg / 7.1

Using the 2nd average speed equation.

2if

avg

vvv

Rearrange for final speed

iavgf vvv 2

iavgf vvv 2

m/s 0m/s) 7.1(2 fv

iavgf vvv 2

m/s 0m/s) 7.1(2 fv

m/s 4.3fv

Now we can find acceleration.

t

vva if

s 5.0

m/s 0m/s 4.3 a

s 5.0

m/s 0m/s 4.3 a

2m/s 8.6a

Now we can find Fnet

E: Fnet = ma

S: Fnet =(2 kg)(6.8 m/s2)

S: Fnet = 13.6 N

On pg 138 (HP), Do Practice 4B: #

3 & 5.

Forces always exist in pairs.

Ex: When you push against the wall, the wall pushes

back. The forces are equal, but opposite.

Newton’s 3rd Law

If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal

in magnitude of the force simultaneously exerted on

object 2 by object 1, and these two forces are opposite in

direction.

A simpler alternative statement for

Newton’s 3rd Law:For every action,

there is an equal and opposite reaction.

Action-reaction pair

A pair of simultaneously equal, but opposite forces resulting from the interaction of 2 objects.

Action-Reaction forces each act on different objects.

They do not result in equilibrium.

Reread pg 139

Recoil is an example of the 3rd Law

Field Forces also exist in pairs.

Newton’s 3rd Law also applies to field forces.

When an object is falling, its falling due to the force exerted by the earth, the reaction force is that the body is exerting an equal and opposite force on the

earth.

Why don’t we notice the this reaction force?

Because of Newton’s 2nd Law, the mass of the earth

is so great that the acceleration is so small it is

negligible.

Section 4-4: Everyday Forces

Weight (Fg)The magnitude of the force of gravity acting on an object.

Weight is NOT mass!

The weight of an object depends on the object’s mass.

In fact, an object’s weight is directly proportional to the object’s mass.

The weight of an object also depends on the object’s location.

The weight of an object also depends on the object’s location.

In fact, an object’s weight is directly proportional to its free fall acceleration, g at its current location.

Fg= mgWhere g = 10 m/s2, unless

otherwise specified.Weight is dependent on the

force of gravity. It depends upon location. And acts downward.

The farther away from the center of the earth, the less

‘g’ becomes.

Also, the gravitational pull of the moon is about 1/6th of the earth’s.

So if you way 180 lb or 900 N on earth you’d weigh 30 lb or 150 N on the moon.

EX 6: A rocket with a mass of 10 kg is launched

vertically with a force of 150 N. What is the rocket’s

net force? What is the acceleration produced by

this net force?

What forces are acting on this object?

Weight – downward

Force of Engine - upward

G: m = 10 kg, g = 10 m/s2 Fengine = 150 N

U: Fnet = ?

E: Fnet = Fengine - Fg

Fnet = Fengine - mg

S: Fnet = 150 N - (10)(10)

S: Fnet = 50 N

Remember the net force is what accelerates the object.

U: a = ?

E: a = Fnet /mS: a = 50 N / 10 kgS: a = 5 m/s2

EX 7: A 20 kg rocket is accelerated upwards

(vertically) at 3 m/s2. What is the Force that provides

this acceleration, this is the net force? What is the force

provided by the rocket’s engine?

•Remember the Net Force causes the object to accelerate.

G: a = 3 m/s2, m = 20 kg, g = 10 m/s2

U: Fnet = ?

E: Fnet = ma

S: Fnet = (20 kg)(3 m/s2)

S: Fnet = 60 N

U: Fnet = Fengine - Fg

Fengine = Fnet + Fg

Fengine = Fnet + mg

Fengine = 60 + (20)(10)

Fengine = 260 N

Normal Force (FN)A force exerted by one object on another in a direction perpendicular to the surface of contact.

N

The normal force is always to the surface

of contact, but is not always opposite the direction of gravity.

FN = Fg, but opposite if

The FN can be calculated by the equation FN = mgcos, if the object is on an inclination.

Fg

FN

The value for is the same for both.

Force of Friction

Is the force that opposes motion.

There are 2 types of friction:

Static Friction (Fs)

The resistive force that opposes relative motion of 2 contacting surfaces

that are at rest with respect with one another.

As long as an object does not move when a force is applied:

As the applied force increase, the force of static friction increases. It increases until it reaches its max value Fs,max.

applieds FF

Once you exceed the max value the object begins to

move.

