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Aristotle (384 -322 B.C.) :
of CELESTIAL objects (Moon, planets, stars, Sun) was
circular - without beginning or end.
of TERRESTRIAL bodies (apple, smoke, you) was
for light things to rise up and heavy things to fall
objects would seek their natural resting places: apple on the
ground and smoke high in the air like the clouds.
no need for gravity to explain this motion – it is JUST NATURAL –
what a life for physics student!!!!
was imposed motion – result of forces that pushed or pulled.
Important: violent motion had an external cause, it was not natural to the objects
No wonder that most thinkers before the 16th century consider it obvious that the
Earth must be in its natural resting place and assumed that the force large enough
to move it was unthinkable, it was clear that Earth did not move.
And in this intellectual climate of the 15th century Nicolaus Copernicus (14731543) formulated, in secret to escape persecution, his famous HELIOCENTRIC
THEORY – idea that was extremely controversial at the time - the Earth is just a
small planet and together with other planets circle around Sun.
Only in the final days of his life he sent his ideas to the printer. The first copy of his
work, De Revolutionibus, reached him on the day of his death.
One of his most outspoken supporters was Galileo Galilei, the foremost scientist of lateRenaissance Italy.
It took the genius of Galileo to claim that NO FORCE is needed to keep an object in the
motion (straight-line, constant speed)
Galileo argued (brainstorm – just pure thought – no experimental proof)
that forces only CHANGE THE MOTION
Left alone the things would travel in a straight line with constant speed
forever. It is the force of friction that slows them down.
Aristotle: It is the nature of the ball to come to rest.
Galileo: In the absence of friction the ball would keep on moving.
No force needed to maintain the motion. The force changes the motion – velocity.
Every object resists change to its state of motion/velocity. To change it, the force
must act on it. We call this resistance INERTIA.
Galileo’s findings about motion and his concept of inertia discredited Aristotle’s
theory of motion.
So why in the world do we STILL sometimes think the same way???
On Christmas day in the year Galileo died
Isaac Newton (1642-1727) was born.
By the age of 24 he gave the world
his famous three laws of motion.
Before we talk about force, let us
introduce inertia, mass and weight.
Inertia is resistance an object has to a change of velocity.
• sort of laziness
(inerzia – laziness in Italian)
Mass is numerical measure of the inertia of a body
unit: 1 kg
• 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.
• 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, but 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.
• depends on its mass and acceleration due to gravity:
W = mg
unit: 1 N
All forces result from interactions between 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
FORCE is an influence on an object that causes the object to
Forces are vector quantities, having both direction and magnitude.
unit: (F) = Newton (N),
1 N is the force that causes a 1-kg object to accelerate 1 m/s2.
The net force – resultant force
is the vector sum of all forces acting on ONE object.
Fnet or ΣF
the object accelerates as if only one force – net force is applied
Applied forces
Net force
Galileo’s Law of inertia
so, if Fnet = 0, a = 0  no change in velocity, then
An object continues in motion in a straight line at constant speed
or at rest unless acted upon by a net external force."
"How many ways can you state Newton's First Law?"
Translational equilibrium
If the net force acting on an object is zero, the speed and direction of
the motion will not change (the object won’t accelerate). If it was at
rest it will stay at rest, and if it was in motion it will continue the
motion with constant velocity (in the straight line at constant speed) .
We say the object is in (TRANSLATIONAL) EQUILIBRIUM.
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 is moving with a constant velocity
2. object is moving at 3 m/s in a straight line.
Two forces are acting on it. Find F
Since velocity is constant, the body is in translational equilibrium:
- which means that the object’s acceleration is zero
- therefore net force is zero
● F = 8N, 00
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 net F = 0
Six force are acting on an object. What can you
tell about the motion of that object? Is it at rest?
Is it moving? If it is moving, how?
The tendency of moving objects to continue in motion can have
very unpleasant consequences.
Seat belts: Passenger and the vehicle share the same destiny.
Straps provide the force for accelerated and decelerated
motion for passengers too.
No seat belts: The passengers maintain their state of motion assuming
a negligible friction between the passengers and the seats.
The passengers can become projectiles and continue in
projectile-like motion.
In a car accident, the safest place to be is in the car; yet in a
motorcycle accident, the worst place to be is on the motorcycle.
Car: Wear your seat belt.
Remember it's the law
- the law of inertia.
