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Unit 4: Newton’s LawsGuiding Light #5

Unit 4: Newton’s LawsGuiding Light #5

AP Physics C - Mechanics


Mechanics within the Physics Curriculum

Physics

Mechanics Electricity Magnetism Optics Thermodynamics Nuclear

Kinematics DynamicsKinematics: deals with motion description

Dynamics: deals with what causes motion

Slide - 1


Newton's Laws

• This unit will explore:– Newton’s three laws of motion – Forces– Static and Dynamic Applications

• Sir Isaac Newton– 1642 – 1727– Formulated

• Basic concepts and laws of mechanics• Laws of Universal Gravitation• Calculus• Initial theories pertaining to the study of light and optics

Slide - 2


Forces(1 of 4)

• Commonly imagined as a push or pull on some object

• Forces are Vector quantities

• May be a contact force or a field force– Contact forces result from physical contact

between two objects– Field forces act between disconnected object

Slide - 3


Forces(2 of 4)

Contact Forces

Field Forces

Slide - 4


Forces(3 of 4)

• Since they are vectors, arrows are used to represent forces. – The length of the arrow is proportional to the

magnitude of the force. – The arrow points in the direction of the force

15 N5 N

Slide - 5


Newton’s First Law

• An object moves with a velocity that is constant in magnitude and direction (aka zero acceleration), unless acted on by a non-zeronet external force

Where: The net force is defined as the vector sum of all the external forces exerted on the object

• Sometimes referred to as the “Law of Inertia”

Slide - 6


Inertia• Is the tendency of an object to resist a change

in motion

• An object will stay at rest unless a force causes it to move

• An object in motion will stay in motion unless a force causes it to stop

• Inertia has no units

Slide - 7


Net Force(1 of2)

• The net force on an object is the sum of all forces acting on that object.

Slide - 8

Individual Forces Net Force

10 N4 N 6 N


Net Force(2 of2)

Slide - 9

Individual Forces Net Force

3 N

4 N

5 N$36


Newton’s Second Law• The acceleration of an object is directly

proportional to the net force acting on it and inversely proportional to its mass.

• Can also be applied three-dimensionally

Ԧ𝑎 =σ Ԧ𝐹𝑁𝐸𝑇𝑚

Slide - 10


Net Force & the 2nd Law

• When forces act in the same line, we can just add or subtract their magnitudes to find the net force.

2 kg

15 N 32 N

Fnet = 27 N to the right

a = 13.5 m/s2

10 N

Slide - 11


Units of Force

• SI unit of force is a Newton (N)

Slide - 12


Gravitational Force

• Mutual force of attraction between any two objects

• Expressed by Newton’s Law of Universal Gravitation:– Every particle in the Universe attracts every other particle

with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them

Slide - 13


Weight• The magnitude of the gravitational force

acting on an object of mass m near the Earth’s surface is called the weight w of the object– W = m g is a special case of Newton’s Second Law

• g is the magnitude of the acceleration due to gravity

• Weight depends upon location

Slide - 14


• If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1.

Newton’s Third Law

Slide - 15


Some Action-Reaction Pairs

Ԧ𝐹𝑇 𝑜𝑛 𝐶

Ԧ𝐹𝐶 𝑜𝑛 𝑇

Slide - 16


More Action-Reaction pairs

Ԧ𝐹𝐸 𝑜𝑛 𝐶

Ԧ𝐹𝐶 𝑜𝑛 𝐸

Slide - 17


Questionsfor you

18


Question 1Two equal-magnitude horizontal forces act on a box. Is the object accelerated horizontally?

a) Yes

b) No

c) You can’t tell from this diagram.

Slide - 19

0


Question 2Is it possible that the box is moving, since the forces are equal in size but opposite in direction?

a) Yes, it is possible for the object to be moving.

b) No, it is impossible for the object to be moving.

Slide - 20

0


Question 3Two equal forces act on an object in the directions shown. If these are the only forces involved, will the object be accelerated?

a) Yes

b) No

c) It is impossible to determine from this figure

Slide - 21

0


Question 4A ball hangs from a string attached to the ceiling. What is the net force acting on the ball?

a) The net force is downward.

b) The net force is upward.

c) The net force is zero.

Slide - 22

0


Question 5Two masses connected by a string are placed on a fixed frictionless pulley. If m2 is larger than m1, will the two masses accelerate?

a) Yes

b) No

c) You can’t tell from this diagram.

Slide - 23

O


Circle the correct answer (True of False)

Question 6

1 An object can move even when no force acts on it. T F

2 If an object isn't moving, no external forces act on it. T F

3 If a single force acts on an object, the object accelerates. T F

4 If an object accelerates, a force is acting on it. T F

5 If an object isn’t accelerating, no external force is acting on it.

T F

6 If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction.

T F

Slide - 24

O

OO


Question 7

The force with which earth attracts bodies towards its center is calleda) Mass

b) Inertia

c) Gravitational force

d) Weight

Slide - 25

Special type of Gravitationalforce


Question 8

If a bus takes a sharp turn then passengers inside move outward due toa) Force

b) Inertia

c) Normal force

d) Friction

Slide - 26

O


Free-body diagrams• A picture showing all of the external forces acting

on one object• Used to determine the net force (𝑭𝒏𝒆𝒕) acting on

an object• Which in turn allows us to determine one or

more of the following:(1) Is an object accelerating and at what rate(2) What additional force(s) is required to keep an

object in static equilibrium(3) What force(s) is required to produce a specified type

of motion- Acceleration- Velocity- Displacement

Slide - 27


The Power of Newton′s 2nd Law

Slide - 28


Rules of the road when drawing Free-body Diagrams

• Identify all external forces acting on the object• Determine the direction in which each force is

acting • Represent the object as either a box or a circle

and add arrows for each external force in the appropriate direction

• Remember that the relative magnitude of the force is depicted by it’s length so a 20 N force should be roughly twice as long as a 10 N force

Slide - 29


Example #1(Free-body Diagram)

Free-body diagram of a book at rest on a table top.

Slide - 30

FNTableonBook NTable

onBook

FGEarthon Book WBook



Free-body diagram of a girl suspended motionless from the ceiling by a rope. Diagram the forces acting on the girl as she holds onto the ropes shown below.

Slide - 31

ftp.opeiTRope1 wfFTRope2 TRope2

EarthagirlWgirl



Free-body diagram of an egg falling from a nest in a tree. Neglecting air resistance, draw a diagram of the external forces acting on the egg as it falls.

Slide - 32

ForEarthon Egg

Wegg



Free-body diagram of an egg that is falling (do not neglect air resistance) from a nest in a tree. Diagram the external forces acting on the egg as it falls.

Slide - 33

f FdrayDo

ForEarthonegg

Wegg



Free-body diagram of a car parked on a sloped street.

Slide - 34

et on tiresFestre

µFNstreet orCor NStreeton Car

Fgm car



Free-body diagram of a car that accelerating to the right (+ x). Diagram the forces acting upon the car.

Slide - 35

F rollingNStreeton car

resistor 9 FFriationstreetontires

ForayWear



Free-body diagram of a car that is coasting to the right (+ x) and slowing down. Diagram the forces acting upon the car.

Slide - 36

F rollingN'Streeton car

resistances

ForayWear



A box in the bed of a truck as the truck moves forward at constant speed. Diagram the forces acting upon the box.

Slide - 37

FNbedonbox

Ubox



A box in the bed of a truck as the truck accelerating forward. Diagram the forces acting upon the box.

Slide - 38

FNbedonbox

FFbedonbotUbox



A lamp is suspended from two cables of unequal length as shown below. Diagram the forces acting upon the lamp.

Slide - 39

T.EYI.mn

Wlamp



A lamp is suspended from two cables of unequal length as shown below. Diagram the forces acting upon the lamp.

Slide - 40


Using FBD’s to solve dynamics problems

• Step 1: Draw FBD’s of the objects(s) of interest

• Step 2: For any force that doesn’t lie along the x or y-axis, break those forces into components that do lie on the x or y axis

• Step 3: Write 𝑭𝑵𝑬𝑻𝒙 and 𝑭𝑵𝑬𝑻𝒚 equations

• Step 4: Solve the resulting equationsSlide - 41


Example #1

A 1 kg physics book is at rest on a table top as shown below. What force is exerted by the table top on the book?

Slide - 42

Steps N A All forces in y dimensionSteps Fret equation

Frety FNTableonbook Wbook

Step Solvefor FNTableonbookstep Draw FBD Fnets Fortune

onbook Wbook9FNTable

onbook MY FNtableonbook MgO tontine onbook 4kg 98mbH

FSEarthonbook Wbooktntabiewbooh9 SN


Example #2A gymnast is holding onto two ropes that are being accelerating upward at 3 m/s2. Assuming the mass of the gymnast is 51 kg, what would be the tension in each rope?

Slide - 43

Steps Foret equationSteph DrawFB'D they Titta Wgym

T f Ta Steph Solvefor IAssumingT I T

FSEarthongym Wgym Forty 2T WgymMa 2T my

Step2 NIA nfy m Sir.gl 3ms4 2T l5lkg l9.8msT326.4NQ


Example #3A 3000 kg car is parked on a road that rises 10° above the horizontal. What are the magnitudes of the normal force and the static frictional force that the ground exerts on the tires?

Slide - 44

step FretequationsStep Draw FBD an

Fnety Fn Egg fnetx fgxFFJFNroadoncarfney.fmwcarcoslooffnetx

Vcars.NO FFFFMoo step Solvefor Fn'sFeL

Hoo IE gt.is Iiigx 0 FN 3000119.81651000 13000719.8sin100 F

Warsaw r

Step ComponentsofWearshownaboue tn 28953 SN FF5l05.26NO


Example #4

A 10 kg object slides down an inclined plane at a constant velocity. If the plane makes an angle of 15°, what is the normal force acting on the object?

Slide - 45

Enplaneonblow step3 Foret equation c step so'Enfor

Too Steph EBD knety FNPY.co.bw FgyLFgyago M4T FNplaneonbloch WblookCosts

www.coslsf O FNPlaneonblock mycostseg.ie pgea u u pn yoy a.gm c sWbiousink

S q2 Components shownaboveFNpianeonbiou 94 be


Example #5A young girl pulls a 20 kg sled across a flat road with a force of 100 N directed at an angle of 15° with respect to the horizontal. If the road exerts a frictional force of 15 N on the sled determine the following:

a. The normal force exerted by the road on the sledb. The coefficient of friction between the sled and the roadc. The distance the sled travels in 3 seconds if it starts from rest

Slide - 46

AP Physics C - MechanicsSlide - 47

step Draw FBD step Solvefor FN µk dFapp FI they FappytEN Usted

g.jo EfnFarPy Y5gsgif miff 25.88N ten mgWg rpx 100N 150 96.59N o 25.88Mt FN 120kg19.8mW

IRL Componentsshownabove 0 25.88N 1 FN 196N

steep c e eaErmannoII Ff MkFNFnetx Fappy FF 15N ur 170.12N K

noE xfexyiotvx.tt faithFnety FappytFn UstedLinnet Egg jf igwP a 408

Xf I 4.084432 _18.36mL


Example #6A cart is placed on a flat frictionless table with a string attached via a frictionless pulley to a 2 kg object. If a motion detector indicates the cart’s acceleration is 4 𝑚

𝑠2, what is the mass of the cart?

Slide - 48


Step Draw FBDD Steph Solvefor McaHymes Equation2 Eanatun3

femme.at ft m iii E It tenia IYII.ini.iooz twang F 219.8 athroato

step NIAI Mcartor 219.8 a

step Foretequations Mart 41 219.8 4

Eat 2kgmass_

they Fn Wcartzo Mcart L9kgLOFnetmot.on T

FretmotouWay I


Example #7

Two masses are hung from a frictionless pulley using a massless string. If m1 = 17 kg and m2 = 6 kg, determine the acceleration of the system.

Slide - 50


step Draw EBD's tsp solve for a

a

mini's ah S0

WitMig ma Mag Maa

Steph.CN A I

step3 Fretequations a Mitha g m Mam a gfmni.ITIna W TF ta T Wa

a 9.8451454gai4 amsQ


Homework

A 9-kg book is held at rest against a vertical wall by an applied force (Fapp) as shown below. What is the maximum allowable Fapp before the block starts moving up the wall if the static coefficient of friction (μs) between the wall and the block is 0.2?

Slide - 52


StepI2 Draw FBD step Find Fappaty Fnety Ff t Fappy U

fapp Maji regentFappsin68 my7h 0 0.2Fn t 0.87Fapp 88.2

ftp.krrikppsinbo in osnkrr 88IO9tx 0.2Fn Foret Fappx Fnffvwtjggkppco.to mageFappcos600 FN

O OStapp FNFn 0.5Fapp

step Fret equationsO.ME 882

o.gfappOr 2

Fnety Fft Fappy W 0.87Earp 88.2 0 Fapp

0.97Epp 88.2Fretx Fappx FNFapp 90.9

unit 4: newton’s lawshurrellphysics.com/apphysicscmechfiles/newtons... · ap physics c -...

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