WHAT DO OBJECTS DO WHEN NO FORCE IS ACTING ON THEM ??????

Aristotle (384 -322 B.C.) :

objects would seek their natural resting places: apple on the ground and smoke high in the air like the clouds.

of CELESTIAL objects (Moon, planets, stars, Sun) was circular - without beginning or end.

no need for gravity to explain this motion – it is JUST NATURAL – what a life for physics

student!!!!

of TERRESTRIAL bodies (apple, smoke, you) was for light things to rise up and heavy things to

fall

was imposed motion – result of forces that pushed or pulled.

Important: violent motion had an external cause, it was not natural to the objects

THOUGHT FOR NEARLY 2000 YEARS: IF AN OBJECT WAS MOVING, IT IS AGAINST ITS NATURE AND THE FORCE OF SOME KIND WAS

RESPONSIBLE.

NO FORCE – NO MOTION, 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. – THE CENTER OF UNIVERSE

And in this intellectual climate of the 15th century Nicolaus Copernicus (1473-1543) 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 late-Renaissance 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

By the age of 24 he gave the world his famous three laws

of motion.

Isaac Newton (1642-1727) was born.

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 • 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

unit: 1 kg

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 pull.“

FORCE is an influence on an object that causes the object to accelerate.

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.

Applied forces Net force

the object accelerates as if only one force – net force is applied

Fnet or ΣF

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?"

Definition:

If an object is at rest, then it is in static equilibrium and, if it is moving with constant velocity, then it is in dynamic equilibrium.

It follows from Newton’s 1. law that the condition for both equilibriums is that the net force acting on the

object is zero so the object won’t accelerate.

The common name for static and dynamic equilibrium is translational equilibrium

Translational equilibrium

Since velocity is constant, the body is in translational equilibrium:

2. object is moving at 3 m/s in a straight line.

Two forces are acting on it. Find

- which means that the object’s acceleration is zero - therefore net force is zero

● F = 8N, 00

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 8 N F

F

8 N 8 N

if net F = 0 then a = 0, and velocity is constant or zero

translational equilibrium math:

if velocity is constant 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.

greater mass – greater inertia (laziness) – smaller acceleration more force – greater acceleration

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 force,

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 force,

netFa

m

RRRRRRRRRRRRRR

If net force is zero, acceleration is zero, velocity is constant (or zero).

The object is in translational equilibrium.

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 reactionis 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.

Whenever object A exerts a force on object B, object B exerts an equal in magnitude and

opposite in direction force on object A.

Whenever object A exerts a force on object B, object B exerts an equal in magnitude and

opposite in direction force on object A.

YOU CAN’T TOUCH

WITHOUT BEING

TOUCHED

action: foot pushes the groundreaction: the ground pushes the foot that propels the turtle forward

You push the water backward, the water pushes you forward.

action: tire pushes roadreaction: road pushes tire

action: earth attracts ball a = F/m = 9.80 m/s2

reaction: ball attracts earth aE = F/ME ≈ 0

action: cannon pushes the cannonballreaction: cannonball pushes the cannon (recoil)The same force F (opposite direction), BUT

cannonball:

cannon:

a

=

Fm

a =

Fm

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.

Please help me! Why don’t action and reaction forces cancel? Should I find myself a less educated horse, or should I teach

better?

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!

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 thatwhen they clinch forces are equal – would you expect that?

Sudden acceleration can kill

again, the same force but different acceleration

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

physics

Tension: the force that the end of the rope exerts on whatever is attached to it. Direction of the force is along the rope.

T1T2

T2

Normal force (support force, normal reaction force)

The force which is preventing an object from falling through the surface of another body .

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 imperceptibly and produces a

reaction force equal to the force pressing the object into the surface.

That’s why normal force is always perpendicular (normal) to the surfaces in

contact.

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

For an object sitting on a horizontal surface, the normal force is equal to

the weight of the object.

