Meters of Motion, a watercolor by Champaign-Urbana artist, Billy Morrow Jackson, is the basis for the poster announcing the 20th International Congress of Theoretical and Applied Mechanics, held in Chicago in August of 2000.

ForcesForces

Chapter 3Chapter 3

Sections 1 - 3Sections 1 - 3

Chp 3 - ForcesChp 3 - Forces

• Section 1 – Weathering Section 1 – Weathering slides 3 - 20slides 3 - 20• Section 2 – Gravity Section 2 – Gravity slides 21-38slides 21-38• Section 3 – The Third Law of Motion Section 3 – The Third Law of Motion

slides 39-52slides 39-52

Section 1 - WeatheringSection 1 - Weathering

• What You’ll Learn:What You’ll Learn:• How force, mass, & acceleration are How force, mass, & acceleration are

relatedrelated• The three different types of frictionThe three different types of friction• How air resistance affects falling How air resistance affects falling

objectsobjects

Force, Mass, and Force, Mass, and AccelerationAcceleration

• You read about Newton’s first law of You read about Newton’s first law of motion which says that the motion of motion which says that the motion of an object changes only if an an object changes only if an unbalanced force acts on it.unbalanced force acts on it.

• Newton’s second law of motion Newton’s second law of motion describes the relationship between describes the relationship between the acceleration of an object, its the acceleration of an object, its mass, and the forces exerted on it.mass, and the forces exerted on it.

How are force & How are force & acceleration related?acceleration related?

                                                                                          

How are throwing a ball as hard as you can & tossing it gently different?

                                                                                                                                                                                                               

How are force & How are force & acceleration related?acceleration related?

                                                                                          

How are throwing a ball as hard as you can & tossing it gently different?

The first requires more force creating a greater velocity in less time. Tossing gently takes less force as well as less velocity and acceleration.                                                                                                                                                                                              

Are mass & acceleration Are mass & acceleration related?related?

• If you throw a If you throw a softball and a softball and a baseball as hard you baseball as hard you can, will they have can, will they have the same speed?the same speed?

• Because a softball Because a softball has more mass, it will has more mass, it will have less velocity have less velocity even though you even though you applied the same applied the same force. This means force. This means that acceleration also that acceleration also depends mass as well depends mass as well as force.as force.

<http://www.essexfellsrec.com>

Newton’s Second LawNewton’s Second Law

• Newton’s second law of motion Newton’s second law of motion states that the net force acting on an states that the net force acting on an object causes the object to accelerate object causes the object to accelerate in the direction of the net force.in the direction of the net force.

• To find the acceleration, you must To find the acceleration, you must know the mass and the net force.know the mass and the net force.

• Acceleration (Acceleration (αα)= net force (in )= net force (in N)/mass (kg) or N)/mass (kg) or αα= F/m= F/m

How can the second law How can the second law help find net force?help find net force?

• If you know an object’s mass & If you know an object’s mass & acceleration, you can use Newton’s acceleration, you can use Newton’s second law to find the force by using second law to find the force by using the equation F=ma.the equation F=ma.

• Suppose a tennis ball leaves a racket Suppose a tennis ball leaves a racket with a speed of 100 km/h with an with a speed of 100 km/h with an acceleration of 5,000 m/sacceleration of 5,000 m/s22. The ball’s . The ball’s mass is 0.06 kg. F=ma so: (0.06 kg)mass is 0.06 kg. F=ma so: (0.06 kg)(5,000m/s(5,000m/s22)= 300 kg m/s)= 300 kg m/s22 = 300 N = 300 N

FrictionFriction

• FrictionFriction is the force is the force that opposes the that opposes the sliding motion of two sliding motion of two surfaces that are surfaces that are touching each other. touching each other. The amount of friction The amount of friction between the two between the two depends on two depends on two things: the kind of things: the kind of surfaces & the amount surfaces & the amount of force pressing them of force pressing them together.together.

<http://z.about.com/d/skateboard/1/5/i/M/axlestall4.jpg>

What causes friction?What causes friction?

• Microwelds occur Microwelds occur where two where two surfaces stick surfaces stick together due to together due to roughness. roughness. Friction is caused Friction is caused by the microwelds by the microwelds that form where that form where the surfaces are in the surfaces are in contact.contact.

<http://www.sra-developments.co.uk/img/micrograph_01.gif>

polymer fabric welded with ultrasound

What makes things stick What makes things stick together?together?

• The stronger the force pushing two The stronger the force pushing two surfaces together, the stronger the surfaces together, the stronger the microwelds will be.microwelds will be.

