topic 4.1: gravitational fields

TOPIC 4.1: GRAVITATIONAL FIELDSStudents define the gravitational force constant g as a force per unit mass in N/kg,and the weight as Fg = mg. The acceleration due to gravity (i.e., ag = g) is derivedfrom Newton’s laws and determined in the laboratory. Students describe thenormal force in terms of the mutual attraction of masses, and draw simple free-body diagrams.The student will be able to:S3P-4-01: Define the gravitational field qualitatively as the region of space around

a mass where another point mass experiences a force.S3P-4-02: Diagram the Earth’s gravitational field, using lines of force.S3P-4-03: Define the gravitational field quantitatively as a force per unit mass. S3P-4-04: Compare and contrast the terms “mass” and “weight.”S3P-4-05: Describe, qualitatively and quantitatively, apparent weight changes in

vertically accelerating systems. Examples: elevators, spacecraft…

S3P-4-06: Derive the acceleration due to gravity from free fall and Newton’s laws.S3P-4-07: Perform an experiment to calculate g near the surface of the Earth.S3P-4-08: Solve free-fall problems.S3P-4-09: Describe terminal velocity, qualitatively and quantitatively.S3P-4-10: Define the coefficient of friction (µ) as the ratio of the force of friction

and the normal force.S3P-4-11: Distinguish between static and kinetic friction.S3P-4-12: Compare the effects of the normal force, materials involved, surface

area, and speed on the force of friction.S3P-4-13: Solve problems with the coefficient of friction for objects on a horizontal

surface.

Topic 4: Fields • SENIOR 3 PHYSICS

Topic 4.1 – 6

SPECIFIC LEARNING OUTCOMES

S3P-4-01: Define thegravitational field qualitatively asthe region of space around a masswhere another point massexperiences a force.

S3P-4-02: Diagram the Earth’sgravitational field using lines offorce.

GENERAL LEARNING OUTCOMECONNECTION

Students will…Understand how stability,motion, forces, and energytransfers and transformationsplay a role in a wide range ofnatural and constructedcontexts (GLO D4)

Notes to the TeacherDiscuss with students the universal natureof the attraction between any two masses.Extend the discussion to the case of theEarth’s gravitational field. Michael Faradayintroduced the concept of “field lines” torepresent the strength and direction of theforce. More field lines per unit arearepresent a stronger field. This occurs inregions where the lines are closer together.The direction of the field is the direction theforce would act on a “test mass” broughtinto the field. A “test mass” simply means“as if we put a mass of 1 kg in the field.”

Note: The gravitational field is continuousand the field lines just provide a visualrepresentation of the field.

The diagram indicates that the field linesget further apart as the gravitational fieldstrength gets weaker.

Teacher DemonstrationDemonstrate the field of the Earth with amass and spring scale (calibrated innewtons).

Senior Years Science Teachers’Handbook ActivitiesStudents use a Concept Frame and ConceptOverview (see Senior Years ScienceTeachers’ Handbook, Attachments 11.2 and11.3) to develop the concepts of thegravitational field and its associated fieldlines.

Use a Listen-Draw-Pair-Share sheet for anintroduction to the gravitational fieldconcept (see Success for All Learners: AHandbook on Differentiating Instruction,Attachment 5, and Senior Years ScienceTeachers’ Handbook, Building a ScientificVocabulary, Developing Scientific ConceptsUsing Graphic Displays, Attachments 10.2,11.2, and 11.3).

SUGGESTIONS FOR INSTRUCTION

Topic 4.1 – 7

SENIOR 3 PHYSICS • Topic 4: Fields

SKILLS AND ATTITUDES OUTCOMES

S3P-0-1c: Relate the historicaldevelopment of scientificideas and technology to theform and function ofscientific knowledge today.

S3P-0-2a: Select and useappropriate visual, numeric,graphical, and symbolicmodes of representation toidentify and representrelationships.


Students will…Understand the composition ofthe Earth’s atmosphere,hydrosphere, and lithosphere,as well as the processesinvolved within and amongthem(GLO D5)

Visual DisplayStudents explain, with the aid of diagrams,the gravitational field of the Earth.

Self-AssessmentUse a vocabulary strategy with students(e.g., Three-Point Approach) to demonstratetheir qualitative and quantitativeunderstanding of the term “gravitationalfield.” (See Senior Years Science Teachers’Handbook, Building a Scientific Vocabulary,page 10.1.)

SUGGESTIONS FOR INSTRUCTION SUGGESTIONS FOR ASSESSMENT

SUGGESTED LEARNING RESOURCES

Appendix 4.2: Journal Entry: GravitationalFields

��


Topic 4.1 – 8


S3P-4-03: Define gravitationalfield quantitatively as a force perunit mass.

S3P-4-04: Compare and contrastthe terms “mass” and “weight.”


S3P-0-1c: Formulate operationaldefinitions of major variablesor concepts.




Notes to the TeacherThe gravitational field strength is definedas the gravitational force that a “test mass”would experience at some point in the field.That is, g = . The units of g are .

Near the surface of the Earth, g is 9.8 N/kgdirected towards the centre of the Earth.Students should understand that everykilogram of mass near the Earthexperiences 9.8 newtons of force. Studentsshould also recognize that to define goperationally, we can measure force, using aspring scale, and mass, using a balance.

Student ActivitiesStudents solve for various problemsituations, using Fg = mg. See Appendix 4.1:Vertical Motion at the Earth’s Surface.

Teacher DemonstrationDiscuss or demonstrate (by changing thefaceplate of a spring scale) what a springscale would read on the surface of variouscelestial bodies (Moon, planets, Sun, etcetera).

Nkg

Fgm

Senior Years Science Teachers’Handbook ActivitiesStudents use a vocabulary strategy (e.g.,Three-Point Approach) to demonstrate theirquantitative understanding of the term“gravitational field.” (See Senior YearsScience Teachers’ Handbook, Building aScientific Vocabulary.)

Students compare and contrast mass andweight, using the Senior Years ScienceTeachers’ Handbook Compare and ContrastFrame.

Students research the g value for variouslocations (e.g., Winnipeg), using the Internet(National Research Council). Provideexamples of different values of g on Earth(equator versus poles; Winnipeg versusMount Everest) and different values of g forcelestial bodies (planets/moons, stars).

Interpretation of Media ReportsDiscuss the effects on the human body whenexposed to lower/higher g environments foran extended period of time (e.g.,International Space Station astronauts).


Topic 4.1 – 9



S3P-0-2f: Record, organize, anddisplay data, using anappropriate format.Include: labelled diagrams,tables, graphs

S3P-0-3b: Describe examples ofhow technology has evolvedin response to scientificadvances, and how scientificknowledge has evolved asthe result of new innovationsin technology.



Students prepare a lab report usingLaboratory Report Outline, Attachment11.4, Senior Years Science Teachers’Handbook.Students use a Concept Frame and ConceptOverview, Attachments 11.2 and 11.3,Senior Years Science Teachers’ Handbook.Students solve problems for any variable inFg = mg, given the other two. Assume thatfrictional effects are negligible.



ReferencesIona, M. (April 1999) “Weight—An OfficialDefinition.” The Physics Teacher 37:4: 238.

Senior Years Science Teachers’ Handbook,Writing to Learn Science, Technical Writingin Science, and Building a ScientificVocabulary (Manitoba Education andTraining, 1997)

Appendix 4.1: Vertical Motion at theEarth’s Surface

Appendix 4.2: Journal Entry: GravitationalFields

��


Topic 4.1 – 10

SPECIFIC LEARNING OUTCOME

S3P-4-05: Describe, qualitativelyand quantitatively, apparentweight changes in verticallyaccelerating systems. Examples: elevators, spacecraft…



Notes to the TeacherDraw free-body diagrams of an object in amoving system (elevator) under differentconditions (i.e., constant velocity,acceleration upward, or accelerationdownward).

Solve problems for apparent weight in amoving system (elevator) under differentconditions (i.e., constant velocity,acceleration upward, or accelerationdownward).

Fnet = Fg + FN , where FN isthe apparent weight of theobject, sometimes referred toas FSCALE.

