Mechanics Lab Experiments

8/19/2019 Mechanics Lab Experiments

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Imam Mohammedbin Saud IslmicUniversity

Ph ys ics

Science

Collage

Physics 011MechanicsLab Manual

Prepared andDesigned by:

Hanan Akhdar (MSc)

2008


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For any questions:

[email protected]

Imam University

Science Collage

Physics e!artment

Prepared and

Designed by: Hanan Akhdar (MSc)


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Table of ContentsLa b

Physics011

Page 1

Section 1: "a# rules Page $

Section $: "a# re!ort Page %

Section %: &ra!hing Page '

Section ': (qui!ment use) in "a# Page *

Section +: (,!eriments Page 11 (,!eriment 1: -cceleration o linear uni orm motion Page 1$

(,!eriment $: Free all Page 1+

(,!eriment %: /e ton s secon) la Page 12

(,!eriment ': 3he incline) !lane Page $%

(,!eriment +: Friction o an incline) !lane Page $*

(,!eriment *: Hoo4 s la Page %0

(,!eriment 5: Conservation o mechanical energy Page %1 (,!eriment 2: (quili#rant orce Page %'

(,!eriment 6: 3orque Page %5

(,!eriment 10: Center o mass Page '1

Section *: -!!en)i, Page '5


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Lab RulesSe c t ion 1

Physics011

Page 2

78ou must atten) the la# section.7/o one is a)mitte) to the la# once the la# #egins.

7(ach stu)ent must have her o n la# note#oo4.7/o oo). /o )rin4s.73he la# must #e clean at all time.7-s4 your teacher to chec4 your equi!ments #e orestarting your e,!eriment.7-t the en) o each la# arrange all equi!ment ti)ily on

the #ench.73he la#oratory manuals are /93 meant to #e stan)7alone )ocuments stu)ents are e,!ecte) to use a te,t

#oo4 or su!!lementary rea)ing.7"a# re!orts must #e su#mitte) in a ee4 s time.7"a# re!orts riting must #e an in)ivi)ual e ortalthough the e,!eriments ill #e !er orme) in grou!s.73he gra)ing o the la# ill #e as ollo s: + gra)es orthe la# re!orts; + gra)es or the inal theoretical e,aman) 10 gra)es or the inal e,!erimental e,am.7- misse) la# ill receive a


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Lab ReportSe c t ion

Physics011

Page 3

3he la# re!ort shoul) contain:

3itle: 3his shoul) #egin each re!ort. 3he stu)ent=s nameollo e) #y the )ate on hich the e,!eriment as !er orme)

an) the )ate the re!ort is su#mitte) an) the name oe,!eriment.

3heory: - #rie intro)uction inclu)ing im!ortant ormulasan) units.

9#>ective: 3he main o#>ectives o the e,!eriment.Proce)ure: 3his #rie ly an) clearly )escri#es #oth the

e,!erimental a!!aratus an) ho it as use).

ata -nalyses: 3his is the heart o the re!ort. Here you)escri#e ho )erive) quantities ere calculate) rom the ra

)ata. 8ou shoul) e,!lain care ully an) concisely the ste!sinvolve) in mani!ulating the )ata. 8ou shoul) inclu)ea!!ro!riate analysis o any uncertainties. Inclu)e any ta#lesan) igures that are necessary to e,!lain your e,!eriment.

Conclusion: 3his is here you summari


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- gra!h is the clearest ay to re!resent the relationshi! #et een the quantities o interest.

- gra!h in)icates a relation #et een t o quantities; x an) y; hen other varia#les or !arameters have i,e) values.?e ore !lotting !oints on a gra!h; it may #e use ul toarrange the corres!on)ing values o x an) y in a ta#le .It is very im!ortant to use gra!h !a!er.Choose a convenient scale or each a,is so that the !lotte)

!oints ill occu!y a su#stantial !art o the gra!h !a!er; #ut )o not choose a scale hich is )i icult to !lot an)rea)."a#el each a,is to i)enti y the varia#le #eing !lotte) an)the units #eing use).I)enti y !lotte) !oints ith a!!ro!riate sym#ols.9 ten there ill #e a theory concerning the relationshi! othe t o !lotte) varia#les. - linear relationshi! can #e)emonstrate) i the )ata !oints all along a single straightline. 3he straight line shoul) #e )ra n as near the mean othe all various !oints as is o!timal. 3he line shoul) #e)ra n ith a#out as many !oints a#ove it as #elo it; an)

ith the =a#oves= an) =#elo s= )istri#ute) at ran)om alongthe line.

