AND chapter 12

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What is a FORCE?

• A FORCE is a push or pull that acts on an object.

• A force can cause a resting object to move• OR…• Accelerate a moving object by:

– changing the object’s speed– direction

How do we MEASURE force?

• Forces can be measured on a scale– WEIGHT is a FORCE

• UNITS OF FORCE:– Newton (N)– A Newton is a force that causes a 1 kg mass to

accelerate at a rate of 1 meter per second each second

• Which is written as: 1 N = 1 kg m/s2

Representing Forces

• Forces can be represented with an arrow– The length of the arrow shows strength or

magnitude– Direction of the arrow shows the direction of the

force• Figure 2 on page 357 shows an example of weight

Normal Force

Friction ForceApplied Force

Combining Forces (Vectors)

• Rules of Vector Addition– Forces in the same direction add together + = 1x 1x 2x

– Forces in opposite direction subtract from one another

+ =1x + -2x = -1x

NET FORCE• NET FORCE is the overall force acting on an object

after all the forces are combined + = 1x + 1x = 2x

• The net force above is 2x

• NOTE: Forces that are equal in strength and opposite in direction result in NO NET FORCE!!!

– page 358 figure 4

+ = ZERO

Balanced Forces

• Question: what are some examples where the net force would equal zero?

• HINT: When the forces on an object are balanced

• Balanced Forces = the net force is zero, there is no change in the object’s motion

ANSWER

• Net force would be zero when:– You play tug-of-war and neither team moves– You arm wrestle and neither person wins– Others???

Unbalanced Forces

• Question: What happens to the object when the net force acting on an object is NOT ZERO, or unbalanced? (like the example below)

+ =

Unbalanced Forces = the net force acting on an object does not equal zero = acceleration!

Answer• When an unbalanced force acts on an object,

the object accelerates– 3 examples of a net force causing an object to

accelerate • Pushing against the side of a book that is resting• A team winning a game of tug-of-war• A person in freefall

Try these problems

1. Two tugboats are moving a barge. Tugboat A exerts a force of 3000 newtons on the barge. Tugboat B exerts a force of 5000 newtons in the same direction. What is the combined force on the barge? Draw arrows showing the individual and combined forces of the tugboats in this problem to help you answer the question

Answer to Question 1

2. Now suppose that Tugboat A exerts a force of 2000 newtons on the barge and Tugboat B exerts a force of 4000 newtons in the opposite direction. What is the combined force on the barge? Draw arrows showing the individual and combined forces of the tugboats in this problem.

Answer to Question 2

3. Could there ever be a case when Tugboat A and Tugboat B are both exerting a force on the barge but the barge doesn't move? Draw arrows showing the individual and combined forces in such a situation.

Answer to Question 3

FRICTION

FRICTION• Friction: a force that opposes the motion of

objects that touch as they move past each other

• Without friction, it would be a very different world!!!– Food would not stay on your fork!– Cars would slide all over the road!– Walking would be almost impossible!

• Friction acts at the surface where objects are “in contact”

The 4 Types of Friction

• There are 4 main types of friction:– Static Friction

– Sliding Friction

– Rolling Friction

– Fluid Friction

STATIC FRICTION

• friction force that acts on objects that are not moving

• Static friction always acts in the direction opposite to the applied force

• Examples: – every time you take a step and push off– glass of water sitting stationary on the table

SLIDING FRICTION• a force that opposes the direction of motion

of an object as it slides over a surface• Sliding friction is a weaker force than static

friction– This is why less force is needed to keep an object

moving than it is to start it moving

ROLLING FRICTION• The friction force that acts on rolling objects• Rolling friction is about 100-1000 times less

than static or sliding friction– This is why we use wheeled dollies to move heavy

objects!– In machines, ball bearings, are often used to

reduce friction between two surfaces

FLUID FRICTION• Force that opposes the motion of an object

through a fluid– Water and a mixture of gases such as air are

known as fluids– Example: stirring cake batter

• The motion of stirring is slowed by fluid friction• Fluid friction increases as the speed of the object

moving through the fluid increase– So the faster you stir the greater the friction!!!