Fn = mg

Fn

mg

Fn

mg

F

Fn

mg

F

If there is a force F trying to lift up the

object, it helps the normal force – the clever desk

doesn’t need to exert so much force

If there is a force F trying to lift up the

object, it helps the normal force – the clever desk

doesn’t need to exert so much force

Fnet = ma = 0

Fn + F = mg

Fn = mg - F

Fnet = ma = 0

Fn + F = mg

Fn = mg - F

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

Applied force F at an angle θ

vertical component of applied force, F sinθ, is helping the surface, so surface doesn’t need to provide as much force as without F. So, the force pressing the object into the surface is not full weight mg, but only part of it: mg - F sinθ

mg

F

Fn

horizontal: Fnet = ma = 0

Fn = F

FFn

mg

θFfr

Fn

mg

θFfr

F s

in θ

=

vertical: Fnet = ma = 0

Fn + F sinθ = mg

Fn = mg - F sinθ

Pushing an object into a wall

An object is on a rough incline θ.

Ffr

Fn

The first step is to draw free-body diagram with three forces acting on the body:

W = mg, normal force N, friction force Ffr.

Next step: solve equation

This is a vector equation.

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 net, = maF

Why? Simply because we know that a┴ , acceleration perpendicular to the surface is zero, and a║ is acceleration in the direction of the motion.

That will help us to find normal force.

=

Ffr

Fn

Resolve vector mg into two components. Now instead of three forces, we have four forces

direction perpendicular to incline:

Fnet = ma = 0 Fnet = Fn - mg cos θ

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 is in free fall not pressing the surface: θ = 900 → Fn = 0

Friction force Ffr

motion

friction

pulling force

friction

at rest

NRRRRRRRRRRRRRR

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 = 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.

surface-on-surface μs μk

hook velcro-on-fuzzy velcro >6.0 >5.9

avg tire-on-dry pavement 0.9 0.8

grooved tire-on-wet pavement 0.8 0.7

glass-on-glass 0.9 0.4

metal-on-metal (dry) 0.6 0.4

smooth tire-on-wet pavement 0.5 0.4

metal-on-metal (lubricated) 0.1 0.05

steel-on-ice 0.1 0.05

steel-on-Teflon 0.05 0.05You 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.

At the points of direct molecular contact, electrons become confused.They forget which object they belong to, and wind up trying to orbit 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 now force is required to break this bond 

1. Mechanical interlocking of "rough" surfaces

2. Microscopic level – in modern theory due to cold weld that is at atomic scale

Origin of friction is twofold:

On an atomic scale, few surfaces are very smooth. Bumps far smaller then we can see loom like mountains to an atom. Only a few of protrusions of one body are actually in contact with the protrusions of another body.

Thoughts of an electron with an identity crisis...

In this first example, a block of wood is shown sliding across a wooden table.  (notice the cause of this sliding is not shown)  Notice that the force of kinetic friction (fk) is equal to 40% of the normal force (FN).   Another way of writing this relationship would be

if the weight of the block is doubled, the normal force doubles, and the force of friction becomes doubled.  Once again we find that the force of kinetic friction (fk) is equal to 40% of the normal force (FN).  Another way of writing this relationship would be

As we compare the simulation of wood on wood to wood on asphalt, we find that the amount of friction on the block increased for for the same amount of weight.  Notice that the force of kinetic friction (fk) is equal to 60% of the normal force (FN) or we could say

Air Drag and Terminal Velocity

Kinematics equations: If a raindrops start in a cloud at a height h = 1200m above the surface of the earth they 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 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. 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.

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.

Draw all forces that act on a parachutist. Find Fnet and acceleration for

a. parachutist that has just stepped out of the airplane.

b. parachutist is falling at increasing speed.

a = g

c. parachutist is traveling downward with constant velocity (terminal velocity)

=

=

mg

mg

mg

Fdrag

Fdrag

Fnet

Fnet = 0

Fnet = mg a = Fnet/m = mg/m

Fnet = 0 a = 0

Fnet = mg - Fdrag a = (mg - Fdrag) /m

a = Fnet/m

a < g

the speed is still increasing, and therefore air friction too until

Air Drag and Terminal Velocity

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 ForcesFrictional Force

Tension Force

Normal Force

Air Resistance Force – Drag Force

Applied Force

Spring Force

Field ForcesGravitational Force

attraction between objects due to their masses

Electromagnetic Forcebetween charges

Strong Nuclear Forcekeeps nucleus together

Weak Nuclear Forcearise 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)

Although there are many different contact forces, they are all some form of only four different fundamental field

forces existing in the nature.

