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Information about Mechanics

Published on March 30, 2013

Author: LKOTZE



Grade 11 Mechanics

Based on DocScientia

Vectors in two dimensions
Newton's Laws of motion
Newton's Law of Universal Gravitation


Vectors in twodimensions

Physical quantity havingmagnitude and a unit but not direction.DocScientia p. 12 Scalar definition

Physical quantity having Magnitude, unit and direction.DocScientia p. 12 Vector definition

Graphical representation of vectorsDocScientia p. 12

b length end (head) a θ start (tail)DocScientia p. 12

Division of a vector into componentsDocScientia p. 12

one dimension vectors: straight line ǁ to the vertical or horisontal axesDocScientia p. 12

two dimension vectors: form an angle to the axesDocScientia p. 12

components of a force at an angle: divided into 2 parts, 2 vectors at ┴, same effect as original vectorDocScientia p. 12

Fy F Fx = Fcosθ Fy = Fsinθ r y Cosθ = x/r = Fx/F Sinθ = y/r = Fy/F θ x FxDocScientia p. 13

Object on slopes experienceforces like gravity that are not ║ or ┴ to plane DocScientia p. 14

Forces are divided with respect to the plane.DocScientia p. 13

Trig functions calculate the componentsDocScientia p. 13

cosθ = x/r = Fg┴/Fg sinθ = y/r = Fg║/Fg Fg┴ = Fgcosθ Fg║ Fg║ = Fgsinθ θ r x θ Fg Fg┴DocScientia p. 14 y

Pull or pushWhat isa force Vector F N → Length = size › = direction of forceDocScientia p. 20

forces non-contact A act over a distance contact B objects are in contact with each otherDocScientia p. 20

non-contact forces A act over a distance Magnetic forces 1 Electrostatic forces 2 Gravitational forces 3DocScientia p. 21

contact forces B objects are in contact with each other Applied forces 1 Friction 2 Normal forces 3DocScientia p. 21

contact forces B objects are in contact with each other Tension 4 Air friction 5 Compression 6DocScientia p. 21

contact forces B objects are in contact with each other Applied forces 1Same line as direction of motion ORAt an agle to the direction of motionDocScientia p. 21

contact forces B objects are in contact with each other Friction 2f or Ff tries to minimise motion, ∴opposite direction to the movement║ to contact surfaceDocScientia p. 21

DocScientia p. 21

B 1 Same line as direction of motion OR At an agle to the direction of motion Fg┴ Fy Fx Fg║DocScientia p. 21

contact forces B objects are in contact with each other Normal forces (FN) 3Force exerted by a surface on an objecton that surfaceAlways perpendicular to the surfaceSupporting force is equal and opposite tothe force of the objectDocScientia p. 21

contact forces B objects are in contact with each other Tension (FT) 4 Pulled cable/rope = tension Tension is constant Two directions Mass = negligible, if asked to add: Gravitational force will act on the center of the ropeDocScientia p. 22

contact forces B objects are in contact with each other Air friction (Fair) 5 Offer resistance to objects moving through air Acts in the opposite direction to movementDocScientia p. 22

contact forces B objects are in contact with each other Compression (Fspring) 6 Equal in magnitude, exerted on any object touching the springDocScientia p. 22

Forces and free body diagramsDocScientia p. 22

FNF FN Fo r f F F er f ec Fge b Fg o Object represented as d a dot – can be a bit bigd Object w all forces y All forces = arrows wi Simplify as block magnitude anda Arrow shows d directiong magnitude and i Arrows point away direction a from the dotr Arrow at position g Force @ angle isa where force is r represented by eitherm exerted a the force itself ORDocScientia p. 22 m components

Friction forceDocScientia p. 28

Contact forceTwo objects in close contact, and it tries to move across each other.Surface of solids = generally rough.DocScientia p. 28

Uneven sections hook on each other when sliding. Friction = opposes motion of two surfaces.DocScientia p. 28

Factors that influence the size of the frictionalDocScientia p. 29 force Surface type Normal force

FN = Fg = w Fx = Fcosθ Fx = Fcosθ F Fy = FsinθNormal N Fy = Fsinθ FN = Fg – Fy force FN = Fg + Fy Fg║ FN FN Fg┴ Fy Fg║=Fgsinθ Fx Fg┴=Fgcosθ Fy FN=Fgcosθ Fx θDocScientia p. 30 Fg

Surface type Smooth tiles are very slippery Slightly melted ice on an ice rink – it is easy to glideDocScientia p. 31

Surface type The rougher the surface, the greater the frictionDocScientia p. 31

The extent they affectSurface one another is type represented by the coefficient of friction (μ)DocScientia p. 31

Coefficient of frictionDocScientia p. 31

Symbol: μNo unit – factor of roughness Surface pairs have two coefficients: static friction: μs kinetic friction: μkDocScientia p. 31

Proportionality constant of The relationship fαF is known N as the coefficient of friction μs max > μk The smaller the μ, the less the resistance offered by a surface, value < 1DocScientia p. 31

How to reduce frictionDocScientia p. 31

Lubricate: Oil Grease Finely powdered graphiteWet the surface with waterDocScientia p. 31

Frictional force of one contact surfaceon another when there is no relative motion between the objectsDocScientia p. 32 Static friction (fs)

Independent of surface areaDependent on mass & weight → mass + weight = FNDepends on nature of surfaces Acts opposite to motionDocScientia p. 32

Directly proportional to the normal forceDocScientia p. 32

Frictional force of one contact surfaceon another when one or both objects are movingDocScientia p. 32 Kinetic friction (fk)

Independent of surface areaDependent on mass & weight → mass + weight = FNDepends on nature of surfaces Acts opposite to motionDocScientia p. 32

Smaller than fs(max) Directly proportional to the normal forceDocScientia p. 32

Applied force, no motion: fs = Fapplied Applied force increased, on the verge of motion:An object fs≤μsFN and fs(max)=μsFN fs(max) = FTat rest on a but mass is the same No horisontal force: fs(max) = μsFN Fg, FN, fs are Fapplied = 0 Nrough unchanged Thus fs = 0 N FNhorisontalsurface FT FT f fDocScientia p. 33 W

AppliedApplied force. @ angle:When it force > fs(max) Object begins to move. FN: FN = Fg – Fy Get componentsfinally FrictionNonow kinetic. – fk = μFN is vertical force Applied push @ angle: fk=µkGet∴fk = μ·(F – F ) = F + F FN c mponentsstarts to o g N y g No vertical motion: fk = μFN ymove ∴fk = μ·(Fg + Fy)on a FN FT F FT Thorisontal θθsurface f WDocScientia p. 34

@ rest: fs≤μsFN accelerating:Graph of fs=μsFN fwhen an Frictional force f (N) About to start moving ∴fs(max) = μsFs Fk constantobject starts tomove over arough surface Applied force FT (N)DocScientia p. 35

Object at rest: Fg║=Fgsinθ Fg║and fs: equal andAn object Fg┴=Fgcosθ opposite, fs=Fgsinθat rest on arough fs(max)=μsFN FNsurface fs(max)=μs(Fgcosθ)@ an Fg║ fsangl Fg┴e θ wDocScientia p. 35

Object at rest: Fg║=Fgsinθ OBJECT SLIDING Fg┴=FgcosθMoving F fand F F ININ THE and f <f DOWN A SLOPE THE kk s g║g║on a SAMEk=ma Fg║ - f DIRECTION SAME DIRECTION F-Fg║-fk=ma F+Fg║-fF=ma F cosθ fk=μk k N=μk g FN Fslope fk=μkFkN=μk(F(Fgcosθ) fk=μ FN=μk cosθ) g@ an F Fg║ Fg┴ fk fkangle θDocScientia p. 35

Object at rest: Fg║=Fgsinθ Fg┴=FgcosθMoving fs=Fg║=Fgsinθon a Object begins sliding fs(max)=Fg║=Fgsinθslope fs(max)=μs·Fgcosθ ∴Fg·sinθ = μ·Fg·cosθ@ an But fs(max)=μsFNangl μs= Fgsinθ = tanθeDocScientia p. 36 Fgsinθ

Applications of frictionTyres vs road Walking/running oversurface loose sand/snowHand and lids of During road racesbottles velocity decreasesSoles of shoes Falling ouch!and floorGears – motionStepping onbrakesDocScientia p. 36

Forces in equilibriumDocScientia p. 32

Σ forces on an object = 0. Forces are balanced.DocScientia p. 43 Equilibrium

Object is in equilibrium if: Object is at Moves at a constant rest velocityDocScientia p. 43

FN = Fg FN In opposite Fg directionsDocScientia p. 43

@ constant height and velocity: Lifting force No acceleration – not vertically nor horisontally No net forces Air resistance Applied force Upwards lifting force = gravitational force downwards of the engine Applied engine force = air resistance weightDocScientia p. 43

Forward force > resistance Forward applied force increases Net force = forward Plane will accelerate forwardDocScientia p. 44

Is the vector Σ of all the forces acting on the object. One force with the same effect as all the other forces together.DocScientia p. 44 Resultant or net force Fnet