Student ActivitiesStudents videotape apparentweight changes in anaccelerating elevator orexamine various amusementpark physics demonstrationsinvolving verticalaccelerations (e.g.,rollercoaster).

Senior Years ScienceTeachers’ HandbookActivitiesStudents research and reporton various micro-gravityenvironments and theireffects on the human body.


Fg

FN

Fg

FN

Fg

FNFN FN FN

Fg Fg Fg

Diagram Aconstant velocity(a = 0 m/s2)Fnet = maFN + Fg = 0FN = –FgFN= Fg

Diagram Baccelerated motionupward(a > 0)Fnet = maFN + Fg = (+)FN = (+) + (–Fg)= (+) + (+)∴FN> Fg

Diagram Caccelerated motiondownward(a < 0)Fnet = maFN + Fg = (–)FN = (–) + (–Fg)= (–) + (+)∴FN< Fg

Note that this applies toelevator acceleratingwhile going up or slowingwhile going down.

Note that this applies toelevator slowing whilegoing up or acceleratingwhile going down.

Topic 4.1 – 11




S3P-0-2b: Propose problems, statehypotheses, and plan,implement, adapt, or extendprocedures to carry out aninvestigation where required.


Students will…Describe and appreciate howthe natural and constructedworld is made up of systemsand how interactions take placewithin and among thesesystems(GLO E2)

Visual DisplaysStudents explore directly (by visiting), orthrough a simulation, the physics of anamusement park ride. Complete a poster,diagram, or model that outlines forcesrelationships, and apparent weight changes.

Answering Questions Based on DataStudents calculate apparent weight underdifferent conditions.



Jensen, L. (1986) “Apparent WeightChanges in an Elevator.” A Potpourri ofPhysics Teaching Ideas: 89.

Evans, L. and J. Stevens. (1978) “WhichWay Is Up?” The Physics Teacher 16:8: 561.

Multimedia Physics at Work: Side A/B, Frames 491,acceleration; 494, skydivers; 511, free fall;393-94, 605, 613-17, 639-40, 648-51.

Physics of Flight: Frames 37277..., ViscousFlow; 27115..., 30642..., Aerodynamic Lift;41399..., Motion of free-fall parachutist;1155-59

Interactive Physics Simulations

��


Topic 4.1 – 12


S3P-4-06: Derive the accelerationdue to gravity from free fall andNewton’s laws.

S3P-4-07: Perform an experimentto calculate g near the surface ofthe Earth.




Students will…Demonstrate appropriatescientific inquiry skills whenseeking answers to questions (GLO C2)

Notes to the TeacherShow the derivation for acceleration due togravity:For free fall:

Fnet = ma whereFnet = Fapplied + Ffriction

Fapplied = Fg and Ffriction = 0 (assuming no air resistance)Fnet = Fg

ma = mga = g

There are several ways to calculate gexperimentally. Examples of these include:• Perform a tickertape experiment, using a

free-falling mass, and plot d-t, v-t, and a-tgraphs.

• Conduct microcomputer-basedexperiments to determine g:

• Use spring scales (calibrated in newtons)and masses to determine g by plotting thegravitational force (spring scale reading)versus mass on a graph. The slope of thegraph determines the value of g.

Student ActivitiesStudents solve problems, using kinematicequations from learning outcome S3P-1-07and Fg = mg.

Students interpret free-fall motion fromvideos, using graphs produced withVideograph software.

Students perform free-fall simulations,using Interactive Physics Simulationssoftware.

Multimedia SimulationsSoftware: Interactive Physics Simulations,Activities #3: Free Fall; #6: Grape DropPhysics with Computers (Vernier)—Experiment #5: Picket Fence Free FallPhysics with Computers (Vernier)—Experiment #6: Ball Toss


Topic 4.1 – 13



S3P-0-2d: Estimate and measureaccurately, using SystèmeInternational (SI) units.

S3P-0-2e: Evaluate the relevance,reliability, and adequacy ofdata and data-collectionmethods.Include: discrepancies in dataand sources of error

S3P-0-2g: Interpret patterns andtrends in data, and infer orcalculate linear relationshipsamong variables.