!raphin"Se c t ion #

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!raphin"Se c t ion #

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- Slo!e is o ten use) to )escri#e the measurement o thestee!ness; incline; gra)ient; or gra)e o a straight line.

3he slo!e o a line in the !lane containing the x an) y a,es isgenerally re!resente) #y the letter m; an) is )e ine) as thechange in the y coor)inate )ivi)e) #y the corres!on)ingchange in the x coor)inate; #et een t o )istinct !oints on theline. 3his is )escri#e) #y the ollo ing equation:

x

ym

∆

∆=


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Lab $%uipmentSe c t ion &

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(lectronic Sto! Cloc4

Use) to measure short time intervals

3iming starts an) sto!s manually or )ynamically

Hol)ing (lectromagnet(lectromagnet ith tem!orally7)e ine) triggering o motions


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3rac4Contains t o running rails on its to! sur ace an) it is

equi!!e) ith a recesse) measuring scale on one si)e an)groove) rails on each si)e or attaching accessories

PulleyUse) to hang eights using threa)s


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3rolley3he heels are )esigne) so as to ma4e the trolley sel 7

centering an)a string hol)er is !rovi)e) at #oth en)s o the trolley

ass HangerUse) to slot eights


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Slotte) eights

Use) ith the eigh hanger

"ight ?arrier Use) as a sensor


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Helical S!ringAith scale on trans!arent tu#e or goo) visi#ility o the s!ring

#alance construction


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Theory:(quations o motion are use) to stu)y the linear motion o auni ormly accelerate) #o)y.

here:

From the equation o motion:) B v 0t D1E$ at$

I the o#>ect starts at rest; e get:) B D1E$ a t$ (quation 1.1

'cceleration ofLinear Uniform

Motion

$ ( p e rim e n t ) 1

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$a)vv

atvv

at$1

tv)

$0

$

0

$0

=−

+=

+=): is!lacement or change in !osition

vo:9riginal velocity; the velocity at the start othe acceleration

v :Final velocity; the velocity at the en) o theacceleration.

a: -cceleration; this is a constant accelerationt: 3ime; this is the time !erio) o theacceleration.


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Motion

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Objective:3o calculate the acceleration o an o#>ect moving in a

straight line ith a constant acceleration using equations omotion.

Equipment:3rac4 G trolley G hol)ing magnet G electronic sto! cloc4 Glight #arrier G !ulley G mass hanger G slotte) eights Gca#les.


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Motion

$ ( p e rim e n t ) 1

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Procedure:Set the equi!ment; use the ca#le to connect the trolley ith

the !ulley an) the hanging mass.Connect the hol)ing magnet to the sto! cloc4 an) a)>ust thevoltage so that the trolley is hel).

Put the light #arrier at a certain )istance.elease the trolley #y sto!!ing the magnet an) recor) the

time the trolley too4 to !ass the light #arrier.e!eat an) recor) the time three times then calculate the

average time.Change the )istance an) re!eat the !revious ste!s or each

)istance.3a#ulate your )ata.

Plot a gra!h #et een the square time D,7a,is an) the

)istance Dy7a,is or )is!lacement travele) #y the trolley.ra the #est line an) in) its slo!e.

Calculate the acceleration rom the slo!e using equation1.1.

istancem

3ime 1s

3ime $s

3ime %s

-verage3ime

s

3ime squares$


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Theory:Un)er ree all all o#>ects have the same constantacceleration; hich in the metric system is 6.2 mEs $ at sea

level; )irecte) to ar)s the center o the earth.

(quations that )escri#e ree all ithout air resistance are:

here

*ree *all$ ( p e rime n

t )

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y: Jertical )is!lacement

vo:9riginal velocity; the velocity atthe start o the acceleration

v :Final velocity; the velocity at the

en) o the acceleration.g: -cceleration )ue to gravity

t: 3ime; this is the time !erio) o theacceleration.

Iy$gvv

gtvv

gt$1

tvIy

$0

$

0

$0

=−

+=

+=


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t )

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From the equation o motion:

I the o#>ect starts at rest; e get:y B D1E$ g t$ (quation $.1

Objective:3o calculate the gravitational acceleration o a ree alling

#all.

Equipment:Steel #all G contact !late G hol)ing magnet G hol)ing magneta)a!ter ith a release mechanism G electronic sto! cloc4 Gstan) #ase G ro)s G scale G connecting lea)s.

$0 gt$

1tvIy +=


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t )

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Procedure:Set the equi!ment an) hol) the steel #all using the hol)ing

magnet at a certain height.elease the #all an) rea) the time the #all too4 traveling thevertical )istance; then reset the sto! cloc4 an) reattach the

#all an) rea) the time again ; you shoul) ta4e three rea)ingso the time then in) the average time the #all has travele).

e)uce the height an) re!eat the !revious ste!s.3a#ulate your )ata.

Plot a gra!h #et een the square time D,7a,is an) the heightDy7a,is or )is!lacement o #all.

ra the #est line an) in) its slo!e.Calculate the gravitational acceleration rom the slo!e using

equation $.1.Fin) the !ercentage error.

Heightm

3ime 1s

3ime $s

3ime %s

-verage3ime

s

3ime squares$


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Theory: /e ton=s la s o motion are three !hysical la s hich !rovi)e relationshi!s #et een the orces acting on a #o)y an)

the motion o the #o)y; irst com!ile) #y Sir Isaac /e ton.

/e ton=s First "a : an o#>ect ith no orce acting on itmoves ith a constant velocity.

/e ton=s Secon) "a : the acceleration o a #o)y is )irectly !ro!ortional to the net orce acting on it an) inversely

!ro!ortional to its mass.KF B ma (quation %.1 /e ton=s 3hir) "a : or every action there is an equal an)o!!osite reaction.

In or)er to a!!ly /e ton s secon) la a ree #o)y )iagramshoul) #e )ra n or every o#>ect in the system.

+e,ton-s SecondLa,

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I t o masses connecte) #y a string over a !ulley. 9ne mass;; is a trolley resting on a horiect to

a )o n ar) orce )ue to gravity Dits eight A B mg; an) anu! ar) orce )ue to the tension 3 in the string. 3he masses othe string an) !ulley as ell as the rictional resistance o the

!ulley are assume) to #e negligi#le.

Cart at Rest: Ahen the cart is hel) stationary; there is no netorce on the hanging mass; so the tension in the string is given

#y: 3 B A.

Cart accelerating: Since the length o the string )oes notchange; the cart an) the hanger accelerate at the same rate; a.

+e,ton-s SecondLa,

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From the ree #o)y )iagram o the hanging mass; e get:

3 G A B 7 ma

or A 7 3 B ma

or 3 B mg 7 ma (quation %.$

here m is the hanging mass.

+e,ton-s SecondLa,

$ ( p e rim e n t ) #

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From the ree #o)y )iagram o the cart , e get:

3 7 4 B a

here is the mass o the cart an) 4 is the rictional orce #et een the cart an) the trac4 an) 4 B L4 D / ; here L 4 is the4inetic riction coe icient an) / is the normal orce )one #ythe trac4 on the cart. In this case / B A B g; Ahich givesthat:

3 G A B aor

3 7 L4 D g B aor

3 B a L 4 D g (quation %.%

From equations %.$ an) %.% e get:

a L 4 D g B mg G ma L4 B Dmg G ma G a E g (quation %.'

