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5.1 Describing Motion: Examples from Daily LifeObjects in MotionThe Acceleration of GravityThe Acceleration of Gravity (g)ForcesIs Mass the Same Thing as Weight?5.2 Newton’s Laws of MotionSir Isaac Newton (1642-1727)Newton’s Laws of MotionSlide 10Slide 11Slide 12Angular MomentumSlide 14Conservation of Angular Momentum5.3 The Force of GravityNewton’s Universal Law of GravitationSlide 18Slide 19PowerPoint PresentationSlide 21Recall Kepler's Laws:Understanding Kepler…Orbital Paths5.4 TidesTidesSlide 27Tidal FrictionSynchronous RotationOrbital Energy and Escape Velocity© 2004 Pearson Education Inc., publishing as Addison-Wesley5.1 Describing Motion: Examples from Daily Life•Distinguish between speed, velocity, and acceleration.•What is the acceleration of gravity?•How does the acceleration of gravity depend on the mass of a falling object?Our goals for learning:© 2004 Pearson Education Inc., publishing as Addison-WesleyObjects in Motion•speed – rate at which an object moves, i.e. the distance traveled per unit time [m/s; mi/hr]•velocity – an object’s speed in a certain direction, e.g. “10 m/s moving east”•acceleration – a change in an object’s velocity, i.e. a change in either speed or direction is an acceleration [m/s2]© 2004 Pearson Education Inc., publishing as Addison-WesleyThe Acceleration of Gravity•As objects fall, they accelerate.•The acceleration due to Earth’s gravity is 10 m/s each second, or g = 10 m/s2.•The higher you drop the ball, the greater its velocity will be at impact.© 2004 Pearson Education Inc., publishing as Addison-WesleyThe Acceleration of Gravity (g)•Galileo demonstrated that g is the same for all objects, regardless of their mass!•This was confirmed by the Apollo astronauts on the Moon, where there is no air resistance.© 2004 Pearson Education Inc., publishing as Addison-WesleyForces•Forces change the motion of objects.•momentum – the (mass x velocity) of an object•force – anything that can cause a change in an object’s momentum •As long as the object’s mass does not change, the force causes a change in velocity, or an…© 2004 Pearson Education Inc., publishing as Addison-WesleyIs Mass the Same Thing as Weight?•mass – the amount of matter in an object•weight – a measurement of the force which acts upon an object© 2004 Pearson Education Inc., publishing as Addison-Wesley5.2 Newton’s Laws of Motion•What are Newton’s three laws of motion?•Why does a spinning skater spin faster as she pulls in her arms?Our goals for learning:© 2004 Pearson Education Inc., publishing as Addison-WesleySir Isaac Newton (1642-1727)•Perhaps the greatest genius of all time•Invented the reflecting telescope•Invented calculus•Connected gravity and planetary forces Philosophiae naturalis principia mathematica© 2004 Pearson Education Inc., publishing as Addison-WesleyNewton’s Laws of Motion1A body at rest or in motion at a constant speed along a straight line remains in that state of rest or motion unless acted upon by an outside force.© 2004 Pearson Education Inc., publishing as Addison-WesleyNewton’s Laws of Motion2The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it, but is inversely proportional to the body’s mass.F = m aF/ m = a© 2004 Pearson Education Inc., publishing as Addison-WesleyNewton’s Laws of Motion3For every applied force, a force of equal size but opposite direction arises.© 2004 Pearson Education Inc., publishing as Addison-WesleyNewton’s Laws of Motion© 2004 Pearson Education Inc., publishing as Addison-WesleyAngular Momentum•angular momentum – the momentum involved in spinning /circling = mass x velocity x radius•torque – anything that can cause a change in an object’s angular momentum (twisting force)© 2004 Pearson Education Inc., publishing as Addison-WesleyAngular Momentum•torque – anything that can cause a change in an object’s angular momentum (twisting force)•torque = radius x force•torque = radius x mass x acceleration© 2004 Pearson Education Inc., publishing as Addison-WesleyConservation of Angular Momentum•In the absence of a net torque, the total angular momentum of a system remains constant.© 2004 Pearson Education Inc., publishing as Addison-Wesley5.3 The Force of Gravity•What is the universal law of gravitation?•What types of orbits are possible according to the law of gravitation?•How can we determine the mass of distant objects?Our goals for learning:© 2004 Pearson Education Inc., publishing as Addison-WesleyNewton’s Universal Law of Gravitation Isaac Newton discovered that it is gravity which plays the vital role of determining the motion of the planets - concept of action at a distance© 2004 Pearson Education Inc., publishing as Addison-WesleyNewton’s Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.© 2004 Pearson Education Inc., publishing as Addison-WesleyNewton’s Universal Law of Gravitation G=6.67 x 10-11 m3/(kg s2)© 2004 Pearson Education Inc., publishing as Addison-Wesley•How does the acceleration of gravity depend on the mass of a falling object?•It does not. All falling objects fall with the same acceleration (on a particular planet).•Now see why… •F = ma and on Earth acceleration due to gravity denoted “g” so F=mg or g=F/m•If mass of earth is ME then Fg=GMEm/d2 •mg=GMEm/d2 g=GME/d2© 2004 Pearson Education Inc., publishing as Addison-Wesley•Every mass attracts every other mass through the force called gravity•The strength of the gravitational force attracting any two objects is proportional to the product of their masses•The strength of gravity between two objects decreases with the square of the distance between their centers© 2004 Pearson Education Inc., publishing as Addison-WesleyRecall Kepler's Laws:Kepler's Second Law: Line joining planet and the Sun sweeps out equal areas in equal timesKepler's First Law:Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus.Kepler's Third Law: The squares of the periods of the planets are proportional to the cubes of their semi-major axes:© 2004 Pearson Education Inc., publishing as Addison-WesleyUnderstanding