1
Inertia is resistance an object has to a change of velocity
• sort of laziness
(inerzia – laziness in Italian)
• tendency of a body to maintain its state of rest
or uniform motion in a straight line
Mass is numerical measure of the inertia of a body.
• more mass – harder change of velocity
is a measure of the amount of matter in the object
• depends only on the number and kind of atoms in it.
• unit: (m) = 1 kg
( platinum – iridium cylinder
– kept at IBWM near Paris)
• doesn’t depend on the location of the object
If the object has mass of 1 kg here on earth it
would have the mass of 1 kg on the moon, even
though it would weigh only one-sixth as much.
Weight is the gravitational force acting on an object
• acting straight down toward the center of the earth
(moon …)
• depends on the location of the object – whether it is
on the moon or on the earth, even on how high from
center of the earth the object is.
• depends on its mass and acceleration due to gravity:
W = mg
unit: 1 N
Objects have no weight in space. Nevertheless it is equally
hard to move an object in the space. Any mass resists the
change in motion – inertia.
All forces result from interactions between TWO objects.
To have a force, you have to have 2 objects
one object pushes, the other gets pushed .
Force is an interaction between two objects involving a push
or a pull.“
Newton's 1. Law says that if the net force on an
object is zero it won't accelerate.
Fnet = 0, a = 0
If
 no change in velocity
Translational equilibrium:
It follows from Newton’s 1. law that if the net force acting
on the object is zero, the object won’t accelerate.
Definition:
Object is in translational equilibrium if it is not
accelerating, therefore the net force acting on he object is
zero. Object is at rest, or it is moving with constant velocity.
how to apply concept of translational equilibrium:
1. Two forces are acting on a body.
Describe the motion of the body.
Since the net force on this body is zero, it is in equilibrium:
- which means that the object is not accelerating
- the body is either:
● at rest, or
● moving with a constant velocity
2. Object is moving at 3 m/s
in a straight line. Find force F.
Since velocity is constant, the body is in translational
equilibrium:
- which means that the object’s acceleration is zero
- therefore net force acting on it is zero
●
F = 8N, 00
VERY, VERY IMPORTANT: translational equilibrium math:
 if net F = 0 then a = 0, and velocity is constant or zero
 if velocity is constant or zero, then a = 0, and Fnet = 0
Force is an influence on an object that causes the object to
accelerate.
Forces are vector quantities, having both direction and
magnitude.
unit: Newton (N)
1 N is the force that causes a 1-kg object to accelerate 1 m/s2.
The net force, 𝐹⃗𝑛𝑒𝑡 is the vector sum of all forces acting
on an object. The object accelerates as if only one force, net
force is applied to that object
Applied forces
Net force

greater mass
– greater inertia (laziness)
– smaller acceleration

more force
– greater acceleration

greater mass
– greater inertia (laziness)
– smaller acceleration

more force
– greater acceleration
If net force is zero, acceleration is zero, velocity is constant
(or zero). The object is in translational equilibrium.
2
Common definition:
- to every action there is an equal and opposite reaction
is very dangerous, so please do not use it. It is not defined
what is action and what is reaction, so it looks as if we were
talking about one body, but that’s not true. We are talking
about forces acting on two different bodies.
When swimming you interact with water.
You push the water backward, and the
water pushes you forward.
Koka: when the ground pushes forward on the horse harder
than the cart pulls backward Koka accelerates forward.
(Fnet = F1’ – F2’ > 0)
Cart : accelerates forward when horse force is greater the
frictional force (Fnet = F2 – Ffr > 0)
Once moved from rest (acceleration required) to maintain the
velocity it is enough that Fnet = 0 (equilibrium)
action: tire pushes road
reaction: road pushes tire
action: foot pushes the ground
reaction: the ground pushes the foot that
propels the turtle forward
When we want to find acceleration of one body we have
to find all forces acting on that body.
● Forces between roller-skaters
If one skater pushes another, they both feel a force.
The forces must be equal and opposite, but the acceleration
will be different since they have different masses.
action: cannon pushes the cannonball
reaction: cannonball pushes the cannon
(recoil)
The same force F (opposite direction),
BUT
The person with a smaller mass will gain the greater velocity,
because of greater acceleration.
action: earth attracts ball
● The force on the girl causes her to accelerate backwards.
