DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
LSN 10-: MOTION IN A GRAVITATIONAL FIELD
Questions Fom Reading Activity?
Gavity Waves?
Essential Idea: Simila appoaches can be taken in analyzing electical and gavitational potential poblems.
Natue Of Science: Communication of scientific explanations: The ability to apply field theoy to the unobsevable (chages) and the massively scaled (motion of satellites) equied scientists to develop new ways to investigate, analyze and epot findings to a geneal public used to scientific discoveies based on tangible and discenible evidence.
Undestandings: Potential and potential enegy Potential gadient Potential diffeence Escape speed Obital motion, obital speed and obital enegy Foces and invese-squae law behavio
Applications And Skills: Detemining the potential enegy of a point mass and the potential enegy of a point chage Solving poblems involving potential enegy Solving poblems involving the speed equied fo an object to go into obit aound a planet and fo an object to escape the gavitational field of a planet
Applications And Skills: Solving poblems involving obital enegy of chaged paticles in cicula obital motion and masses in cicula obital motion Detemining the potential inside a chaged sphee Solving poblems involving foces on chages and masses in adial and unifom fields
Guidance: Obital motion of a satellite aound a planet is esticted to a consideation of cicula obits (links to 6.1 and 6.) Students should ecognize that lines of foce can be two-dimensional epesentations of thee-dimensional fields
Guidance: Both unifom and adial fields need to be consideed Students should assume that the electic field eveywhee between paallel plates is unifom with edge effects occuing beyond the limits of the plates.
Data Booklet Refeence: V g = GM V e = kq g = V g E = V e E p = mv g = GMm E p = qv e = kq 1q V esc = GM F G = G m 1m F E = k q 1q V obit = GM
Utilization: The global positioning system depends on complete undestanding of satellite motion Geostationay/pola satellites The acceleation of chaged paticles in paticle acceleatos and in many medical imaging devices depends on the pesence of electic fields (see Physics option subtopic
Aims: Aim : Newton s law of gavitation and Coulomb s law fom pat of the stuctue known as classical physics. This body of knowledge has povided the methods and tools of analysis up to the advent of the theoy of elativity and the quantum theoy
Aims: Aim 4: the theoies of gavitation and electostatic inteactions allows fo a geat synthesis in the desciption of a lage numbe of phenomena
Newton s Law of Univesal Gavitation Last yea we leaned, F G M M 1 This yea we look at it fom an enegy standpoint M M E W Fd G 1
Gavitational Potential Enegy The gavitational foce is an attactive foce Wok must be done to sepaate two bodies in space a cetain distance R This wok is conveted to potential enegy called the gavitational potential enegy M M E G 1 p
Gavitational Potential Enegy Fo a satellite obiting a body, its total enegy is the sum of its kinetic and potential enegy 1 M M E mv G 1 T
Gavitational Potential Enegy If the satellite is in a stable, continuous obit, the kinetic enegy is equal to its potential enegy 1 M M mv G 1
Gavitational Potential Enegy Newton s Second Law tells us that the gavitational foce will be balanced by the centipetal acceleation G F Mm ma c m v GM v
Gavitational Potential Enegy Substituting into the taditional value fo kinetic enegy gives us GM v E k 1 mv 1 GMm E k
Gavitational Potential Enegy And total enegy fo an obiting body becomes E k E 1 E k GMm E p E 1 GMm GMm E GMm
Gavitational Potential Enegy Gaph of kinetic, potential, and total enegy as a function of distance fo a cicula obit
Gavitational Potential Enegy As you get futhe away fom the eath s suface, the less potential enegy thee is, so less kinetic enegy is equied
Gavitational Potential Enegy Because is squaed, it is an exponential and not a linea elationship
What will happen? Suppose you launch a ocket with a given velocity. Thee ae thee options: If total enegy is positive (E K > E P ), the ocket will follow a hypebolic obit and neve etun If total enegy is zeo (E K = E P ), the ocket will follow a paabolic obit to infinity and neve etun If total enegy is negative (E K < E P ), the ocket will ente a cicula o elliptical obit (o cash and bun)
Escape Velocity Total enegy of a mass m moving nea a lage mass M is given by 1 M M E mv G 1 R We assume the only foce acting on m is the gavitational foce ceated by M
Escape Velocity We want to know if a mass m is launched fom the suface of M, will it escape M s gavitational field? 1 mv esc G Mm 1 mv
Escape Velocity 1 M M E mv G 1 R If total enegy is geate than zeo, m escapes If total enegy is less than zeo, m will eventually etun to the suface of M
Escape Velocity The sepaation point is when V is equal to zeo 1 mv esc G Mm R 1 mv 0 1 mv esc G Mm R v esc GM R
Escape Velocity This is the minimum velocity needed to exceed the gavitational attaction of M and is called the escape velocity GM v esc R What happens if we double the value of m?