AIR RESISTANCE• Air resistance is a type of fluid friction

– Remember…gases are considered “fluids”

• Fluid Friction acting on an object moving through the air is called AIR RESISTANCE

GRAVITY

GRAVITY• Gravity: a force that acts between any two

masses– Gravity is an attractive force so it pulls objects

together– Gravity does not require objects to be in contact

for it to act on them• Gravity can act over large distances!!!

More GRAVITY!• Earth's gravity acts downward toward the center

of the Earth.

• There is usually an upward force that acts against gravity to balance out the forces and allow objects to remain still.

FALLING OBJECTS

• QUESTION: What forces are acting on an object as it falls?

• ANSWER: Only two forces acting on a falling object are gravity and air resistance

Forces Acting on Falling Objects

• Gravity causes object to accelerate downward• Air resistance acts in the opposite direction of

the motion– Which means it reduces acceleration

• Recall…what happens to the amount of fluid friction as an object speeds up?

Falling Objects• If an object in freefall falls for long enough, the

upward force of air resistance will become equal to the downward force of gravity.

– At this point, the two forces are BALANCED

– Acceleration is zero when forces are balanced

– The object will continue to fall at a constant velocity

Terminal Velocity• Terminal Velocity: the constant velocity of a

falling object when the force of air resistance equals the force of gravity

Projectile Motion

• Projectile Motion: The motion of a falling object (projectile) after it is given an initial forward velocity

Projectile Motion

• Question: What are the ONLY 2 FORCES that act on a projectile???

All 3 balls are experiencing projectile motion!

Projectile Motion

• Answer: Air resistance and gravity!!!

– Refer to figure 9 on page 362 in textbook

– The combination of an initial forward velocity and the downward vertical force of gravity causes the ball to follow a curved path

• If I shoot a bullet horizontally and at the same time drop a bullet from the same height as the gun…which will hit the ground first?

FALLING OBJECTS

• The two bullets WILL hit the ground at the same time!

The two balls fall with the same acceleration and strike the ground at the same time!!!

Remember the “Investigating Freefall Lab” with the marbles? How did that lab compare with the previous statement???

12.2 Newton’s First & Second Laws of Motion

It’s not ALL about Newton…• Aristotle incorrectly proposed that force is required

to keep an object moving at a constant speed• Galileo studied how gravity produces constant

acceleration. He concluded that objects not subjected friction or any other force would continue to move indefinitely

• Newton built off the work of Galileo and later published his work in a book entitled Principia

• Newton summarized his study of force and motion in several laws of motion

1st Law of Motion – Law of Inertia

1st Law of Motion – Law of Inertia

• 1st Law: The state of motion of an object does not change as long as the net force acting on the object is zero

– In other words: Unless an unbalanced force acts, an object at rest remains at rest, and an object in motion remains in motion with the same speed and direction

1st Law – Law of Inertia• Example: A soccer ball resting on the grass

remains motionless until a force is applied to it in the form of a kick.– The kicked ball begins rolling…and continues to

roll…– Will the ball ever stop? If so, why?

Will the ball stop rolling?

• YES…BECAUSE • Friction between the ball and grass acts on

the ball as it rolls, the ball slows• The force of friction slows the ball and

eventually brings it to a stop

Why is it called the “Law of Inertia”• INERTIA: the tendency of an object to resist a

change in its motion (an object at rest tends to remain at rest, and an object in motion tends to remain in motion with the same direction and speed) – Remember…soccer ball sat motionless (forces were

balanced) until an unbalanced force acted on it– The ball has inertia– Everything with mass has inertia– The more mass, the more inertia

Inertia…Front-end collision

• Example: Front-end collision • Collision makes car stop suddenly• Since you have inertia you continue moving

forward• Page 364/365 Figure 12

Newton’s Second Law of Motion

2nd Law of Motion

• 2nd Law: The acceleration of an object is equal to the net force acting on it divided by the object’s mass.

Net ForceAcceleration = --------------

Mass

Acceleration…Force & Mass Relationship

What would be the acceleration?

ANSWER

• Acceleration is calculated by dividing the FORCE by the MASS

Acceleration = 100 N / 50 kg A = 2 m/s2

Question…• How do unbalanced forces affect the motion

of an object???

Identify the UNBALANCED force in the picture above.

