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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. Forces Chapter 3 Sections 1 - 3 Chp 3 - Forces • Section 1 – Weathering slides 3 - 20 • Section 2 – Gravity slides 21-38 • Section 3 – The Third Law of Motion slides 3952 Section 1 - Weathering • • • • What You’ll Learn: How force, mass, & acceleration are related The three different types of friction How air resistance affects falling objects Force, Mass, and Acceleration • You read about Newton’s first law of motion which says that the motion of an object changes only if an unbalanced force acts on it. • Newton’s second law of motion describes the relationship between the acceleration of an object, its mass, and the forces exerted on it. How are force & acceleration related? How are throwing a ball as hard as you can & tossing it gently different? How are force & 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 related? <http://www.essexfellsrec.com> • If you throw a softball and a baseball as hard you can, will they have the same speed? • Because a softball has more mass, it will have less velocity even though you applied the same force. This means that acceleration also depends mass as well as force. Newton’s Second Law • Newton’s second law of motion states that the net force acting on an object causes the object to accelerate in the direction of the net force. • To find the acceleration, you must know the mass and the net force. • Acceleration (α)= net force (in N)/mass (kg) or α= F/m How can the second law help find net force? • If you know an object’s mass & acceleration, you can use Newton’s second law to find the force by using the equation F=ma. • Suppose a tennis ball leaves a racket with a speed of 100 km/h with an acceleration of 5,000 m/s2. The ball’s mass is 0.06 kg. F=ma so: (0.06 kg)(5,000m/s2)= 300 kg m/s2 = 300 N Friction • Friction is the force that opposes the sliding motion of two surfaces that are touching each other. The amount of friction between the two depends on two things: the kind of surfaces & the amount of force pressing them together. <http://z.about.com/d/skateboard/1/5/i /M/axlestall4.jpg> What causes friction? polymer fabric welded with ultrasound • Microwelds occur where two surfaces stick together due to roughness. Friction is caused by the microwelds that form where the surfaces are in contact. <http://www.sra-developments.co.uk/img/micrograph_01.gif> What makes things stick together? • The stronger the force pushing two surfaces together, the stronger the microwelds will be. • To move one surface over another, a force must be applied to break the microwelds. What is static friction? • Static friction is the force that keeps two surfaces at rest from sliding across each other. • The mechanic shown here is attempting to break a nut seize caused by static friction. <http://www.beisansystems.com/procedures/ e39_fan_procedure_files/image010.jpg> What is sliding friction? • Sliding friction is the force that works against the motion of two surfaces that are sliding across each other. • Another example would be wheels spinning in snow or mud. Sand or gravel will increase the <http://www.superphysics.netfirms.com/fricti1.jpg> sliding friction so the wheels can roll w/o slipping. What is rolling friction? • Rolling friction is the frictional force between a rolling object and the surface it rolls on. • A wheel digs into the surface it is rolling over deforming both the wheel and the surface. <http://www.ofs.edu.sg/our-schools> Air Resistance • Air resistance is a force that opposes the movement of objects through the air. Similar to friction, air resistance acts in the direction opposite to the object’s motion. <http://www.bmw.ie/ie/en/insights/technology/efficient_dynamics/innovative_technolo gies/_shared/img/air_vent_control.jpg> Air Resistance • Objects falling toward Earth are being pulled downward by the force of gravity. • Air resistance is a force that opposes the movement of objects through the air. • Air resistance is similar to friction. <http://www.nasa.gov/centers/mars hall/images> Air Resistance • In the case of a falling object, air resistance pushes up as gravity pulls down. • If there were no air resistance, only gravity would affect falling objects. • All objects would fall at the same rate. <http://z.about.com/d/inventors/1/5/0 /2/1/parachute2.jpg> Air Resistance <http://www.bioinformaticszen.com/> <http://up load.wikim edia.org/wi kipedia/co mmons/3/ 3f/Paper_s heet.jpg> • Different objects fall with different accelerations and different speed due to their size and shape. • Compare the forces on a sheet of paper to those on a crumpled