Transcript Forces - Uplift Education

An Historical Overview
Click me
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.
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.
Conclusion: EARTH is THE CENTER OF UNIVERSE
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.
Click me
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.
Lets look at animated model of solar system and universe in general
Remember when we talked about speed of our Earth:
• 0.4 km/s (0.25 mi/s) rotating around the center of the Earth
• 30 km/s relative to the Sun
• at about 250 km/s relative to the center of our galaxy
• together with the whole galaxy at 600 km/s (1.34 million mi/h)
in the direction of the constellation Hydra.).
Here is a wonderful animation
http://www.youtube.com/watch?v=0jHsq36_NTU
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, not cause 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.
Aristotle’s views of motion were
discredited almost 400 years ago. So
why do we still tend to follow his
thinking about motion?
Forces throughout History
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.
Together, Galileo and Newton discredited the Aristotelian view
of motion and developed the theories that still form the basis
of mechanics today.
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
• An interaction between two objects involving a push or a pull
• Causes objects to accelerate
NOTE: ALL forces are INTERACTIONS between 2 objects
Forces are vector quantities, having both direction and magnitude.
unit: Newton (N) = kg m/s2
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
Check your understanding
Galileo’s Law of inertia
"How many ways can you state Newton's First Law?"
if ΣF = 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."
Remember: net force (sum of all forces acting on an object)
causes acceleration /change in velocity of that object
BIG IDEA 1: Zero NET force means no acceleration / no change in
velocity. Balanced forces will not cause acceleration.
BIG IDEA 2: An object is in equilibrium (i.e. it has zero net force)
whenever it has constant velocity (including constant velocity of 0).
Translational equilibrium
Definition:
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 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.
8N
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 𝑭 = 0 then 𝒂= 0, change in velocity = 0
and velocity is constant or zero
if velocity is constant or zero, then 𝒂= 0, and
8N
𝑭=0
8N
F
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.
The seatbelt provides the force to keep the driver
from moving out of the position
No seat belts: The passengers maintain their state of motion unless
there is a force strong enough to stop them.
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.
Imagine you have two baskets of strawberries. You place one on
the passenger seat of the car, near the car door. The other you
forget on top of the car. Oops!
Like pancakes for the French club meeting. Still remember
You then drive out of the parking lot, turning at a constant speed.
What happens to each basket of strawberries, and why?
Although the car accelerates (changes direction!) , the baskets
will tend to continue in the same straight line motion unless a
force stops them.
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,
𝐹
𝑎=
𝑚
 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.
Even Spiderman has the weight, right?
Pulling him downward.
what propels him upward?
His muscles? Hm…. No!!!!!!
Just imagine Spiderman hanging
on a rope.
Can his muscles help him to
climb up into the thin air?????
To understand what propels us forward
( or, if someone choses backward) we’ll
introduce third Newton’s law and come
back to this problem later.

YOU CAN’T
TOUCH WITHOUT
BEING TOUCHED
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
cannonball:
a
cannon:
a
=F
m
=F
m
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 particular 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
So what propels him upward?
Upward force exerted by the WALL !!!!
Friction force!!!!!
He is pushing wall downwards and the wall is …..
𝑚𝑔
𝐹𝑓𝑟
𝑚𝑔
1. How many horizontal forces are acting on the person?
Label them
2. Draw free body diagram for the cart?
Tension 𝑻 is the force that the end of the string exerts on whatever is
attached to it. Direction of the force is along the rope.
Normal force (unfortunate name – reaction force) R
The force which is preventing an object from falling
through the surface of another body. That’s why it is normal
(perpendicular) to the surface .
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.
Fn
Ffr
pulling force
mg
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
N
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
0.05
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 Resistance 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. 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
𝐹 and acceleration for
a. parachutist that has just stepped out of the airplane.
Σ𝐹 = 𝑚𝑔
𝑎=
𝑚𝑔
𝑚
mg
a=g
b. parachutist is falling at increasing speed.
Σ𝐹 = 𝑚𝑔 − 𝐹𝑎𝑖𝑟
𝐹 air
=
Σ𝐹
mg
𝑎=
𝑚𝑔 − 𝐹𝑎𝑖𝑟
𝑚
a<g
the speed is still increasing, and therefore air friction too until
c. parachutist is traveling downward with constant velocity (terminal velocity)
Fnet = 0
𝐹 air
=
mg
a=0
Σ𝐹 = 0
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.
m1m2
F=G 2
r
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.
The force between an object of mass m close to the Earth surface and
the Earth
mEm
mE
F = G 2 = G 2 m = gm
rE
rE
rE – Earth’s radius
mE – Earth’s mass.
mE
g = G 2 = 9.80m/s2
rE
Force between an object of mass m close to the Earth surface and the Earth
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 ONE body to be isolated
dog or the cart?
decision: cart
F
𝐹𝑛
dog
F2. Make a simple sketch of the system – point system
fr
ΣF
mg
4. Find out the net force by
adding the force vectors
5. Apply Newton’s second law
Fnet = ma
So
1. Add all vectors to get net force
2. Apply newton's second law
𝐹= m𝑎
Are you kidding me??