• To move one surface over another, a To move one surface over another, a force must be applied to break the force must be applied to break the microwelds.microwelds.

What is static friction?What is static friction?

• Static frictionStatic friction is is the force that keeps the force that keeps two surfaces at rest two surfaces at rest from sliding across from sliding across each other.each other.

• The mechanic The mechanic shown here is shown here is attempting to attempting to break a nut seize break a nut seize caused by static caused by static friction.friction. <http://www.beisansystems.com/

procedures/e39_fan_procedure_files/image010.jpg>

What is sliding friction?What is sliding friction?• Sliding frictionSliding friction is is

the force that works the force that works against the motion against the motion of two surfaces that of two surfaces that are sliding across are sliding across each other.each other.

• Another example Another example would be wheels would be wheels spinning in snow or spinning in snow or mud. Sand or gravel mud. Sand or gravel will increase the will increase the sliding friction so sliding friction so the wheels can roll the wheels can roll w/o slipping.w/o slipping.

<http://www.superphysics.netfirms.com/fricti1.jpg>

What is rolling friction?What is rolling friction?

• Rolling friction Rolling friction is is the frictional force the frictional force between a rolling between a rolling object and the object and the surface it rolls on.surface it rolls on.

• A wheel digs into A wheel digs into the surface it is the surface it is rolling over rolling over deforming both the deforming both the wheel and the wheel and the surface.surface. <http://www.ofs.edu.sg/our-schools>

Air ResistanceAir Resistance

• Air resistance Air resistance is a force that opposes the is a force that opposes the movement of objects through the air. movement of objects through the air. Similar to friction, air resistance acts in Similar to friction, air resistance acts in the direction opposite to the object’s the direction opposite to the object’s motion.motion.<http://www.bmw.ie/ie/en/insights/technology/efficient_dynamics/

innovative_technologies/_shared/img/air_vent_control.jpg>

Air ResistanceAir Resistance

• Objects falling Objects falling toward Earth are toward Earth are being pulled being pulled downward by the downward by the force of gravity. force of gravity.

• Air resistance Air resistance is a is a force that opposes force that opposes the movement of the movement of objects through the objects through the air. air.

• Air resistance is Air resistance is similar to friction.similar to friction.<http://www.nasa.gov/

centers/marshall/images>

Air ResistanceAir Resistance

• In the case of a In the case of a falling object, air falling object, air resistance pushes resistance pushes up as gravity pulls up as gravity pulls down.down.

• If there were no air If there were no air resistance, only resistance, only gravity would affect gravity would affect falling objects.falling objects.

• All objects would All objects would fall at the same fall at the same rate.rate.<http://z.about.com/d/

inventors/1/5/0/2/1/parachute2.jpg>

Air ResistanceAir Resistance

• Different objects fall Different objects fall with different with different accelerations and accelerations and different speed due to different speed due to their size and shape.their size and shape.

• Compare the forces Compare the forces on a sheet of paper to on a sheet of paper to those on a crumpled those on a crumpled sheet. Which has the sheet. Which has the greater net greater net downward force?downward force?

<http://www.bioinformaticszen.com/>

<http://upload.wikimedia.org/wikipedia/commons/3/3f/Paper_sheet.jpg>

Section 2 - GravitySection 2 - Gravity

• What You’ll Learn:What You’ll Learn:• How gravity & weight are relatedHow gravity & weight are related• The difference between mass & The difference between mass &

weightweight

What is gravity?What is gravity?• Gravity Gravity is an is an

attractive force attractive force between two objects. between two objects.

• It increases as the It increases as the mass of either object mass of either object increases, or as the increases, or as the objects move closer objects move closer to one another.to one another.

• You can’t feel You can’t feel gravitational force gravitational force between you and the between you and the table. Why?table. Why?

<http://openlearn.open.ac.uk/file.php>

<http://hegel.lewiscenter.org/users/mhuffine/subprojects/Department/images/psci2.jpg>

Law of Universal Law of Universal GravitationGravitation

• This lets us find the This lets us find the force of gravity force of gravity between any two between any two objects if their masses objects if their masses & the distance & the distance between them are between them are known.known.

• G=universal G=universal gravitational constant gravitational constant (never changes)(never changes)

• D=distance; m=massD=distance; m=mass

<http://www.williamsclass.com/EighthScienceWork/ImagesEighth/GravitationalForce.jpg>

Why is gravity called a Why is gravity called a long-range force?long-range force?

• Gravitational force Gravitational force between two masses between two masses decreases as the decreases as the distance between distance between them increases.them increases.