Kinetic Friction (Fk)

The resistive force that opposes the relative

motion of two contacting surfaces that are moving

past one another.

Since it is easier to keep an object moving than it is to start it moving, the kinetic friction is less

than static friction.kappliednet FFF

Frictional forces arise from the

complex interaction of the surfaces, at a microscopic level.

It’s easier to push a chair than it is to move a desk

at the same speed.Since the desk is heavier,

it has a greater normal force.

Therefore, the force of friction is proportional to

the normal force.Also, friction depends upon the nature of the

surfaces in contact.

The frictional force between a chair and tile floor is less than the the force between

a chair and carpet.

Coefficient of Friction

Is the ratio of the force of friction and the

normal force acting between the objects.

Ffriction

= ---------- Fnormal

Note: The coefficient of

friction has no units. From the equation

the units cancel out.

Coefficient of Kinetic Friction

N

kk F

F

Coefficient of Static Friction

N

ss F

F max,

On pg 144, are values for the coefficient of

friction, for both static and kinetic.

Ex 8: A 19 kg crate initially at rest, on a

horizontal floor, requires a 75 N forces to set it in

motion. Find the coefficient of static

friction.

G: m =19 kg, F =Fs =75 N

U: s = ?

E: Fs Fs

s = ----- = ------

FN mg

S: 75 N

s= ---------------------

(19 kg)(10 m/s2)

S: s = 0.39

From the Coefficient of friction what are the two surfaces in

contact?

Wood on Wood

Overcoming Friction Example

Ex 9: Andy pulls a wagon with a force of 90 N at an angle of 30o

to a horizontal surface. The mass of the wagon is 20 kg, and the coefficient of kinetic friction between the wagon and the side

walk is 0.50. Find the acceleration of the wagon due to

the net force.

Fg

FN

Fk

Fapplied

Which way does the object accelerate?

Only in the ‘x’ direction

In order to find the acceleration, we will use

Newton’s 2nd Law.Fnet,x = max

We don’t know the Fnet,x, so we need to find it.

Since the object doesn’t move in the ‘Y’

direction the Fnet,y = 0 N. We need to find the net

force in the ‘x’ direction.

Fnet,x = Fapplied,x + Fk

Since the applied force is at an angle, we only want the x-

component.

Fapp,x = Fapp cos

Fapp,x = 90 N cos(30)

Fapp,x = 77.9 N

Next find the Fk

Fk = FN We need to find the Normal Force. Does it equal the weight?

NO, since the Fapp

has a y-component. We know the net force in the y-direction is zero, so:

Fnet,y = FN + Fapp,y - Fg =0

FN + Fapp,y - Fg = 0

FN = Fg - Fapp,y

Fg = mgFg = (20)(10)

Fg = 200 N

Fapp,y = Fapp sin

Fapp,y = 90N sin(30)

Fapp,y = 45N

FN + Fapp,y - Fg = 0

FN = Fg - Fapp,y

FN= 200 N - 45N

FN = 155 N

Fk = kFN Fk = (0.50)(155 N)

Fk = 77.5 N to the left

So Fk = 77.5 N

Now, find the Fnet,x

Fnet,x = Fapp,x - Fk

Fnet,x =(77.9 N - 77.5 N)

Fnet,x = 0.4 N

Now, find the horizontal acceleration.

ax = Fnet,x /m

ax = 0.4 N / 20 kg

ax = 0.02 m/s2

Air Resistance is a form of friction (FR)

When an object moves through a fluid, that fluid provides resistance in the direction opposite of the object’s motion.

Terminal VelocityWhen a free falling body accelerates, the object’s

velocity increases. As the velocity increases, the object’s air resistance

increases.

When the air resistance balances the force of

gravity, the net force is zero. The objects continues to move

downward at a constant maximum speed.

The maximum speed a free-falling body reaches due to air resistance equaling the force of gravity.

Eventually, the force R of air

resistance becomes equal to the force exertedby the earth, and

the object reaches equilibrium.

Why does the heavierperson fall faster?

What does Pressure mean to you?

• Under Pressure• Peer Pressure• Feeling Pressured• Air/Atmospheric• Tire

Pressure•The amount of force per unit area.

Force

Pressure = ----------

Area

Pressure Units•N/m2

•1 N/m2 = 1 Pascal (Pa)

Ex: