L14 Dynamics Conceptual Change

8/10/2019 L14 Dynamics Conceptual Change

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Physics 30 Lesson14

Forces & Dynamics Conceptual Change

At this point in the course you have learned about Kinematics (the description of motion)and you have learned about vectors (addition, components). Kinematics and vectorsprovide us with the tools to learn why objects move as they do and how changes in

motion occur.

I. Natural motion

Our everyday experience tells us that the natural motion of an object is to be at rest andif we wish to have an object maintain a uniform speed, we must continually apply aforce on the object. !orce " # is a push or a pull in a gi$en %irection. (!otice that

!orce is a $ectorsince it has a magnitude anda direction.) or example, if we wish to havesome boo"s move across a table at constantspeed we must apply a constant force.

#owever, what if we push a heavy steel ball across atable$ %nli"e the boo"s, we only have to give the ball asmall push to get it going. Assuming a smooth levelsurface, once the ball is moving no force is re&uired to"eep it moving. 'here is something strange going on here

any years ago *alileo *alilei (+- / +-0 12) thought about these things as well.#e realised that our everyday experience with objects always involved friction in oneway or another. #e wondered what the resulting motion would be if friction wereminimised or eliminated. 3ith the materials at his disposal *alileo was only moderately

successful at minimising friction so he devised the following thought experiment4

5uppose we release a heavy, smooth ballfrom point A on a smooth ramp. 'he ballrolls down the ramp, along a hori6ontalsection, and then up another ramp on theother side. 'he ball is observed to cometo a stop at the same height on the secondramp at point 7.

!ext we ma"e the second ramp less steep.

3hat happens$ 'he ball still rolls up theramp and once again stops at 7 which is atthe same height as A.

!ow suppose we lay the second ramp downso it is hori6ontal. 3hat happens$ *alileoargued that, in the absence of friction or anincline, the ball would continue to go at aconstant speed forever.

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A 7

A 7

A

v


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Our usual common sense view is that the natural motion of an object is to be rest.#owever, based on his experimentation and reasoning, *alileo proposed that thenatural motion of an object is to maintain a constant velocity, whether at rest or alreadyin motion. *alileo stated this as the La o! Inertia4

9nertia is the tendency of an object to remain in its current motion. 9f the object isat rest, it tends to remain at rest. 9f an object is in motion, it tends to remain inmotion. urther, the inertia of an object is proportional to its mass.

(9n case you missed it, this is a very important idea.)

II. Neton's las o! motion

9saac !ewton (+-0 / +:0: 12), who was born on the day that *alileo died, too" thewor" of *alileo further. !ewton agreed that the natural motion of an object is uniformmotion, but he went on to as"4 3hat causes a change in motion$ #e reasoned that ifan object;s velocity remains constant, then its acceleration is 6ero. 9n addition, when achange in velocity occurs, an acceleration is involved.


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rom considerations li"e these, !ewton proposed three laws of motion4

Neton's First La *! +otion ",he La o! Inertia#

2very object continues in a state of rest or uniform motion, unless acted on by anunbalanced force. (see errill pages @@ to @)

Neton's -econ% La *! +otion

9f an object is subjected to an unbalanced net force, it will accelerate in thedirection of the net force4

Acceleration is directly proportional to the magnitude of the net force. (i.e.

the greater the force, the greater the acceleration)

a

Acceleration is inversely proportional to the mass (inertia). (i.e. thegreater the mass, the smaller the acceleration)

+a

m

r

3hen we combine the proportionality statements above we get4

a

m=

r


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i.

A. 3hat is the reaction force to a person pushing her hand against a wall$

7. 3hen wal"ing across a floor, what is the direction of the force of your foot on thefloor$ 3hat is the reaction force$ 3hich force propels you forward$ 3hat wouldhappen if the friction between your foot and the floor became 6ero$

1. An apple on a tree is pulled down toward the 2arth. 3hat is the reaction force$

Answers4A. 'he reaction force is the wall pushing bac" on the hand.

7. 'he reaction force is the floor on the foot. 9t is the reaction force that propels thefoot forward. 9f the friction became 6ero, no forces could be made and thereforeno change in motion could occur.

1. 'he reaction force is the 2arth being pulled up to the apple.

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hand on wall


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III. +ass an% eight

9n everyday usage the words massand weightare used interchangeably, but in physicsthey have very precise and different meanings.

+ass (9nertia)'he mass of an object is the amount of matter within the object. 'he basic unit ofmass is the "ilogram ("g). 'he terms mass and inertiamean the same thing.!ote that the mass of an object is completely independent of where the object isand the changes in motion of the object. A +> "g mass on 2arth is still a +> "gmass on the oon. ass is a scalar.

/eight (orce due to gravity)'he weight of an object is the common name for the !orce %ue to gra$ity(g) onan object. 'he force due to gravity depends on two factors4 (+) 'he strength ofthe acceleration of gravity (g) and (0) on the mass of an object. 'he e&uation forthe force due to gravity is4

gmg=

5ince weight is a force, its basic unit is the !ewton (!). 9n addition, since weight isa force, it also has a definite direction ? downward. 3eight is a vector.

