physics proj class 11

8/18/2019 Physics Proj Class 11

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Physics Assignment

Atwood’s Machine and Levers

DONE B

Siddharth. L

Class 11

Roll no: 09

INDEX

1. Atwood’s Machine

1.1. Introduction


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1.2. Deriving e!ression "or tension using Atwood’s #achine

1.$. A!!lications o" Atwood’s Machine

2. %i#!le Machines

$. Levers

$.1. Classes o" levers

$.1.1. &irst Class

$.1.2. %econd Class$.1.$. 'hird Class

$.2. Law o" the Lever

$.$. Mechanical advantage

$.(. )ses o" Levers in hu#an *od+

$.(.1. &irst Class

$.(.2. %econd Class

$.(.$. 'hird Class$.,. )sing ro!e as a lever

A'-D’% MAC/I

'he Atwood #achine or Atwood3s #achine4 was invented in 156( *+ the

nglish #athe#atician 7eorge Atwood as a la*orator+ e!eri#ent to veri"+

the #echanical laws o" #otion with constant acceleration. 'wo weights connected *+

string running over a !ulle+ is 8nown as an Atwood’s Machine. Atwood3s #achine is a

co##on classroo# de#onstration used to illustrate !rinci!les o" classical #echanics.

'he #achine t+!icall+ involves a !ulle+ a string and a s+ste# o" #asses.

https://en.wikipedia.org/wiki/Mathematicianhttps://en.wikipedia.org/wiki/George_Atwoodhttps://en.wikipedia.org/wiki/Newton's_laws_of_motionhttps://en.wikipedia.org/wiki/Accelerationhttps://en.wikipedia.org/wiki/Classical_mechanicshttps://en.wikipedia.org/wiki/George_Atwoodhttps://en.wikipedia.org/wiki/Newton's_laws_of_motionhttps://en.wikipedia.org/wiki/Accelerationhttps://en.wikipedia.org/wiki/Classical_mechanicshttps://en.wikipedia.org/wiki/Mathematician


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Atwood’s Machine was created in order to veri"+ ewton’s second law relating &orce

&4 Mass #4 and Acceleration a4 *+ the relation:

F = m * a

)sing the Atwood’s Machine an e!eri#ental acceleration can *e #easured and

co#!ared to the theoretical acceleration which is !redicted *+ ewton’s %econd law

and is de!endent on onl+ two #ass #easure#ents and the 8nown value o" acceleration

due to gravit+. I" these values #atch then the %econd Law holds true. I" the values do

not #atch then the %econd law is not valid. It is e!ected that the %econd law will hol

true and indeed the results o" this law con"ir#ed ewton’s %econd Law within a

!ercent error o" 2.19.

The ideal Atwood Machine consists of two objects

mass m1 and m2, connected by

an inextensible massless string over an ideal

massless pulley.

-hen m1 ; m2 the #achine is in neutral

e


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Let two #asses m1 and m2 o" weights 1 and 2 *e sus!ended

*+ a string o" negligi*le #ass on a #assless and "rictionless !ulle

'hen

' )>-ARD &RC:

'?#1@g4 ; #1@a4 ? 14

' D--ARD &RC:

#2@g4?' ; #2@a4 ?24

Adding e< 14 and e< 24 :

#2@g4?#1@g4;#1@a4#2@a4

g#2?#14;a#1#24

-e Bnow that

'?#1@g4 ; #1@a4

%u*stituting value o" a in the a*ove e


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A!!+icati"ns "# At&""'(s )achine:

Atwood3s original illustrations show the #ain !ulle+3s ale resting on the ri#s o"

another "our wheels to #ini#ie "riction "orces "ro# the *earings. Man+ historical

i#!le#entations o" the #achine "ollow this design.

An elevator with a counter*alance a!!roi#ates an ideal Atwood #achine and there*+

relieves the driving #otor "ro# the load o" holding the elevator ca* it has tooverco#e onl+ weight di""erence and inertia o" the two #asses. 'he sa#e !rinci!le is

used "or "unicular railwa+s with two connected railwa+ cars on inclined trac8s and "or

the elevators on the i""el 'ower which counter*alance each other.

%IM>L MAC/I%

A si#!le #achine is a #echanical device that changes the direction or #agnitude o" a

"orce. In general the+ can *e de"ined as the si#!lest #echanis#s that use #echanical

advantage to #ulti!l+ "orce. )suall+ the si#!le #achines re"er to si classical devices

• Lever

• -heel and ale

• >ulle+

• Inclined >lane

• -edge

• %crew

A si#!le #achine uses a single a!!lied "orce to do wor8 against a single load "orce.

'he #achine can increase the a#ount o" out!ut at the cost o" a !ro!ortional decrease

the distance #oved *+ the load. %i#!le #achines can *e regarded as the *uilding

*loc8s o" all the co#!ound #achines. &or ea#!le wheels lever and !ulle+s are use

in the #echanis# o" *ic+cle.