sheet. Which has the greater net downward force? Section 2 - Gravity • What You’ll Learn: • How gravity & weight are related • The difference between mass & weight What is gravity? • Gravity is an attractive force between two objects. • It increases as the mass of either object increases, or as the objects move closer to one another. • You can’t feel gravitational force between you and the table. Why? <http://openlearn.open.ac.uk/file.php> <http://hegel.lewiscenter.org/users/mhuffine /subprojects/Department/images/psci2.jpg> Law of Universal Gravitation • This lets us find the force of gravity between any two objects if their masses & the distance between them are known. • G=universal gravitational constant (never changes) • D=distance; m=mass <http://www.williamsclass.com/EighthS cienceWork/ImagesEighth/Gravitational Force.jpg> Why is gravity called a long-range force? • Gravitational force between two masses decreases as the distance between them increases. • No matter how far apart two objects are, the gravitational force between them never completely goes to zero. • This is also called the inverse square law. <http://schoolnet.gov.mt/earth_universe/i mages/10184_w.jpg> How did gravity help astronomers find other planets? <http://www.redorbit.com/modules/refli b/article_images/8_d7f84ec36dbfda23aff 1a01e00a4b5e6.jpg> • The motion of every planet is affected by the gravitational forces of the other planets. • In 1840 the farthest known planet was Uranus, but its motion could not be explained by the attraction of the other known planets. • Neptune’s discovery resulted from this. Earth’s Gravitational Acceleration • A falling object in free fall accelerates at about 9.8 m/s2 (acceleration of gravity or g). • The force of Earth’s gravity on a falling object is the object’s mass times g. • Force of gravity (N)=mass (kg) X accel of g (m/s2) or F=mg • You can use this equation to find the gravitational force on a sky diver with a 60 kg mass. Earth’s Gravitational Acceleration • You can use this equation to find the gravitational force on a sky diver with a 60 kg mass. • F=mg or • F= (60 kg)(9.8 m/s2) = 588 Newtons. • The gravitational force on the sky diver is 588 N. <http://verticalextremeskydiving.com/ESW /Images/single.jpg> How is weight calculated? • The gravitational force Earth exerts on an object is its weight. • Weight (N)=mass (kg) X acceleration of gravity or W=mg. <http://www.global-b2bnetwork.com/direct/dbimage/50331349/Pers onal_Training_Weight_Scale.jpg> Is there a difference between weight & mass? • Weight is a force while mass is the measure of the amount of matter in an object. • Weight & mass are related, but they are not the same. • Mass stays the same but weight changes as the location the object is in changes. • You weigh more on Earth than on the moon because the gravity decreases yet mass remains the same. Weightlessness & Free Fall • What would happen if you are standing on the scale & the elevator begins to fall rapidly? • Astronauts in the space shuttle experience “weightlessness” because they are farther from Earth’s gravitational pull. • The orbiting shuttle is in free fall so everything seems to float. <http://www.batesville.k12.in.us/Physics/> <http://www.nasa.gov/images/> Projectile Motion <http://www.mrfizix.com/home/projectil emotion_files/image080.jpg> • Thrown objects’ path curves downward due to gravity. • Anything thrown or shot is called a projectile. • Throwing exerts a forward force on the ball propelling it horizontally. • At the same time gravity acts downward on the it. What happens when an object has both horizontal & vertical motion? <http://www.mrfizix.com/home/projectile motion_files/image080.jpg> • The ball has a constant horizontal velocity, but increasing vertical velocity. • Gravity exerts an unbalanced force on the ball, changing the path from only forward to forward and downward producing a curve. Are horizontal & vertical distance always the same? • Which ball lands first? • Which one travels the farthest distance? <http://www.mrfizix.com/home/proje ctilemotion_files/image080.jpg> Are horizontal & vertical distance always the same? • Which ball lands first? Neither one; they land at the same time. • Which one travels the farthest distance? The ball that is thrown travels farthest. <http://www.mrfizix.com/home/proje ctilemotion_files/image080.jpg> Centripetal Force • Acceleration toward the center of a curved path is called centripetal acceleration. • According to Newton’s second law of motion, the direction of the net force on the ball must be toward the center of the curved path. <http://content.answers.com/main> Centripetal Force • A ball inside a coiled