• No matter how far No matter how far apart two objects are, apart two objects are, the gravitational force the gravitational force between them never between them never completely goes to completely goes to zero.zero.

• This is also called the This is also called the inverse square law.inverse square law.

<http://schoolnet.gov.mt/earth_universe/images/10184_w.jpg>

How did gravity help How did gravity help astronomers find other astronomers find other

planets?planets?• The motion of every The motion of every planet is affected by planet is affected by the gravitational the gravitational forces of the other forces of the other planets.planets.

• In 1840 the farthest In 1840 the farthest known planet was known planet was Uranus, but its Uranus, but its motion could not be motion could not be explained by the explained by the attraction of the attraction of the other known planets.other known planets.

• Neptune’s discovery Neptune’s discovery resulted from this.resulted from this.

<http://www.redorbit.com/modules/reflib/article_images/8_d7f84ec36dbfda23aff1a01e00a4b5e6.jpg>

Earth’s Gravitational Earth’s Gravitational AccelerationAcceleration

• A falling object in free fall accelerates A falling object in free fall accelerates at about 9.8 m/sat about 9.8 m/s22 (acceleration of (acceleration of gravity or g).gravity or g).

• The force of Earth’s gravity on a falling The force of Earth’s gravity on a falling object is the object’s mass times g.object is the object’s mass times g.

• Force of gravity (N)=mass (kg) X accel Force of gravity (N)=mass (kg) X accel of g (m/sof g (m/s22) or F=mg) or F=mg

• You can use this equation to find the You can use this equation to find the gravitational force on a sky diver with a gravitational force on a sky diver with a 60 kg mass.60 kg mass.

Earth’s Gravitational Earth’s Gravitational AccelerationAcceleration

• You can use this You can use this equation to find the equation to find the gravitational force on gravitational force on a sky diver with a 60 a sky diver with a 60 kg mass.kg mass.

• F=mg or F=mg or • F= (60 kg)(9.8 m/sF= (60 kg)(9.8 m/s22) = ) =

588 Newtons.588 Newtons.• The gravitational force The gravitational force

on the sky diver is 588 on the sky diver is 588 N.N.

<http://verticalextremeskydiving.com/ESW/Images/single.jpg>

How is weight How is weight calculated?calculated?

• The gravitational The gravitational force Earth exerts force Earth exerts on an object is its on an object is its weight.weight.

• Weight (N)=mass Weight (N)=mass (kg) X acceleration (kg) X acceleration of gravity or of gravity or W=mg.W=mg.

<http://www.global-b2b-network.com/direct/dbimage/50331349/Personal_Training_Weight_Scale.jpg>

Is there a difference Is there a difference between weight & mass?between weight & mass?

• Weight is a force while mass is the Weight is a force while mass is the measure of the amount of matter in an measure of the amount of matter in an object. object.

• Weight & mass are related, but they are Weight & mass are related, but they are not the same. not the same.

• Mass stays the same but weight changes Mass stays the same but weight changes as the location the object is in changes.as the location the object is in changes.

• You weigh more on Earth than on the You weigh more on Earth than on the moon because the gravity decreases yet moon because the gravity decreases yet mass remains the same.mass remains the same.

Weightlessness & Free Weightlessness & Free FallFall

• What would happen if What would happen if you are standing on the you are standing on the scale & the elevator scale & the elevator begins to fall rapidly?begins to fall rapidly?

• Astronauts in the space Astronauts in the space shuttle experience shuttle experience “weightlessness” “weightlessness” because they are because they are farther from Earth’s farther from Earth’s gravitational pull.gravitational pull.

• The orbiting shuttle is The orbiting shuttle is in free fall so in free fall so everything seems to everything seems to float.float.

<http://www.batesville.k12.in.us/Physics/>

<http://www.nasa.gov/images/>

Projectile MotionProjectile Motion

• Thrown objects’ path Thrown objects’ path curves downward due curves downward due to gravity. to gravity.

• Anything thrown or Anything thrown or shot is called a shot is called a projectile.projectile.

• Throwing exerts a Throwing exerts a forward force on the forward force on the ball propelling it ball propelling it horizontally.horizontally.

• At the same time At the same time gravity acts downward gravity acts downward on the it.on the it.

<http://www.mrfizix.com/home/projectilemotion_files/image080.jpg>

What happens when an What happens when an object has both horizontal object has both horizontal

& vertical motion?& vertical motion?• The ball has a The ball has a

constant horizontal constant horizontal velocity, but velocity, but increasing vertical increasing vertical velocity.velocity.