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LER%

A lever is a si#!le #achine consisting o" a *ea# or rigid rod !ivoted at a "ied hinge

or "ulcru#. It is one o" the si si#!le #achines identi"ied *+ Renaissance scientists. A

lever a#!li"ies an in!ut "orce to !rovide a greater out!ut "orce which is said to

!rovide leverage. 'he ratio o" the out!ut "orce to the in!ut "orce is the #echanical

advantage o" the lever.

LER

Levers have $ classes. a#el+

• First ,+ass:


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&irst?class levers have the "ulcru# !laced *etween the load and the e""ort as in the

seesaw crow*ar and *alance scale. I" the two ar#s o" the lever are o" eliers

crow *ar

tongs

scissors

can o!ener

Sec"n' ,+ass:

Second-class levers have the load between the eort and the

fulcrum. A wheelbarrow is a second-class lever. The wheel!s axle is

the fulcrum, the handles ta"e the eort, and the load is placed

between them. The eort always travels a greater distance and is

less than the load.


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S"me "# the Sec"n' ,+ass -evers:

-heel *arrow

hole !uncher

sta!ler

wagon

nutcrac8er

*ottle o!ener

nail cli!!er

!liers

can o!ener

!a!er cutter

$hir' ,+ass:

Third-class levers have the eort placed between the load and the

fulcrum. The eort always travels a shorter distance and must be

greater than the load. A hammer acts as a third-class lever when it

used to drive in a nail# the fulcrum is the wrist, the eort is applied

through the hand, and the load is the resistance of thewood. Another example of a third-class lever is the human forearm#

the fulcrum is the elbow, the eort is applied by the biceps muscle,

and the load is in the hand.

S"me "# the $hir' ,+ass -evers:


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Ar#

Fase*all *at

Froo#

Doors

&ishing Rod

%ling

'weeers %ta!ler

Mouse 'ra!

7ol" Clu*

Cata!ult

Diving *oard

&or8 Bni"e

-A OF $.E -E/E0:

A lever is a *ea# connected to ground *+ a hinge or !ivot called a "ulcru#. 'he idea

lever does not dissi!ate or store energ+ which #eans there is no "riction in the hinge o

*ending in the *ea#. In this case the !ower into the lever e


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out!ut "orce is a!!lied !oint F4 then the lever a#!li"ies the in!ut "orce. n the other

hand i" the distance a "ro# the "ulcru# to the in!ut "orce is less than the

distance "ro# the "ulcru# to the out!ut "orce then the lever reduces the in!ut "orce.

)E,.ANI,A- AD/AN$A3E:

Mechanical advantage is a #easure o" the "orce a#!li"ication achieved *+ using a tool

#echanical device or #achine s+ste#. Ideall+ the device !reserves the in!ut !ower an

si#!l+ trades o"" "orces against #ove#ent to o*tain a desired a#!li"ication in the

out!ut "orce. 'he #odel "or this is the law o" the lever. Machine co#!onents designed

to #anage "orces and #ove#ent in this wa+ are called #echanis#s. An ideal#echanis# trans#its !ower without adding to or su*tracting "ro# it. 'his #eans the

ideal #echanis# does not include a !ower source and is "rictionless and constructed

"ro# rigid *odies that do not de"lect or wear. 'he !er"or#ance o" a real s+ste# relativ

to this ideal is e!ressed in ter#s o" e""icienc+ "actors that ta8e into account "riction

de"or#ation and wear.

Mechanical Advantage o" a lever ; aG or M2GM1

-E/E0S IN .4)AN BODY:

• First ,+ass: &irst?class levers in the hu#an *od+ are rare. ne ea#!le is the

Hoint *etween the head and the "irst verte*ra. 'he weight resistance4 is the head

the ais is the Hoint and the #uscular action "orce4 co#e "ro# an+ o" the

!osterior #uscles attaching to the s8ull such as the tra!eius.


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• Sec"n' ,+ass: In the hu#an *od+ an ea#!le o

a second?class lever is "ound in the lower leg whenso#eone stands on ti!toes. 'he ais is "or#ed *+

the #etatarso!halangeal Hoints the resistance is the

weight o" the *od+ and the "orce is a!!lied to the

calcaneus *one heel4 *+ the gastrocne#ius and soleu

#uscles through the Achilles tendon.

$hir' ,+ass: 'here are nu#erous third?class levers the hu#an *od+ one ea#!le can *e illustrated in the el*ow Hoint. 'he Hoint is th

ais "ulcru#4. 'he resistance weight4 is the "orear# wrist and hand. 'he "orce

is the *ice!s #uscle when the el*ow is "leed.


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4SIN3 0OPE AS A -E/E0:

A ro!e can also *e used as a lever. It is shown in the "ollowing case:

Arrange a strong colu#n at a stee! angle a!!l+ a "ir# attach#ent "ro# a ro!e to the

colu#n and the o*Hect to *e li"ted and a!!l+ the "orce horiontall+ and get a great

#ulti!lier o" "orce.

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