Answer…• An unbalanced force causes an object’s

velocity (change in speed or direction) to change. In other words, accelerate!– Example: You apply force to a ball when you

throw it • The harder you throw, the more the ball accelerates• If you double the force, the acceleration of the ball

doubles as well• If you double the mass of the ball the acceleration is

cut in half

Newton learned that the acceleration of an object depends upon its mass…

• MASS: a measure of the inertia of an object and depends on the amount of matter the object contains

Important Notes…Regarding Newton’s 2nd Law of Motion

• The acceleration of an object is always in the same direction as the net force.

• In using Newton’s second law, it is helpful to realize that the units N/kg and m/s2 are equivalent

• Newton’s second law also applies when a net force acts in the direction opposite to the object’s motion – producing deceleration (See figure 13, page 368)– This is the principle used by automobile seat belts

• See Math Skills page 367 (in textbook) for extra help

Weight & Mass…What really is the difference?

• We often talk about weight and mass as if they were the same thing

• Weight: is the force of gravity acting on an object.– An object’s weight is the product of the object’s

mass and acceleration due to gravity acting on it.– Written mathematically as w = m x g

Weight lessens as…

Weight will DECREASE if gravity DECREASES!!!

Mass Versus Weight

• Mass is a measure of the inertia of an object; weight is a measure of the force of gravity acting on an object (Different Ideas)

• Weight = Mass x Acceleration due to gravity– W = mg– Value of g = 9.8 m/s2 (Earth)

Important Note Regarding Units

• Be sure when you use the weight formula or Newton’s second-law formula that you use the CORRECT units!!!

• Force (F or W) in N (newtons)• Acceleration (a or g) in m/s2 (meters per

second per second)• Mass (m) in kg (kilograms)

Practice Problem

• If an astronaut has a mass of 112 kilograms, what is his weight on Earth where the acceleration due to gravity is 9.8 m/s2?

• What would his weight be on the moon (g=1.62 m/s2)?

Answer to Practice Problem

• ON EARTH: Weight = Mass Acceleration due to gravity W = 112 kg x 9.8 m/s2

W = 1097 kgm/s2 = 1097 N

• ON MOON:– W = 112 kg x 1.62 m/s2

– W = 181 kgm/s2 = 181 N

Mass & Weight are Proportional

• Doubling the mass of an object also doubles the object’s weight– Example: Think about the astronaut above… – On the moon, the acceleration due to gravity is

only about 1/6 that on Earth– Thus, the astronaut weighs only about 1/6 as

much on the moon as on Earth

• In both locations, the mass of the astronaut is the same!

12.3 Newton’s 3rd Law of Motion

Forces CAN’T Exist Alone…• Forces always exist in pairs.

• According to Newton’s 3rd law of motion, whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.

• These two forces are called action and reaction forces

Action – Reaction Forces• Example: The book lying on the table is

exerting a downward force on the table, while the table is exerting an upward reaction force on the book.

Newton’s Third Law Ex: A rocket

• More Examples: Jumping off of a raft

Action force = you push on the raftReaction force = raft pushes back

A swimmer in a poolAction force = swimmer’s arm pushes on waterReaction force = water pushes back on swimmer

Action – Reaction Forces• Question: Since these action/reaction forces

are equal in size and opposite in direction then why don’t they cancel each other out and produce a net force of zero?

Action – Reaction Forces

• Because the action/reaction forces do not act on the same object!

• Swimmer Example: – The action force acts on the water– The reaction force acts on the swimmer

Momentum

• Momentum = the product of an object’s mass and it’s velocity

• An object with a large momentum is hard to stop

• Momentum = mass X velocity

• Practice Problem: What is the momentum of a rock with a mass of 0.5kg that is moving at a velocity of 5m/s?

• Momentum = 0.5kg X 5m/s = 2.5kg x m/s– The units do NOT cancel!

• Momentum can be transferred from one object to another during a collision

12.4 – Universal Forces

Four Universal Forces

1. Electromagnetic forces- only forces that both attract and repel.

2. Strong Nuclear forces- holds neutrons & protons together

3. Weak Nuclear forces- attractive force between particles in nucleus

4. Gravitational forces- attractive force between any two objects

GRAVITY• Gravity is the weakest universal force • On a daily basis, you don’t notice the force of

gravity that you exert on objects—this is because your mass is sooooooo small.

• It takes a huge mass like the Earth’s to exert a large gravitational force.

