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WHAT DO OBJECTS DO WHEN NO FORCE IS ACTING ON THEM ??????. Aristotle (384 -322 B.C.) :. of CELESTIAL objects (Moon, planets, stars, Sun) was circular - without beginning or end. Natural Motion. of TERRESTRIAL bodies (apple, smoke, you) was
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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
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???
Isaac Newton (1642-1727) was born.
By the age of 24 he gave the world his famous three laws of motion.
• 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.
unit: 1 kg
Weightis 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
is the vector sum of all forces acting on ONE object.
Fnet or ΣF
it is the net force that changes the object’s state of motion
the object accelerates as if only one force – net force is applied
Applied forces Net force
Galileo’s Law of inertia
Remember: resultant force causes acceleration /change in velocity
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?"
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.
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
Since velocity is constant, the body is in translational equilibrium:
●F = 8N, 00
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
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 inertiawould 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 force,
If net force is zero, acceleration is zero, velocity is constant (or zero).
The object is in translational equilibrium.
Newton's third law
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.
- 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
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?
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 thatbody.
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.
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.
when they clinch forces are equal – you would expect that
when they clinch forces are equal – would you expect that?
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!!!!!
Tension:the force that the end of the rope exerts on whatever is attached to it. Direction of the force is along the rope.
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 resultsfrom 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 surface.
– object is not accelerating in vertical direction, therefore,
the vertical net force must be zero
how to find Fn
For an object sitting on a horizontal surface, the normal force is equal to the weight of the object.
If there is a forceF tryingto lift up the object, it helps the normal force – the clever desk doesn’t need to exert so much force
If there is push downforceF
– the desk has to exert more force
Fnet = ma = 0
Fn= mg + F
Fnet = ma = 0
Fn + F = mg
Fn = mg - F
If the desk can not exert enough force it will break
Ffr = mFn
coefficient of proportionality μ is called coefficient of friction
mhas 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.
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 :
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.
Thoughts of an electron with an identity crisis...
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, force is required to break this bond
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.
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.
a = Fnet/m
Fnet = mg a = Fnet/m = mg/m
a = g
b. parachutistis falling at increasing speed.
Fnet = mg - Fdrag a = (mg - Fdrag)/m
a < g
the speed is still increasing, and therefore air friction too until
c. parachutistis traveling downward with constant velocity (terminal velocity)
Fnet = 0 a = 0
Fnet = 0
Although there are many different contact forces, they are all some form of only four different fundamental field forces existing in the nature.
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.
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
rE – Earth’s radius
mE – Earth’s mass.
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
The most important one first
Draw free body diagram/force diagram
Draw free body diagram/force diagram
Draw free body diagram/force diagram
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
Third step is to apply second newton’s law
Label them on diagram
How to draw a force diagram
1. Choose ONE body to be isolated
dog or the cart?
2. 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
Add all vectors to get net force
Apply newton's second law
Vector equation ??????
Don’t worry, there is a way out.
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.
Vertical acceleration = 0
Vertical net force = 0
Fn= mg = 6.0 N
mg = 6N
Net force = friction force: Fnet=Ffr =1.2 N
1.2 = 0.60 a a = 2.0 m/s2
Ffr= FnFfr/ = 1.2/6.0 = 0.20 (no units)
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 acceleration = 0
Vertical Fnet= 0
Fn = mg = 52 N
v is constant,
a = 0 and Fnet = 0
Ffr= F = 36 N
Ffr= μ Fn
Ffr / = 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
a = 0, so Fnet= 0
Fn= mg = 50 N →Ffr = μ Fn = 50 μ
horizontal direction: a = 6.0m/s2
F – Ffr = ma
40.0 – Ffr = 30 Ffr= 10 N
Ffr = μ Fn
Ffr / = 10/50 =μ = 0.2
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 Ffr = 40 N
free body diagram components
F sin θ + Fn = mg
50 + Fn = 800
Fn= 750 N
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 tothe 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 cosθ
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
g = 10 m/s2
a = 0
Fn- mg cos θ = 0
Fn= 520 N < 550 N
ice can support him, but he should not eat too much
mg sin θ – Ffr = ma Ffr= μ Fn= 60 N
300 – 60 = 60 a
a = 4 m/s2
cute bear is speeding up!!!!
How does the weight of a person in an elevator depend on the motion of that elevator?
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
YOU HAVE TO DRAW TWO BODY DIAGRAMS !!!!!!
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.
Fnet = ma a is up
T – mg = ma
T – 0.9 = 0.09a first equation
Fnet = ma a is up
mg – T= ma
1.1 – T = 0.11a second equation
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
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.
T = 10a
50 – T = 40a
50 – 10a = 40a a = 1 m/s2
T = 10a = 10 N