Law of inertia would safe
you from sharing the fate
of the motorcycle itself .
No functioning straps: the ladder in motion would
continue in motion. Assuming a negligible friction
between the truck and the ladder, the ladder would
slide off the top becoming a projectile.
You are driving at the same speed as a huge truck behind you.
You apply the brakes. A huge truck behind you applies the brakes
too, but has more inertia. Lazy thing. And then Bang!!!
A car is turning left not changing the speed. But it is still changing
velocity. Imagine a basket full of lazy strawberries in that car sitting on
the seat. It tends to stay in the same state of the motion. If you don’t
support that basket somehow, it will simply continue in the straight line.
For the small speeds friction force is usually strong enough to keep the
basket in place.
When the car makes a turn, the passengers tend to continue in their
straight line path. This straight line motion continues until the presence
of a side door or another passenger pushes upon the passenger in
order to accelerate him/her towards the center of the turn. The force
experienced by the passenger is an inward force; without it, the
passenger would slide out of the car.
The acceleration of an object produced by a net force on
that object is directly proportional to the net force applied,
and inversely proportional to the mass of the object.
Direction of the acceleration is in the direction of the net
 greater mass
– greater inertia (laziness)
– smaller acceleration
 more force
– greater acceleration
F net
If net force is zero, acceleration is zero,
velocity is constant (or zero).
The object is in translational equilibrium.
Whenever object A exerts a force on object B, object B exerts
an equal in magnitude and
opposite in direction force on object A.
In every interaction, the forces always occur only in pairs,
BUT these forces act on two different bodies.
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.
These forces act on different bodies.
You push the water backward,
the water pushes you forward.
action: tire pushes road
reaction: road pushes tire
action: foot pushes the ground
reaction: the ground pushes the foot that
propels the turtle forward
action: cannon pushes the cannonball
reaction: cannonball pushes the cannon (recoil)
The same force F (opposite direction), BUT
action: earth attracts ball
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 taught me 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, right?
So the wagon can never move! Since it 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!
Please help me!
Why don’t action and reaction forces cancel? Should I find
myself a less educated horse, or should I teach better?
Only the forces that act on the same object can cancel.
Koka: when the ground pushes forward on the horse harder than the cart pulls backward
Koka accelerate forward. (Fnet = F1’ – F2’ > 0)
Cart : accelerates forward when horse force is greater the frictional force
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.
The person with a smaller mass
will gain the greater velocity.
A roller-skater pushes off from a wall
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.
It looks unbelievable but it is true.
when they clinch forces are equal – you would expect that
when they clinch forces are equal – would you expect that?
again, the same force but different acceleration
Sudden acceleration can kill
Our organs are not firmly attached to anything.
When head is hit it gains acceleration. But the brain was not hit.
It continues with the same velocity. Skull and brain crash!!!!!
again, the same force but different acceleration
Tension: the force that the end of the rope exerts on whatever is
attached to it. Direction of the force is along the rope.
Normal force (support force, normal reaction force) 𝐹𝑛
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 results 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 slightly and
produces a reaction force equal to the force pressing the object into the
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
If there is a force F trying to
If there is push down
lift up the object, it helps the
force F
normal force – the clever desk – the desk has to exert
doesn’t need to exert so much
more force
Fnet = ma = 0
Fn + F = mg
Fn = mg - F
Fnet = ma = 0
Fn = mg + F
If the desk can not exert
enough force it will break
Friction force 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.
pulling force
Ffr = m Fn
coefficient of proportionality μ is called coefficient of friction
 m 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 (tables). kinetic μ is smaller than static μ.
You probably noticed that once you moved something from rest it becomes easier to push around.
hook velcro-on-fuzzy velcro
avg tire-on-dry pavement
grooved tire-on-wet pavement
metal-on-metal (dry)
smooth tire-on-wet pavement
metal-on-metal (lubricated)
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.
Origin of friction :
1. Mechanical interlocking of "rough" surfaces
– teeth on the surfaces
2. Microscopic level –
On an atomic scale, few surfaces are very smooth. Bumps far
smaller then we can see loom like mountains to an atom.
At the points of direct molecular contact, electrons become confused. Thoughts of an
electron with an
They forget which object they belong to, and wind up trying to orbit
identity crisis...
nuclei in molecules of both! The resulting bond is called molecular
adhesion or a “cold-weld.”