Escape Velocity This is the minimum velocity needed to exceed the gavitational attaction of M and is called the escape velocity What happens if we double the value of m? Nothing changes GM v esc R
Escape fom Planet Eath In eality thee ae othe things to conside when launching a ocket fom eath: Atmospheic fiction Gavitational pull of the Sun, Moon, and othe planets Consides only ballistic motion and not that of a ocket with a continuous foce applied
Obital Motion The law of gavitational attaction combined with Newton s second law show that the obit of any body due to gavitational attaction will follow the path of an ellipse o a cicle (cicles ae ellipses with both foci at the same point).
Obital Speed F ma c Mm v G m GM v
Black Holes What if the equied escape velocity exceeds the speed of light? This means that nothing, even light, can escape the sta and it is a black hole The adius at which this occus is called the Schwazschild adius c c R v esceq GM GM c R
Weightlessness Relative weightlessness occus when the centipetal acceleation is equal to the acceleation due to gavity Motocycle jump Ski jumpe mg m v g v
Weightlessness Weightlessness in Space F ma W mv N N W GMm W F g GMm mv N
Weightlessness Weightlessness in Space When the object is at obit speed, the nomal foce is zeo, i.e. weightless N v obit N N N GMm 0 GMm GM GMm mv m GMm GM
Invese Squae Law Behavio The gavitational and electical foces ae invesely popotional to the squae of the distance fom the souce F F F g e G k m m 1 q q 1
Invese Squae Law Behavio The gavitational and electical foces ae invesely popotional to the squae of the distance fom the souce F F F g e G k m m 1 q q 1
Invese Squae Law Behavio The gavitational and electical foces ae invesely popotional to the squae of the distance fom the souce F
Invese Squae Law Behavio Since these foces adiate fom the souce, thei spheical aea of influence quaduples as distance doubles F m : q : 4 4 q m d d
Invese Squae Law Behavio It is also elated to the fact that photons and gavitons have zeo mass (Chapte 7) F m : q : 4 4 m q d d
One Final Question What if we could fall though the cente of the eath?
Undestandings: Potential and potential enegy Potential gadient Potential diffeence Escape speed Obital motion, obital speed and obital enegy Foces and invese-squae law behavio
Guidance: Obital motion of a satellite aound a planet is esticted to a consideation of cicula obits (links to 6.1 and 6.) Students should ecognize that lines of foce can be two-dimensional epesentations of thee-dimensional fields
Guidance: Both unifom and adial fields need to be consideed Students should assume that the electic field eveywhee between paallel plates is unifom with edge effects occuing beyond the limits of the plates.
Data Booklet Refeence: V g = GM V e = kq g = V g E = V e E p = mv g = GMm E p = qv e = kq 1q V esc = GM F G = G m 1m F E = k q 1q V obit = GM
Utilization: The global positioning system depends on complete undestanding of satellite motion Geostationay/pola satellites The acceleation of chaged paticles in paticle acceleatos and in many medical imaging devices depends on the pesence of electic fields (see Physics option subtopic
Aims: Aim : Newton s law of gavitation and Coulomb s law fom pat of the stuctue known as classical physics. This body of knowledge has povided the methods and tools of analysis up to the advent of the theoy of elativity and the quantum theoy
Aims: Aim 4: the theoies of gavitation and electostatic inteactions allows fo a geat synthesis in the desciption of a lage numbe of phenomena
Essential Idea: Simila appoaches can be taken in analyzing electical and gavitational potential poblems.
QUESTIONS?
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