tube experiences centripetal force which forces it to move in a circle. • The centripetal force is the force toward the center exerted by the walls of the tube on the ball. <http://content.answers.com/main> How does centripetal force depend on traction? • When a car rounds a curve, a centripetal force must be acting on the car to keep it moving in a curved path; otherwise it will slide off the road. • The centripetal force is traction. Rain or ice can reduce traction causing the car to slide in a straight line off the road. <http://webassign.net/serpop/5-13.gif> Can gravity be a centripetal force? • Imagine swinging a yo-yo on a string above your head. • The string places centripetal force on the yo-yo much like the Earth’s gravitational pull places centripetal force on the Moon o keep it moving in a nearly circular orbit. <http://www.aerospaceweb.org/question/astronomy/moon/orbit.jpg> Section 3 – The Third Law of Motion • What You’ll Learn: • Newton’s law of motion • How to find momentum <http://www.president.vt.edu/presreports/pres0102/balls.jpg> Newton’s Third Law • If you push against the wall while wearing skates, you’ll roll backwards. • This example of Newton’s third law of motion describes action & reaction. • “To every action force there is an equal & opposite reaction force.” <http://www.sciencetoymaker.org/balloon /images/newton.gif> How do action & reaction happen? <http://pro.corbis.com/images/4215995438.jpg?size=572&uid=%7B7D48F44BCF66-4720-BED9-7A89BD975B3B%7D> • When a force is applied in nature, a reaction force occurs at the same time. • When you jump on a trampoline you exert a downward force at the same time as the trampoline exerts an upward force on you. How do action & reaction make you move? • Even though the forces are equal when you are walking, they are acting on objects that have different masses. • Earth has more mass than you do; thus, their net force is not equal. • Unequal net forces determine the direction you move. <http://www.qca.org.uk/libraryAss ets/images/walking(1).jpg> What is rocket propulsion? • In a rocket engine, burning fuel produces hot gases. • The rocket engine applies a force on the gases & causes them to escape out of the back of the rocket. • By Newton’s third law, the gases apply a reaction force on the rocket & push it in the opposite direction. <http://exploration.grc.nasa.gov/educati on/rocket/Images/newton3r.gif> • How many different action/reaction pairs can you identify from this NASA poster? • List them. <http://swift.sonoma.edu/education/ newton/newton_3/newpost3.jpg> Momentum • A moving object has a property called momentum which is related to how much force is needed to change an object’s motion. • The momentum of an object is the product of its mass & its velocity. p represents momentum • Momentum (kg∙m/s)=mass (kg) X velocity(m/s) or p=mv. • Two cars can have the same velocity but the one with greater mass has a larger momentum. Momentum • P=mv • What is the momentum of a bicycle with a mass of 18 kg traveling at 20 m/s? <http://www.skiepic.com/amsterdam_bicycles/ps0b_amsterda m_bicycle_cell.jpg> Momentum <http://www.skiepic.com/amsterdam_bicycles/ps0b_amsterda m_bicycle_cell.jpg> • P=mv • What is the momentum of a bicycle with a mass of 18 kg traveling at 20 m/s? • p=(18 kg) X (20 m/s) • p=360 kg∙m/s • The bicycle’s momentum is 360 kg∙m/s. How are force & momentum related? • Recall that acceleration is the difference between final & initial velocity, divided by the time. • Also, net force on an object is its mass times its acceleration. • Combining these two relationships gives the following equation: F=(mvf – mvi)/ t or Force = change in momentum/ time How are force & momentum related? • When you catch a ball, your hand applies a force on the ball that stops it. • The force your hand exerts on the ball & the force the ball exerts on your hand are equal. • The force depends on the mass & initial velocity of the ball & how long it takes to stop. • Final velocity = zero. <http://pro.corbis.com/images/4216083561.jpg> What is the law of conservation of momentum? • Momentum can be passed from one object to another. • When a cue ball hits a group of balls that are motionless, the cue ball slows down and the other balls move. • The momentum lost equals the momentum gained. <http://farm1.static.flickr.com/> What happens when objects collide? • In a game of pool, suppose one ball is moving in one direction & another ball moving the same direction strikes it from behind. • The ball that is struck will continue to move in the same direction, but more quickly. • The striking ball has given it more 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.