+e,ton-s SecondLa,

$ ( p e rim e n t ) #

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+e,ton-s SecondLa,

$ ( p e rim e n t ) #

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Objective:3o in) the 4inetic riction coe icient o a trolley moving

on a trac4 using /e ton s secon) la .

Equipment:3rac4 G trolley G hol)ing magnet G electronic sto! cloc4 Glight #arrier G !ulley G mass hanger G slotte) eights Gca#les.


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+e,ton-s SecondLa,

$ ( p e rim e n t ) #

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Procedure:Set the equi!ment; use the ca#le to connect the trolley ith

the !ulley an) the hanging mass; the hanging mass shoul) #e4e!t constant through out the e,!eriment.

Connect the hol)ing magnet to the sto! cloc4 an) a)>ust thevoltage so that the trolley is hel).

Put the light #arrier at a certain )istance; the )istance shoul) #e 4e!t constant through out the e,!eriment.

elease the trolley #y sto!!ing the magnet an) recor) thetime the trolley too4 to !ass the light #arrier.

e!eat an) recor) the time three times then calculate theaverage time; the acceleration an) the 4inetic rictioncoe icient rom equation %.'.

Increase the eight o the trolley #y a))ing #loc4s on to! oit.

e!eat the !revious ste!s or each mass.

3a#ulate your )ata

&ive your conclusion.

ass D4g

3ime 1s

3ime $s

3ime %s

-verage 3imes

3ime squares$

a B $)Et$

mEs$L4


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Theory:

Ahen an o#>ect sli)es )o n an incline; the com!onent ogravity !ushing the #loc4 )o n the incline !lane is:

A, B mg sinDM (quation '.1

The Inclined Plane$ ( p e rime n

t ) &

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t ) &

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Objective:?alancing a rolling mass on an incline) !lane.

Equipment:agnet #oar) G Incline) !lane G Pulley G asses G S!ring

#alance G olling mass G ass hanger G String.


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Procedure:Aeigh the rolling mass using the #alance s!ring an)

calculate its eight.Set the incline on the magnet #oar) at a certain angle an)

recor) it.-ttach the rolling mass ith a string an) tie the string to the

#alance s!ring an) su!!ort the string ith a !ulley.For accurate results; the string shoul) #e !arallel to the

!lane.3he 3ension o the string is equal to the com!onent o

gravity !ushing the mass )o n the incline A , .3he tension also coul) #e measure) using the #alance

s!ring.Fin) the !ercentage error #et een the t o values o the

orce.

Change the angle o the incline an) re!eat the !reviousste!s.

3a#ulate your )ata.


t ) &

Physics011

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egree F, D easure) A , Dcalculate) Percentage (rror

%0N

'0N

+0N*0N


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3heory:Ahen an o#>ect is !lace) on an incline; /e ton s secon) lacoul) #e a!!lie) as ollo s:

Com!onent o gravity !ushing the #loc4 )o n the incline !lane: A, B mg sinDM . Com!onent o gravity !ushing the #loc4 against the incline !lane: Ay B mg cosD θ

*riction of anInclined Plane

$ ( p e rim e n t ) .

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Using /e ton s secon) la :

KF B ma

9n the y7a,is: / G A y B 0

/ B A y B m g cosDM (quation +.1

9n the ,7a,is:

4 G A , B 7 ma

L4 D / G A, B 7 ma

L4 D / B A , G ma

?y su#stituting rom equation +.1:

L4 Dm g cosM B mg sinM G ma

L4 B Dmg sinM G ma E Dm g cosM (quation +.$

From the equation o motion:) B v 0t D1E$ at$

I the o#>ect starts at rest; e get:) B D1E$ a t$ (quation +.%


$ ( p e rim e n t ) .

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Objective:3o in) the 4inetic riction coe icient o an incline) !lane.

Equipment:agnet #oar) G !lane ith !rotractor G #loc4s G sto! cloc4.


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$ ( p e rim e n t ) .