Don’t worry, there is an easy way out.
Separate everything
into vertical and horizontal components/motion
And remember that magnitudes of forces are positive
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:
Vertical acceleration = 0
Fn
0.60 kg
Ffr
Vertical force ΣF = 0
Fn – mg = 0
Fn = mg = 6.0 N
mg = 6N
Ffr = 𝜇 Fn
𝜇 = Ffr / Fn = 1.2/6.0
𝜇 = 0.20
c. higher
(no units)
Horizontal direction:
Resultant force = friction force
ΣF = Ffr =1.2 N
ΣF = ma
1.2 = 0.60 𝑎
𝑎 = 2.0 m/s2
ΣF
We read this as : SUM of (all) forces,
not as SOME of forces
Although they sound the some, there is a
HUGE difference
Thank you Mr. Bruhn for clarifying possible
confusion -
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 ΣF = 0
Fn–mg = 0
Fn = 52 N
Horizontal direction:
v is constant,
a = 0 and ΣF = 0
Ffr = F = 36 N
Ffr = μ Fn
𝜇 = Ffr / Fn = 36/52
𝜇 = 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 ΣF = 0
Fn = mg = 50 N →
horizontal direction:
ΣF.= ma
F – Ffr = ma
40.0 – Ffr = 30
Ffr = 10 N
Ffr = μ Fn
𝜇 = Ffr / Fn = 10/50
𝜇 = 0.2
a = 6.0m/s2
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
components
vertical direction :
ΣF=0
F sin θ + Fn–mg = 0
50 + Fn = 800
Fn = 750 N
Horizontal direction:
ΣF= ma
F cos θ – Ffr = ma
86.6 – 40 = 80 a
a = 0.58 m/s2
An object is on incline θ.
Fn
We know that acceleration perpendicular to the surface is zero;
acceleration can be only parallel to incline.
Ffr
Therefore the most natural choice of coordinate
system / components is:
● one parallel to the incline
Fn
● one perpendicular to the incline.
Ffr
Now instead of three forces,
we have four forces
direction perpendicular to the incline:
ΣF = ma = 0 → Fn–mg cos θ = 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 panda, 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:
ΣF = ma = 0
Fn - mg cos θ = 0
Fn = 520 N < 550 N
ice can support him, but he should
not eat too much
Ffr = μ Fn = 60 N
Parallel direction:
ΣF = ma
mg sin θ – Ffr = ma
300 – 60 = 60 a
a = 4 m/s2
cute panda is speeding up!!!!
Question:
How does the apparent 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 up with constant speed
2. speeding up (𝑎 = 3𝑚/𝑠 2 ↑ )
3. slowing down (𝑎 = 3𝑚/𝑠 2 ↓ )
m = 65 kg
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
1. draw free body diagram 2. choose upward positive 3. apply Newton’s 2. law : ΣF = ma
Fn
1. elevator is at rest or moving up with constant speed
Fn – mg = ma = 0
apparent weight = weight = 650 N
mg
Fn
1.2. elevator is speeding up: (𝑎 = 3𝑚/𝑠 2 ↑ )
Fn – mg = ma
mg
Fn
→ Fn = mg + ma = 845 N
apparent weight > weight
the scale would show more, and you would feel heavier
1.3. elevator is slowing down: (𝑎 = 3𝑚/𝑠 2 ↓ )
Fn – mg = ma
mg
→ Fn = mg = 650 N
→ Fn = mg + ma = 650 N – 195 N = 455 N
apparent weight < weight
the scale would show less, and you would feel lighter
+
A system of two cables supports a 150-N ball as shown.
a) What is the tension in the right-and cable?
b) What is the tension in the horizontal cable?
𝑇1
𝑇2
mg=150N
x: ΣF = 0
T1 cos 300 – T2 = 0
y:
T2 = 260 N
ΣF = 0
T1 sin 300 – 150 = 0
T1 = 300 N
WHEN THERE ARE TWO BODIES
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.
two equations with two unknowns
T – 0.9 = 0.09a
1.1 – T = 0.11a
(1) + (2):
(1)
(2)
0.2 = 0.2 a ⟹ a = 1 m/s2
T = 0.09a + 0.9
⟹ T = 0.99 N
ΣF = ma
T – mg = ma
T – 0.9 = 0.09a
a is up
ΣF = ma
mg – T= ma
1.1 – T = 0.11a
a is down
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.
ΣF = ma
T = 10a
50 – T = 40a
a is to the right
a is to the right
2 EQS with 2 unknowns
50 – 10a = 40a
T = 10a
a = 1 m/s2
T = 10 N
Please do now:
Draw Free body diagram
for object A and object B:
Block A, with a mass of 10 kg, rests on a 30° incline. The coefficient of
kinetic friction is 0.20. The attached string is parallel to the incline
and passes over a massless, frictionless pulley at the top. Block B,
with a mass of 8.0 kg, is attached to the dangling end of the string.
The acceleration of B is:
Click me