• Gravity exerts an Gravity exerts an unbalanced force on unbalanced force on the ball, changing the the ball, changing the path from only path from only forward to forward forward to forward and downward and downward producing a curve.producing a curve.

<http://www.mrfizix.com/home/projectilemotion_files/image080.jpg>

Are horizontal & vertical Are horizontal & vertical distance always the same?distance always the same?

• Which ball lands Which ball lands first?first?

• Which one travels Which one travels the farthest the farthest distance?distance?

<http://www.mrfizix.com/home/projectilemotion_files/image080.jpg>

Are horizontal & vertical Are horizontal & vertical distance always the same?distance always the same?

• Which ball lands Which ball lands first? Neither one; first? Neither one; they land at the they land at the same time.same time.

• Which one travels Which one travels the farthest the farthest distance? The distance? The ball that is thrown ball that is thrown travels farthest.travels farthest.<http://www.mrfizix.com/

home/projectilemotion_files/image080.jpg>

Centripetal ForceCentripetal Force

• Acceleration toward Acceleration toward the center of a curved the center of a curved path is called path is called centripetal centripetal acceleration.acceleration.

• According to According to Newton’s second law Newton’s second law of motion, the of motion, the direction of the net direction of the net force on the ball must force on the ball must be toward the center be toward the center of the curved path.of the curved path. <http://content.answers.com/

main>

Centripetal ForceCentripetal Force

• A ball inside a coiled A ball inside a coiled tube experiences tube experiences centripetal force centripetal force which forces it to which forces it to move in a circle.move in a circle.

• The centripetal force The centripetal force is the force toward is the force toward the center exerted the center exerted by the walls of the by the walls of the tube on the ball.tube on the ball.

<http://content.answers.com/main>

How does centripetal force How does centripetal force depend on traction?depend on traction?

• When a car rounds a When a car rounds a curve, a centripetal curve, a centripetal force must be acting force must be acting on the car to keep it on the car to keep it moving in a curved moving in a curved path; otherwise it will path; otherwise it will slide off the road.slide off the road.

• The centripetal force The centripetal force is traction. Rain or ice is traction. Rain or ice can reduce traction can reduce traction causing the car to causing the car to slide in a straight line slide in a straight line off the road.off the road.

<http://webassign.net/serpop/5-13.gif>

Can gravity be a Can gravity be a centripetal force?centripetal force?

• Imagine swinging a yo-yo on a string Imagine swinging a yo-yo on a string above your head.above your head.

• The string places centripetal force The string places centripetal force on the yo-yo much like the Earth’s on the yo-yo much like the Earth’s gravitational pull places centripetal gravitational pull places centripetal force on the Moon o keep it moving force on the Moon o keep it moving in a nearly circular orbit.in a nearly circular orbit.

<http://www.aerospaceweb.org/question/astronomy/moon/orbit.jpg>

Section 3 – The Third Law Section 3 – The Third Law of Motionof Motion

• What You’ll Learn:What You’ll Learn:• Newton’s law of motionNewton’s law of motion• How to find momentumHow to find momentum

<http://www.president.vt.edu/presreports/pres0102/balls.jpg>

Newton’s Third LawNewton’s Third Law

• If you push against If you push against the wall while the wall while wearing skates, wearing skates, you’ll roll backwards.you’ll roll backwards.

• This example of This example of Newton’s third law Newton’s third law of motion of motion describes describes action & reaction.action & reaction.

• ““To every action To every action force there is an force there is an equal & opposite equal & opposite reaction force.”reaction force.”

<http://www.sciencetoymaker.org/balloon/images/newton.gif>

How do action & reaction How do action & reaction happen?happen?

• When a force is When a force is applied in nature, a applied in nature, a reaction force occurs reaction force occurs at the same time.at the same time.

• When you jump on a When you jump on a trampoline you exert trampoline you exert a downward force at a downward force at the same time as the the same time as the trampoline exerts an trampoline exerts an upward force on you.upward force on you.

<http://pro.corbis.com/images/42-15995438.jpg?size=572&uid=%7B7D48F44B-CF66-4720-BED9-7A89BD975B3B%7D>

How do action & reaction How do action & reaction make you move? make you move?

• Even though the forces are equal Even though the forces are equal when you are walking, they are when you are walking, they are acting on objects that have different acting on objects that have different masses. masses.

• Earth has more mass than you do; Earth has more mass than you do; thus, their net force is not equal.thus, their net force is not equal.

• Unequal net forces determine the Unequal net forces determine the direction you move.direction you move.

<http://www.qca.org.uk/libraryAssets/images/walking(1).jpg>

What is rocket What is rocket propulsion?propulsion?