Strong nuclear 1 Short range( ~ 10 -15 )

Electromagnetic 10-2 Inverse square (infinite)

Weak nuclear 10-8 Extremely short range(~ 10-17 )

Gravitational 10-45 Inverse square (infinite)

FORCE RELATIVE ACTION DISTANCE STRENGTH

b-BETA decay

During radioactive decay (unstable nuclei), neutron can be disintegrated or transmuted into three particles!!!!!! proton, beta particle and neutrino. None of the known fundamental forces was able to explain this process. Research resulted in realizing that some, till then unknown force, was responsible for that process. It was called WEAK NUCLEAR FORCE.

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.

1 22

m mF = G

r 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.

r

rE – Earth’s radius mE – Earth’s mass. E E

2 2E E

m m mF = G = G m = gm

r r

2E2E

mg = G = 9.80m/s

r

The force between an object of mass m close to the Earth surface and the Earth

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

Newton’s second law is the most powerful because it allows quantitative calculations: how do velocities change when

forces are applied or in other words what is an acceleration of an object.

To be able to apply numerically Newton’s first and second law you have to find net force first.

To do that you have to draw FREE BODY DIAGRAM or FORCE DIAGRAM - sketch of an object and all forces

acting on that object

How to draw a force diagram

2. Make a simple sketch of the system – point system

1. Choose ONE body to be isolated

dog or the cart?

FRRRRRRRRRRRRRR

fr

mgRRRRRRRRRRRRRR

FRRRRRRRRRRRRRR

dog

NRRRRRRRRRRRRRR

FRRRRRRRRRRRRRR

net

3. Identify forces that act on the system Label them on diagram

4. Find out the net force by adding the force vectors

decision: cart

5. Apply Newton’s second law

netF = ma

y

x

Instead of having vector equation, which is very hard to solve, we can resolve vectors into components and have two ordinary equations for components. So:

netF = ma

Fnet = ma in x direction

Fnet = ma in y direction

Fnet = ma in direction

Fnet = ma in direction

we didn’t write indices x,y

means Fnet,x = max & Fnet,y = may

Question:

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

mgRRRRRRRRRRRRRR Fn – mg = ma = 0 → Fn = mg

apparent weight = weight

+

1. elevator is at rest or moving with constant speed

2. elevator is speeding up: a is positive

mgRRRRRRRRRRRRRR Fn – mg = ma → Fn = mg + ma

apparent weight > weightthe scale would show more, and you would feel heavier

3. elevator is slowing down: a is negative

mgRRRRRRRRRRRRRR Fn – mg = - ma → Fn = mg - ma

apparent weight < weightthe scale would show less, and you would feel lighter

Fn

Fn

Fn

FN

mg

θFfrFN

mg

θFfr

F sin θ

F cos θ

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.

1. free body diagram

2. apply Newton’s 2. law to horizontal and vertical component of net force.

x : F cos θ – Ffr = ma m = W/g = 800/10 = 80 kg

100 (cos 300) – 40 = 80 a a = 0.58 m/s2

+

y : F sin θ + N - mg = ma a = 0

100 x sin 300 + N – 800 = 0 N = 750 N

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 friction force is 300 N

(unusually large friction force), what is the acceleration of the bear?

direction perpendicular to incline:

Fnet = ma a = 0

Fn - mg cos θ = 0

Fn = mg cos θ = 520 N

direction along incline: Fnet = ma

mg sin θ - Ffr = ma

300 – 300 = 60a a = 0

m = 60 kg Ffr = 300 N θ = 300

g = 10 m/s2

ice can still support him, but he should not eat too much

Bear is sliding down at constant speed.

nF

Ffr

mg

F

mg

Ffr

mg

F

nF

nF

mg

F

nF

nF

nF

nF

θF

mg

nF

F sin θ

F

nF

mgmg

motion

pulling forceat rest

nF

nF

Ffr Ffr

nF

60 N

600 N