Each time they form a bond between uneven surfaces, force is
required to break this bond
Air Drag and Terminal Velocity
If a raindrops start in a cloud at a height h = 1200m above the surface of the earth
they would hit us at 340mi/h; serious damage would result if they did. Luckily:
When an object moves through air or any other fluid, the fluid exerts drag force on
the moving object. The force is called. 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. Skiers increase their terminal velocity by decreasing
the drag force. They hold their bodies in egg shape and wear smooth clothing and
streamlined helmets. How do skydivers control their velocity? By changing body
orientation and shape, sky divers can both increase and decrease their terminal velocity.
(60 m/s after approximately 430 m)
Parashoot – 5 m/s after approximately 3 m.
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.
Draw all forces that act on a parachutist. Find Fnet and acceleration for
a. parachutist that has just stepped out of the airplane.
Fnet = mg
a = Fnet/m = mg/m
b. parachutist is falling at increasing speed.
Fdrag =
Fnet = mg - Fdrag
a = (mg - Fdrag) /m
a = Fnet/m
the speed is still increasing, and therefore air friction too until
c. parachutist is traveling downward with constant velocity (terminal velocity)
Fnet = 0
Fnet = 0
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
Although there are many different contact forces, they are all some
form of only four different fundamental field forces existing in the
Contact Forces
Field Forces
Frictional Force
Gravitational Force
attraction between objects due to their masses
Tension Force
Normal Force
Air Resistance Force – Drag Force
Applied Force
Spring Force
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)
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 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 2
G = 6.67x10-11 Nm2/ kg2 – “Universal gravitational constant”
the same value anywhere in the universe - very small value
– no significant forces of attraction between ordinary sized objects.
The force between an object of mass m close to the Earth surface and
the Earth
F = G 2 = G 2 m = gm
rE – Earth’s radius
mE – Earth’s mass.
g = G 2 = 9.80m/s2
This force is commonly called weight W = mg.
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 rE , g is 4 times less,
g = 2.45 m/s2 , and so is weight
sketch of an object and all forces acting on that object
No velocity on that diagram, no acceleration on that diagram,
only object (circle or a box, and you can write mass in it)
and all forces acting on that object
3. Identify forces that act on the system
How to draw a force diagram
Label them on diagram
1. Choose
NONE body to be isolated
decision: cart
dog or the cart? F
Make a simple sketch of the system – point system
4. Find out the net force by
adding the force vectors
5. Apply Newton’s second law
Fnet = ma
1. Add all vectors to get net force
2. Apply newton's second law
Fnet = ma
Don’t worry, there is a way out.
Separate everything
into vertical and horizontal motion
Howard, the soda jerk at Bea’s diner, slides a 0.60-kg root beer from the end of the counter
to a thirsty customer. A force of friction of 1.2 N brings the drink to a stop right in front of
the customer.
a) What is the acceleration of root beer?
b) What is the coefficient of kinetic friction between the glass and the counter?
c) If the glass encounters a sticky patch on the counter, will this spot have a higher or
lower coefficient of friction?
Vertical direction:
0.60 kg
mg = 6N
Vertical acceleration = 0
Vertical net force = 0
Fn = mg = 6.0 N
Horizontal direction:
Net force = friction force: Fnet = Ffr =1.2 N
Fnet = ma
1.2 = 0.60 a
a = 2.0 m/s2
Ffr = 𝜇 Fn → 𝜇 = Ffr / Fn = 1.2/6.0 = 0.20 (no units)
c. higher
A boy exerts a 36-N horizontal force as he pulls a 52-N sled across a cement sidewalk at
constant speed. What is the coefficient of kinetic friction between the sidewalk and the
metal sled runners? Ignore air resistance.
W = mg = 52 N
m = 5.2 kg
Vertical direction:
Vertical acceleration = 0
Vertical Fnet = 0
Fn = mg = 52 N
Horizontal direction:
v is constant,
a = 0 and Fnet = 0
Ffr = F = 36 N
Ffr = μ Fn
𝜇 = Ffr / Fn = 36/52 = 0.69
A force of 40.0 N accelerates a 5.0-kg block at 6.0 m/s2 along a horizontal surface.
a. How large is the frictional force?
b. What is the coefficient of friction?
m = 5.0 kg
F = 40.0 N
a = 6.0 m/s2
Vertical direction:
a = 0, so Fnet = 0
Fn = mg = 50 N →
horizontal direction:
a = 6.0m/s2
Fnet = ma
F – Ffr = ma
40.0 – Ffr = 30
Ffr = 10 N
Ffr = μ Fn
𝜇 = Ffr / Fn = 10/50 = μ = 0.2
Ffr = μ Fn = 50 μ
Luke Skywalker starts to pull a sled with Princess Leia across a large ice pond with
the force of 100 N at an angle of 30.0° with the horizontal (with nails on his shoes).