%nli"e the mass of an object, the force due to gravity does depend on where theobject is. 'he acceleration due to gravity on 2arth is .@+ m8s0, on the oon it is+.-+ m8s0, and on ars it is B.:0 m8s0. 'herefore a +> "g mass will weigh @.+ !on 2arth, +-.+ ! on the oon, and B:.0 ! on ars. (9f you want to lose weightfast, go to the moon.)

ii.

3hat is the mass and weight of a B> "g object located on the surface of the 2arth and

on the oon (g C +.-+ m8s0)$

'he mass on the 2arth and on the oon is B> "g.

(2arth) g C m g C B> "g (/.@+ m8s0) C 24.3 N or C 24.3 N %on

(oon) g C m g C B> "g (/+.-+ m8s0) C 4.3 N or C 4.3 N %on

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I. *ther types o! !orces

F pplie% !orce

An applied force is a general force that indicates a push or a pull on an object. 9tmay be applied hori6ontally, vertically or at any angle. 3hen a force is applied atan angle you should immediately thin" in terms of its hori6ontal and vertical (x and

y) components.

F! Frictional !orce

A frictional force is any force (stic"ing between surfaces, air resistance, etc.) thatresists, retards or impedes the motion of an object. 3e will study frictional forcesin more detail in the next lesson, but for now we can say that a !rictional !orceacts in opposition to the motion o! the o()ect .

FN Normal !orce

3hen an object is placed on a surface of some "ind, li"e a table, the surfaceresponds by pushing bac" up on the object. 'his contact force is called thenormal !orce. ('he word DnormalE refers to the >oangle between the surface ofthe table and the contact force. 'he words normal, perpendicular, and right can allrefer to an angle of >o.)

or the illustrated rabbit, the net force acting onthe rabbit is 6ero. 'he downward force ofgravity (g) is balanced by the upward force(!) exerted by the surface on the rabbit.

!C g

'here are two important things to note4

+. Fo not confuse normal force with net force. !is not the same as !2'. 'heymean very different things.

0. !C gonly for hori6ontal surfaces. 3hen a surface is at an angle, for

example an inclined plane, !gfor an object.

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A

A

A

Ax

Ay

g

!


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. 5an%in ssignment

+. 3hy does a child in a wagon fall bac"ward when another child suddenly pulls thewagon forward$

0. 2xplain what the term inertiameans.

B. A rear/end collision between a soft/drin" truc" and a car occurs. A lawsuitdevelops over who is at fault. 'he truc" driver claims the car bac"ed into him,

while the auto driver claims that the truc" hit him from behind. 'he only evidenceis that &uite a number of soft/drin" bottles fell forward in the truc". rom theevidence, can you tell who was at fault$ 2xplain.

. 3hat is the principle behind a magician;s ability to pull a tablecloth from beneathchina and glassware without brea"ing them$ 2xplain.

. 3hiplash is a common result of an auto accident when the victim;s car is struc"from the rear. 3hy does the victim;s head get thrown bac"ward in this "ind of anaccident$

-. 2xplain why automobiles use more gasoline for city driving than for highwaydriving.

:. 3hy do you exert more force on the pedals of a bicycle when you first start outthan when you reach constant speed$

@. 3hen you lift a bag of groceries, you exert an upward force on the bag. !ewton;sthird law says that there is a DreactionE force to your upward force on the bag.3hat object exerts this reaction force and in what direction does this force act$

. 2xplain why when you wal" on a log floating in water, the log moves bac"ward asyou move forward.

+>. 3hy does it hurt your toe when you "ic" a roc"$

++. 5tate the reaction force for each of the following forces.

a. the southward force of a field goal "ic"erGs toe on a football

b. the bac"ward force of a joggerGs shoe on the ground

c. the downward force of a boo" on a des"

d. the bac"ward force of a jetGs engines on its exhaust gases

e. the bac"ward pull of a swimmerGs hands on the water in thebutterfly stro"e.

+0. A beginning physics student, confused by a seeming contradiction in !ewtonGslaws, as"s her teacher the following &uestion4 H9f, for every force there is an e&ual

and opposite reaction force, then all forces in nature come in e&ual and oppositepairs, and are therefore balanced. 'hus, since there can never be such a thing asan unbalanced force, how can any object ever accelerate$H 2xplain the fault inthis common misconception.

+B. A fireman at the scene of a fire is holding a heavy hose out of which water isgushing. 'o "eep his balance, he often has to lean. 3hich way does he lean,forward toward the water or bac"ward away from the water, and why$

+. A s&uirrel with an armful of nuts is sliding helplessly across a flat, icy roof, gettingdangerously close to the edge. #e understands !ewtonGs 'hird Iaw, and is able tosave himself. 2xplain how he does it.

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L14 Dynamics Conceptual Change

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