• In a rocket engine, In a rocket engine, burning fuel produces burning fuel produces hot gases.hot gases.

• The rocket engine The rocket engine applies a force on the applies a force on the gases & causes them to gases & causes them to escape out of the back of escape out of the back of the rocket.the rocket.

• By Newton’s third law, By Newton’s third law, the gases apply a the gases apply a reaction force on the reaction force on the rocket & push it in the rocket & push it in the opposite direction.opposite direction.

<http://exploration.grc.nasa.gov/education/rocket/Images/newton3r.gif>

• How many How many different different action/reaction action/reaction pairs can you pairs can you identify from identify from this NASA this NASA poster?poster?

• List them.List them.

<http://swift.sonoma.edu/education/newton/newton_3/newpost3.jpg>

MomentumMomentum

• A moving object has a property called A moving object has a property called momentum which is related to how much momentum which is related to how much force is needed to change an object’s motion.force is needed to change an object’s motion.

• The The momentummomentum of an object is the product of an object is the product of its mass & its velocity. of its mass & its velocity. pp represents represents momentummomentum

• Momentum (Momentum (kg∙m/skg∙m/s)=mass (kg) X )=mass (kg) X velocity(m/s) or velocity(m/s) or p=mvp=mv..

• Two cars can have the same velocity but the Two cars can have the same velocity but the one with greater mass has a larger one with greater mass has a larger momentum.momentum.

MomentumMomentum

• P=mvP=mv• What is the What is the

momentum of a momentum of a bicycle with a bicycle with a mass of 18 kg mass of 18 kg traveling at 20 traveling at 20 m/s?m/s?

<http://www.ski-epic.com/amsterdam_bicycles/ps0b_amsterdam_bicycle_cell.jpg>

MomentumMomentum

• P=mvP=mv• What is the What is the

momentum of a momentum of a bicycle with a mass of bicycle with a mass of 18 kg traveling at 20 18 kg traveling at 20 m/s?m/s?

• pp=(18 kg) X (20 m/s)=(18 kg) X (20 m/s)• p=p=360 kg∙m/s360 kg∙m/s• The bicycle’s The bicycle’s

momentum is 360 momentum is 360 kg∙m/s.kg∙m/s.

<http://www.ski-epic.com/amsterdam_bicycles/ps0b_amsterdam_bicycle_cell.jpg>

How are force & momentum How are force & momentum related?related?

• Recall that acceleration is the Recall that acceleration is the difference between final & initial difference between final & initial velocity, divided by the time.velocity, divided by the time.

• Also, net force on an object is its mass Also, net force on an object is its mass times its acceleration.times its acceleration.

• Combining these two relationships Combining these two relationships gives the following equation: F=(mvgives the following equation: F=(mv ff – – mvmvii)/ t or Force = change in )/ t or Force = change in momentum/ timemomentum/ time

How are force & momentum How are force & momentum related?related?

• When you catch a When you catch a ball, your hand ball, your hand applies a force on the applies a force on the ball that stops it.ball that stops it.

• The force your hand The force your hand exerts on the ball & exerts on the ball & the force the ball the force the ball exerts on your hand exerts on your hand are equal. are equal.

• The force depends on The force depends on the mass & initial the mass & initial velocity of the ball & velocity of the ball & how long it takes to how long it takes to stop. stop.

• Final velocity = zero.Final velocity = zero.

<http://pro.corbis.com/images/42-16083561.jpg>

What is the law of What is the law of conservation of conservation of

momentum?momentum?• Momentum can be Momentum can be

passed from one passed from one object to another. object to another.

• When a cue ball hits When a cue ball hits a group of balls that a group of balls that are motionless, the are motionless, the cue ball slows down cue ball slows down and the other balls and the other balls move.move.

• The momentum lost The momentum lost equals the equals the momentum gained. momentum gained.

<http://farm1.static.flickr.com/>

What happens when objects What happens when objects collide?collide?

• In a game of pool, suppose one ball is In a game of pool, suppose one ball is moving in one direction & another moving in one direction & another ball moving the same direction ball moving the same direction strikes it from behind.strikes it from behind.

• The ball that is struck will continue The ball that is struck will continue to move in the same direction, but to move in the same direction, but more quickly.more quickly.

• The striking ball has given it more The striking ball has given it more momentum in the same direction.momentum in the same direction.

Meters of Motion, a watercolor by Champaign-Urbana artist, Billy Morrow Jackson, is the basis for the poster announcing the 20th International Congress of Theoretical and Applied Mechanics, held in Chicago in August of 2000.