Determining the resultant vector: Trignometry to Scale diagram; 2 3 1 Scale diagram; calculate tail head to the tail to tail components (parallellogram)DocScientia p. 44

Head to tailTail to tailDocScientia p. 44

θ = 120° 100 N 140 NDocScientia p. 44

Head to tail method Scale 1 cm:20 N 1 Axes 1 vector R = 6,3 cm (from origin) = 126 N 2 New axes F = 100 N = 5 cm 120 to the L 44° 2 vector 120° 3 Join tail of 1 to head of 2 F = 140 N = 7 cm = resultant DocScientia p. 45

Tail to tail method Scale 1 cm:20 N 1 Axes 1 vector from origin Same axes 2 Measure 120 2 vector from origin F = 100 N R = 6,3 cm Parallellogram = 5 cm = 126 N 3 Diagonal from origin No vector heads touch 44° Arrowhead 4 Measure length - N Measure direction 120° F = 140 N = 7 cm DocScientia p. 46

Rough free body 1 diagram - no scale Draw all x and y components, use trig 2 to calculate each of these components Add all x componentsF = 100 N R = 126 N 3 and y componentsCalculate Use pythagoras to calculate R. Use tanƟ to 4 calculate angle (with regards to x- 120° F = 140 N axis) DocScientia p. 46

Newtons laws of motion

1 An object will stay at rest or continue to move at a constant speed in a straight line (at a constant velocity), unless acted upon by an external net force. Professor Mac Spock explainsDocScientia p 59 Newtons first law of motion/Law of inertia

The resistance of an object to a change in its state of motion or rest. Because of inertia objects tend to remain at rest or continue at uniform velocity.DocScientia p 60 Inertia

Not a force – characteristic of matter Anything with mass has inertia Mass is a measure of inertia Greater mass = greater inertiaDocScientia p 60

In a frictionless system: Ball reaches same height as where the motion starts, even when the slope is reduced. Loss in height is due to friction. The ball would continue to roll as long as thereDocScientia p 60 is no friction.

Net force is not necessary for continuous constant motion in a straight line – it is needed to stop an object.DocScientia p 60

Protect against sudden changes in motion. According to Newtons first law, a person will continue to move until Seatbelt safety something stops them.DocScientia p 60

2 If a net force acts on an object, the object will accelerate in the direction of the net force. Acceleration is directly proportional to net force and inversely proportional to mass. Prof Mac Second Law Fnet = maDocScientia p 66 Newtons second law of motion

3 If object A exerts a force on object B, object B exerts an equal but opposite force on object B.1 2 3DocScientia p 88 Newtons second law of motion

Newtons law ofuniversal gravitation

A force of gravitational attraction exists between any two objects in the universe that have mass. This force of attraction is directly proportional to the product of the masses of the objects and inversely proportional to the squared distance between their centres of gravity.DocScientia p 95 Law of universal gravitation

r m1 F1 F2 m2 F = G m1m2 2 rDocScientia p 96

Universal gravitational constant. F = G m1m2 26,67x10 2 r -11 -2 N·m ·kg On the information sheetDocScientia p 97

Mass WeightDefinition Mass = Force with which the earth or amount of another planet attracts an matter. object. Depends on the mass and radius.Scalar/ Scalar VectorVectorFormula Fg = mgUnit kg Newton (N)DocScientia p 97

weightlessness Weight is experienced indirectly due to ical gravity. echan of m ity. t re sult ra v ad irec isti ng g It is s re s Weightlessness fo rce is when gravitational force is exerted on an object or person. The other mechanical forces that cause the feeling the feeling of DocScientia p 98 weight are absent

Gravitational force surrounds everything that has mass.Gg Gravitational acceleration decreases as the distance increases. Gravitational acceleration (g) = 9,8 m·s-2 Weight = attractive force of the earth on any object.Gravitational force surrounds everythingthat has mass. According to Newton: thegravitational attraction between the earthand the object.DocScientia p 98

Gg If one object is a planet m and the other is an object the gravitational attraction force is the r weight. The objects mass is m, M the planets mass is M and the distance (radius of the planet) is r.F = G mM mg = G mM g = G M 2 2 2 r r RDocScientia p 98

All theory is taken from DocScientia text-and workbook book 1, grade 11Slide 1 – Slide 2 – womensquest.comSlide 23 – cairoo software Slide 32 – istockphoto.comSlide 33 – Slide 66a – dreamstime.comSlide 66b – Slide 70 – digimars.netSlide 71 – TedEd on YouTube

Slide 75 – cairoo softwareSlide 77 – Slide 80 –

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