The mass of the wall is so large compared to the girl’s mass
that the force on it does not effectively cause any
acceleration.
a = F/m = 9.80 m/s2
reaction: ball attracts earth
aE = F/ME ≈ 0
● Koka, the clever horse, taught physics by Mrs. Radja says:
You do remember Newton's third law:
to every action there is an equal and opposite reaction.
It says that if I pull on the wagon, the wagon pulls me back. If
these two forces are equal and opposite, they will cancel, so
that the net force is zero. Since wagon is at rest, it must
always remain at rest! Get over here and unhitch me, since I
have just proven that Newton's law says that it is impossible
for a horse to pull a wagon!
Question: Should I find myself a less educated horse, or
should I teach better?
Where is the error in Koka’s argument? Why don’t action and
reaction forces cancel?
Only the forces that act on the same object can cancel.
● It looks unbelievable but
it is true.
when they clinch forces
are equal – would you
expect that?
3
● Force applied at an angle θ
Tension T :
Force that the end of the rope exerts on whatever is
attached to it. Direction of the force is along the rope.
vertical: Fnet = ma = 0
Fn + F sinθ = mg
Fn = mg - F sinθ
Normal force
𝐹⃗𝑛
vertical component of applied force is helping the surface, so
surface doesn’t need to provide as much force as without F.
The force which is preventing an object from falling through
the surface of another body . That’s why normal force is
always perpendicular (normal) to the surfaces in contact.
The normal force is an action-reaction force. It is resulting
from strong repulsive electromagnetic force between
electrons of two bodies. The atoms in the surface are
compressed microscopically to create the normal force. The
surface deforms imperceptibly and produces a reaction force
equal to the force pressing the object into the surface.
Existence: by evidence
– object is not accelerating in vertical
direction, therefore, the vertical net force
must be zero
● For an object sitting on a horizontal
surface, the normal force is equal to the
weight of the object. Fn = mg
The normal force is not always equal to the weight of an
object; it is the force pressing the object into the surface
● If there is a force F trying to lift up the object, it helps the
normal force – the desk doesn’t need to exert so much force
Fnet = ma = 0
Fn + F = mg
Fn = mg – F
● Pushing an object into a wall
horizontal: Fnet = ma = 0
Fn = F
● An object is on an rough incline θ.
Force diagram:
solve equation
Fnet = N + Ffr + mg = ma
This is a vector equation.
The question is now how to solve it?
The easiest way is to resolve this equation into components,
one parallel to the incline and the other one perpendicular to
the incline.
Fnet,|| = ma||
Fnet,  = ma 
Why? Simply because we know that a┴ , acceleration
perpendicular to the surface is zero, and a ║ is acceleration in
the direction of the motion.
perpendicular to the incline:
Fnet = ma = 0
Fn - mg cos θ = 0
● If there is push down force F – the desk has to exert more
force
Fnet = ma = 0
Fn = mg + F
If the desk can not exert enough force
it will break
Fn = mg cos θ
force pressing the object into the surface is not full weight
mg, but only part of it:
horizontal surface: θ = 00 → Fn = mg
object in free fall not pressing the surface: θ = 900 → Fn = 0
4
Friction: Ffr
Friction is a force that is created whenever two surfaces
move or try to move across each other.
• Friction always opposes the motion or attempted motion
of one surface across another surface.
• Friction is dependent on the texture/roughness of both
surfaces.
• Friction acts parallel to surface in direction opposed to
intended motion.
• Friction is also dependent on the force which presses
the surfaces together, normal force.
Ffr = μ Fn
coefficient of proportionality
μ is called coefficient of
friction
 μ has no units
 it is a measure of surface-to-surface roughness
 depends on characteristics of both surfaces
 different values for static and kinetic coefficient of friction
surface-on-surface
hook velcro-on-fuzzy velcro
avg tire-on-dry pavement
grooved tire-on-wet pavement
glass-on-glass
metal-on-metal (dry)
smooth tire-on-wet pavement
metal-on-metal (lubricated)
steel-on-ice
steel-on-Teflon
μs
>6.0
0.9
0.8
0.9
0.6
0.5
0.1
0.1
0.05
μk
>5.9
0.8
0.7
0.4
0.4
0.4
0.05
0.05
0.05
When an object moves through air or any other fluid, the fluid
exerts a frictionlike force on the moving object. The force is
called drag. Unlike the friction between surfaces, however,
this force depends upon the speed of the object, becoming
larger as the speed increases. It also depends upon the size
and the shape of the object and the density and kind of fluid.