Students will…Understand the composition ofthe universe, the interactionswithin it, and the impacts ofhumankind’s continuedattempts to understand andexplore it(GLO D6)

Students solve free-fall problems limited tovertical motion only using kinematicequations and Fg = mg. See Appendix 4.1:Vertical Motion at the Earth’s Surface.



JournalsCourt, J. (1993) “Free Body Diagrams.” ThePhysics Teacher 31:2: 104.

Court, J. (1999) “Free Body Diagrams.” ThePhysics Teacher 37:7: 427.

Fisher, K. (1999) “Exercise in Drawing andUtilizing Free-Body Diagrams.” The PhysicsTeacher 37.7: 434.

Evans, L. and J. Stevens. (1978) “WhichWay Is Up?” The Physics Teacher 16.8: 561.

SoftwareInteractive Physics Simulations,Activities #3: Free Fall; #6: Grape Drop

Physics with Computers (Vernier)—Experiment #4: Determining g on anIncline.

��


Topic 4.1 – 14

SPECIFIC LEARNING OUTCOME

S3P-4-08: Solve free-fallproblems.




Students will…Work cooperatively and valuethe ideas and contributions ofothers while carrying outscientific and technologicalactivities (GLO C7)

Notes to the TeacherIn free fall, air resistance varies with thesquare of the speed (generally, Fair ∝ v2).Therefore, as speed increases, air resistancealso increases. In terms of the force vectors,the progression from a free-falling object asit achieves terminal velocity can bediagrammed as follows:

Students solve free-fall problems using thekinematics relations from outcomeS3P-3-07. It should be noted that eventhough the motion is accelerated and thevelocity changes, the average velocity is stilla useful concept in solving these types ofproblems. It is also useful for students tosketch and compare graphical solutions tothe algebraic relationships.


Fg

Fair

Fg

Fair

Fg

Diagram aFree fall begins (noair resistance)Fnet = Fg

a = g

Diagram bObject falling in air,resistance increasesFnet = Fg + Fair

a =< g

Diagram cAs velocity increases,air resistanceincreases until Fair = –Fg

Fnet = 0 and a = 0 Velocity is constant(terminal velocity)

Fg

Fg

Fg

Fair

Fair

Topic 4.1 – 15



S3P-0-2d: Estimate and measureaccurately, using SystèmeInternational (SI) units.

S3P-0-2e: Evaluate the relevance,reliability, and adequacy ofdata and data-collectionmethods.Include: discrepancies in dataand sources of error



Students will…Evaluate, from a scientificperspective, information andideas encountered duringinvestigations and in daily life(GLO C8)

Teacher DemonstrationDemonstrate and describe terminal velocity(e.g., compare dropping flat paper versuscrumpled paper).

Student ActivitiesStudents interpret free-fall motion fromvideos, using graphs produced withsoftware.

Students perform free-fall simulations usingInteractive Physics Simulation software.

Students solve free-fall problems limited tovertical motion only, using kinematicequations and Fg = mg.

Students compare free-falling objects andterminal velocity of objects, using aCompare and Contrast Frame frompage 10.24 of the Senior Years ScienceTeachers’ Handbook.



SoftwareInteractive Physics, Activities #3: Free Fall;#6: Grape Drop

MultimediaVideodiscs: Physics at Work: penny andfeather

Video Encyclopedia of PhysicsDemonstrations: penny and feather

Physics of Flight: Motion of free-fallparachutist


Topic 4.1 – 16


S3P-4-09: Describe terminalvelocity, qualitatively andquantitatively.

S3P-4-10: Define the coefficientof friction (µ) as the ratio of theforce of friction and the normalforce.

S3P-4-11: Distinguish betweenstatic and kinetic friction.

S3P-4-12: Compare the effects ofthe normal force, materialsinvolved, surface area, and speedon the force of friction.

S3P-4-13: Solve problems withthe coefficient of friction forobjects on a horizontal surface.