Find normal force and initial acceleration if the weight of sled and Princess Leia is
800 N and the friction force is 40 N.
mg = 800 N m = 80 kg F = 100 N
free body diagram
Ffr = 40 N
vertical direction :
F sin θ + Fn = mg
50 + Fn = 800
Fn = 750 N
Horizontal direction:
F cos θ – Ffr = ma
86.6 – 40 = 80 a
a = 0.58 m/s2
An object is on a rough incline θ.
one parallel to the incline
one perpendicular to the incline.
The only force that
we have to resolve
into components is
weight mg
Why? Simply because we know that acceleration perpendicular to the surface is
zero, and acceleration is in the direction of the motion, parallel to incline.
Resolve vector mg into two components. Now instead of three forces, we
have four forces
direction perpendicular to the incline:
Fnet = ma = 0
Fn = mg cos θ
force pressing the object into the surface is not full weight mg, but only part of it,
So the normal force acting on the object is only part of full weight mg: Fn = mg cos θ
If the surface is horizontal: θ = 00
Fn = mg
If the object is in free fall not pressing the surface: θ = 900 → Fn = 0
A cute bear, m = 60 kg, is sliding down an iced incline 300. The ice can support up to 550 N.
Will bear fall through the ice?
If the coefficient of the friction is 0.115, what is the acceleration of the bear?
m = 60 kg
θ = 300
μ = 0.115
g = 10 m/s2
Perpendicular direction:
Fnet = ma
Fn - mg cos θ = 0
Fn = 520 N < 550 N
ice can support him, but he should
not eat too much
Parallel direction:
Fnet = ma
mg sin θ – Ffr = ma
300 – 60 = 60 a
a = 4 m/s2
Ffr = μ Fn = 60 N
cute bear is speeding up!!!!
How does the weight of a person in an elevator
depend on the motion of that elevator?
What will the scale show if the elevator is
1. at rest or moving with constant speed
2. speeding up
3. slowing down
Newton’s 3. law:
Force with which the person acts on the scale (reading of the scale) is
equal to the normal force on the person.
So, if we find normal force we know the
reading of the scale, so called APPARENT WEIGHT
Let’s assume that elevator is moving upward, and let this be positive direction.
1. draw free body diagram 2. apply Newton’s 2. law : Fnet = ma
1. elevator is at rest or moving with constant speed
Fn – mg = ma = 0
→ Fn = mg
apparent weight = weight
2. elevator is speeding up: a is positive
Fn – mg = ma
→ Fn = mg + ma
apparent weight > weight
the scale would show more, and you would feel heavier
3. elevator is slowing down: a is negative
Fn – mg = - ma
→ Fn = mg - ma
apparent weight < weight
the scale would show less, and you would feel lighter
Two blocks are connected by a string and pulley as shown. Assuming that the string and
pulley are massless, find
a) the magnitude of the acceleration of each block
b) Tension force on the blocks
the same string – the same tension
the same acceleration, except that 110 g accelerate down, and 90 g accelerate up.
two equations with two unknowns
T – 0.9 = 0.09a
1.1 – T = 0.11a
0.09a + 0.9 = 1.1 – 0.11a ⟹
0.2a = 0.2
a = 1 m/s2
T = 1.1 – 0.11a = 1.1 – 0.11(1) = 0.99 N
Fnet = ma
T – mg = ma
T – 0.9 = 0.09a
a is up
Fnet = ma
mg – T= ma
1.1 – T = 0.11a
a is up
first equation
second equation
A 10-kg block is connected to a 40-kg block as shown in the figure. The surface on which the
blocks slide is frictionless. A force of 50 N pulls the blocks to the right.
a) What is the magnitude of the acceleration of the 40-kg block?
b) What is the magnitude of the tension T in the rope that connects the two blocks?
As these two objects are connected with the
same rope, tension is the same and
acceleration is the same for two objects.
Fnet = ma
T = 10a
50 – T = 40a
50 – 10a = 40a
a = 1 m/s2
T = 10a = 10 N