A falling object accelerates due to the gravitational force mg,
exerted on it by the earth. As the
object accelerates, however, its speed
increases and the drag on it becomes
greater and greater until it is equal to
the weight of the object. At this point,
the net force on the falling object is
zero, so it no longer accelerates. Its
speed now remains constant; it is
traveling at its terminal speed.
Terminal speed occurs when the
weight force (down) is equaled by the
drag force (up).
Terminal velocity of table tennis ball is 9 m/s after
approximately 10 m. A basketball has a terminal velocity of
20 m/s after approximately 47 m.; the terminal velocity of a
baseball is 42 m/s after approximately 210 m.
Parashoot – 5 m/s after approximately 3 m.
AND THE RAINDROP?
How fast is a raindrop traveling when it hits the ground? It
travels at 7m/s (17 mi/h) after falling approximately only 6 m.
This is a much “kinder and gentler” speed and is far less
damaging than the 340mi/h calculated without drag.
Problem:
● Draw all forces that act on a parachutist.
Find Fnet and acceleration (a = Fnet/m ) in following cases:
a. parachutist that has just stepped out of the airplane.
Fnet = mg
a = Fnet/m = mg/m
a=g
mg
b. parachutist is falling at increasing speed.
kinetic μ is smaller than static μ. You probably noticed that
once you moved something from rest it becomes easier to
push around.
Fdrag
You should keep in mind that it isn't possible to give accurate
values for the coefficient of frictions due to changing surface
smoothness. For example, not all pieces of metal have the
same surface smoothness. Some that are highly polished
may be more slippery than others that are pitted or
scratched. These values are just meant to give you the
approximate values.
mg
=
Fnet = mg - Fdrag
a<g
the speed is still increasing, and therefore
air friction too until Fdrag = mg
c. parachutist is traveling downward with constant velocity
(terminal velocity)
Fdrag
Fnet = mg - Fdrag = 0
a=0
Air Drag and Terminal Velocity
If a raindrops start in a cloud at a height h = 1200 m above
the surface of the earth they hit us at 340mi/h; serious
damage would result if they did. Luckily:
a = (mg - Fdrag) /m
mg
5
G = 6.67x10-11 Nm2/ kg2 – “Universal gravitational constant”
Forces are usually divided into two types or classes.
1. Contact forces, arising because of physical contact
between objects. For example when you push on a door to
open it or throw or kick a ball, you exert a contact force on
the door or ball.
2. Field forces – they act (push or pull) “on distance through
space” - the presence of an object effects the space around it
so, and that region is called a field (for example gravitational
field of the earth).
Contact Forces
Frictional Force
Tension Force
Normal Force
Air Resistance Force – Drag Force
Applied Force
Spring Force
the same value anywhere in the universe - very small value
– no significant forces of attraction between ordinary
sized objects.
We defined weight as gravitational force acting on an object
of mass m: W = mg
We know that the weight of an object of mass m is
gravitational force between that object and the Earth:
F=G
Mm
M
=G 2m
2
R
R
M – mass of the Earth
R – radius of the Earth is distance between Earth and m
W = mg
we conclude that
Field Forces
Gravitational Force
attraction between objects due to their masses
Electromagnetic Force
between charges
Strong Nuclear Force
keeps nucleus together
Weak Nuclear Force
arise in certain radioactive processes
At the atomic level – all contact forces are result of repulsive
electromagnetic forces (at very small distances)
That means that objects have no actual contact, but their
electric fields (outer electrons repel each other)
Newton’s law of gravitation
One of the most significant intellectual achievements in the
history of thought. It is universal – it applies to all objects
regardless of their location anywhere in the Universe.
Every object in the universe attracts every other object.
The force between two objects is proportional to the
product of their masses and inversely proportional to the
square of the distance between their centers. The force
acts along the line joining the two objects.
F=G
m1m2
r2
g=G
M
= 9.80 m/s2
R2
Now we can see that the gravitational acceleration g is a
consequence of the gravitational force. Its magnitude
depends on how far is the object from the center of the earth.
Double the distance from the centre, r = 2 R , g is 4 times less,
g = 2.45 m/s2 , and so is weight