Notes to the TeacherFor a given pair of surfaces, the force offriction generally acts opposite to thedirection of relative motion or attemptedmotion between the two surfaces. Note thata common misconception is that frictionalways acts to oppose motion (i.e., to makethings stop moving). While friction usuallydoes act to make things stop, it is alsocapable of making things move and speedup. An example of this would be a boxsitting on a flatbed truck. If both were atrest when the truck gently acceleratedforward, the inertial tendency of the boxwould be to remain at rest. An acceleratingtruck and a stationary box would producerubbing between the two surfaces. Frictionopposes this relative motion, causing thebox to accelerate with the truck.

The direction of the friction force is notalways immediately obvious, especiallywhen there are multiple forces acting on anobject initially at rest. In such cases, thedirection of the tendency to slide must firstbe determined by finding the direction ofthe net force, ignoring friction.

Static friction occurs when the surfacesdon’t move relative to each other. Kineticfriction occurs between two surfaces thatare moving relative to each other.Generally, the coefficient of static friction,µs, is larger than the coefficient of kineticfriction, µk.

Teacher DemonstrationPull on a block with a spring scale and notethe force just before the block moves (forcenecessary to overcome static friction). Asyou pull the block slowly across the table,compare the scale readings (kinetic friction).

The coefficient of friction can be defined as:

f

N

FF

µ

=


01

234

56

7

N

01

234

56

7

N

Topic 4.1 – 17


SKILLS AND ATTITUDES OUTCOME



Students will…Understand how stability,motion, forces, and energytransfers and transformationsplay a role in a wide range ofnatural and constructedcontexts(GLO D4)

The symbol µ can be thought of as anumerical description of the nature of thesurfaces. The equation µ = 0 corresponds toa frictionless surface: small valuescorrespond to two surfaces that are slippery,with the friction becoming larger withlarger values of µ.

Note that the equations for friction can thenbe written as Ffk = µkFN and Ffs = µsFN.

Surprisingly, the force of friction onlydepends on three things, as discussed above(normal force, nature of surfaces, andwhether the surfaces are rubbing or forcesare attempting to cause rubbing).

The surface area and speed of motion do notgenerally change the force of friction.

ExtensionFor inclined planes, identify the normalforce relevant to the object experiencingfriction. The magnitude of the normal forceis generally found using FN = m · g cosθ,where θ is the angle between the horizontaland the inclined plane. Gravity exerts aforce of Fa = m · g sinθ on the object in adirection down the plane. Students candemonstrate that these equations arecorrect, using vector diagrams andtrigonometry.

Research Report/PresentationStudents perform a lab to determine thecoefficient of friction for various materials,using the “angle of repose” method.



SoftwareInteractive Physics Simulations,Activities #3: Free Fall; #6: Grape Drop

MultimediaVideodiscs: Physics at Work: penny andfeather

Video Encyclopedia of PhysicsDemonstrations: penny and feather

Physics of Flight: motion of free-fallparachutist


Topic 4.1 – 18


S3P-4-09: Describe terminalvelocity, qualitatively andquantitatively.

S3P-4-10: Define the coefficientof friction (µ) as the ratio of theforce of friction and the normalforce.

S3P-4-11: Distinguish betweenstatic and kinetic friction.

S3P-4-12: Compare the effects ofthe normal force, materialsinvolved, surface area, and speedon the force of friction.

S3P-4-13: Solve problems withthe coefficient of friction forobjects on a horizontal surface.



Student Activity: Coefficient of StaticFriction (the following activity couldbe considered an optional extension)To find the coefficient of static friction,increase the angle of the incline until theobject just begins to slide uniformly downthe plane (see diagram). At this time, sinceacceleration is zero:Fg = Ff

Ff = mg sinθ

And the normal force is the cosinecomponent.

FN = mg cosθ

Therefore, the coefficient of friction is

where θ is the angle of inclination.

mg sinmg cossincostan

f

N

s

s

s

FF

µ

θµθ

θµ

θµ θ

=

=

=

=


Topic 4.1 – 19


SKILLS AND ATTITUDES OUTCOME



Students will…Understand how stability,motion, forces, and energytransfers and transformationsplay a role in a wide range ofnatural and constructedcontexts(GLO D4)


��


Topic 4.1 – 20

NOTES

topic 4.1: gravitational fields

Documents