GRAVITY• Gravitational force depends on two things: the

mass of an object and the distance between two objects. – A greater mass will exert a greater gravitational

force on an object.– The greater the distance between two masses

significantly decreases the gravitational force.– Refer to Figure 21 on page 350 that shows the

attractive force of gravity acting between two objects.

GRAVITY…how can it be so weak?• Even though gravity is the weakest universal force, it

is the most effective over large distances.– Gravity holds you on the ground– It holds the moon in orbit around the Earth– It holds the planets in orbit around the Sun– It holds the stars in orbit around their galaxies

Centripetal Force

• The force of gravity from the Earth continuously pulls the moon in a nearly circular orbit around the Earth.

• Centripetal force: center-directed force that continuously changes the direction of an object to make it move in a circle.– As an object moves in a continuous (constant)

circular motion, it is accelerating.– How is it accelerating if it does not change speed?

• Change in direction!!!

Centripetal Force

• It’s a lot like a string tied to an eraser…• The force from the center of the string allows

the eraser to twirl in a circle over your head• As you twirl the eraser, the string exerts a

centripetal force on the eraser.

Orbital Motion

• Objects need only a centripetal force and their own inertia to maintain an orbit.

• Orbital motion is a balance between the centripetal force and inertia.

• If Centripetal force is stronger it will crash, if inertia is stronger it will fly off into space

How is this possible?!?!

Same Place…Same Day…??? HOW!!!???

How is that possible?• Ever been to the seashore? What do you

notice about the level of the water throughout the day? Why does it change? – The gravitational pull from the Moon produces

two tides in the Earth’s oceans as it moves around the Earth.

• One bulge where the moon is closest to the Earth• One bulge where the moon is farthest from the Earth

Tides

• Since the Earth rotates once per day, it results in two high tides and two low tides per day on Earth!

http://home.hiwaay.net/~krcool/Astro/moon/moontides/  

Rotation versus Revolution• The Earth moves in two major ways:

– Rotation- the spinning of the Earth on its axis• This rotation causes day and night

– Revolution- the movement of one body in space around another

• When does the Earth show revolution? Revolves around the Sun

– How long does it take for the Earth to revolve?• 365 Days

Ch 13 Forces in Fluids

13.1 Fluid Pressure

• Why is an Aeron chair so much more comfortable than a bicycle seat?

• Pressure = the result of a force distributed over an area

• Ex: the tip of a pencil easily pokes through a sheet of paper while the eraser end does not

• Ex: finger poke vs needle poke

• Pressure = Force/Area• Units of Pressure = N/m2 = Pascal (Pa)

• Practice problem: A box weighing 2700 N is resting on the ground. If the box is covering 1.5 square meters of area, what is the pressure?

• Pressure = 2700 N/1.5 m2 = 1800 Pa = 1.8 kPa

Pressure in Fluids

• Recall: a fluid is a substance that takes the shape of its container, both liquids and gases are fluids

• What happens to the pressure exerted on your body as you dive deeper in a pool?

• Water pressure increases as depth increases

• The relationship between pressure and the depth of a fluid can be shown with this formula: P = d x h x g

• d = density• h = depth• g = accel due to gravity

• Fluid pressure is determined by the type of fluid and its depth

• Which would exert more fluid pressure at a depth of 20 m, Lake MI or the Gulf of Mexico?

Air Pressure & the Atmosphere

• We live at the bottom of a vast ocean of air. • The weight of the Earth’s atmosphere exerts

pressure. At sea level = 101 kPa

• We refer to a certain altitude instead of a depth

• Air pressure decreases as the altitude increases

• Why do your ears pop while traveling up a mountain?

• The difference in pressure between the inside of your ear and the air outside causes air to pass through a small tube within your ear to equalize the pressure.

• This is the popping sensation you feel

• The atmosphere is exerting more than 1000 N on the top of your head. Why aren’t we crushed by this?

• The inside of your body exerts pressure against the air pressure outside which balances and results in a net force of zero.

Bernoulli’s Principle

• Bernoulli’s Principle = as the speed of a fluid increases, the pressure within the fluid decreases

• Demo: take a piece of paper and blow across the top of the paper

Wings & Lift

• The ability of birds and airplanes to fly is explained by Bernoulli’s principle

• The air traveling over the top of the curved wing travels faster so the pressure is less which create the lift