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Procedure:-ttach the incline) !lane to the magnet #oar) ith a certain

angle; recor) the angle.Put a #loc4 on the !lane an) start the sto! cloc4 at the time

you release the #loc4.Sto! the sto! cloc4 at the time the #loc4 reaches the en) o

the !lane an) recor) the time it too4 the #loc4 to travel the !lane.

e!eat three times an in) the average time o the #loc4sli)ing the !lane.

Use equation +.% to calculate the acceleration o the #loc4.Use the result in equation +.$ to in) the 4inetic riction

coe icient o the !lane s sur ace ith the #loc4.e!eat the !revious ste!s ith t o )i erent angles.

Com!are all results an) give your conclusion.

3ime 1s

3ime $s

3ime %s

-verage3ime

s

3ime squares$

a B $)Et$

mEs$L4


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Theory:

- material has a rest sha!e an) its sha!e )e!arts a ay romthe rest sha!e )ue to stress. 3he amount o )e!arture rom restsha!e is calle) )e ormation; the !ro!ortion o )e ormation tooriginal si


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/oo -s la,$(pansion of a

/elical Sprin"

$ ( p e rim e n t ) 2

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Objective:3o )etermine a s!ring constant using Hoo4 s la .

Equipment:Helical s!ring G magnetic #oar) G mass hanger G slotte)

eights


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/oo -s la,$(pansion of a

/elical Sprin"

$ ( p e rim e n t ) 2

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Procedure:-ttach the s!ring to the magnetic #oar).

3he s!ring is !lace) in a scale) trans!arent tu#e hichallo s rea)ing the e,!ansion or the orce a!!lie) on thes!ring )irectly.

Hang the mass hanger at the en) o the s!ring an) note itsmass.

Start a))ing slotte) masses on the hanger one a ter another.For each mass rea) the e,!ansion an) the orce.3a#ulate your )ata.

Plot a gra!h #et een the orce D,7a,is an) the e,!ansionDy7a,is o the s!ring.

ra the #est line an) in) its slo!e.Calculate the s!ring s constant rom the slo!e using

equation *.1.

ass4g

Aeight /

(,!ansionm


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Theory:(nergy is the a#ility to )o or4 an) is measure) #y Rouls.

echanical energy has t o )i erent orms:

Potential energy is the energy an o#>ect stores )ue to its !osition.3he gravitational !otential energy is given #y:

P( B m g h (quation 5.1Ahere m is the mass o the o#>ect; g is the gravitational

acceleration an) h is the height o the o#>ect.

Kinetic energy is the energy o motion.3he 4inetic energy is given #y:

Q( B D1E$ m v$ (quation 5.$

3he total mechanical energy (; o any isolate) system oo#>ects; is )e ine) as the sum o the 4inetic an) !otentialenergies:

( B P( Q( (quation 5.%

3he !rinci!le o conservation o energy coul) #e ritten as:( i B ( (quation 5.'

Ahere ( i is the initial energy an) ( is the inal energy

Conservation ofMechanical $ner"y

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-n o#>ect on an incline ill move )o n ith constantacceleration. (nergy conservation la : ( i B (

Q( i P( i B Q( P( (quation 5.+

D1E$ m vi$ m g h i B D1E$ m v $ m g h I the o#>ect starts rom rest; e get:

m g h i B D1E$ m v $ m g h (quation 5.*D1E$ m v $ B m g h i G m g h

D1E$ v $ B g h i G g h

(quation 5.5From the equations o motion:

) B D1E$ Dvi v t (quation 5.2I the o#>ect starts at rest; e get:

v B $) E t (quation 5.6Ahich means that the inal velocity coul) #e oun) either #ythe energy conservation la D(qn 5.5 or #y equation omotion D(qn 5.6 .


$ ( p e rim e n t ) 3

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h$gDhv i −=


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$ ( p e rim e n t ) 3

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Objective:3o in) the inal velocity o an o#>ect sli)ing an incline ith

constant acceleration using energy conservation la .

Equipment:3rac4 G trolley G hol)ing magnet G electronic sto! cloc4 Glight #arrier G ca#les.


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$ ( p e rim e n t ) 3

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Procedure:Set the trac4 so that it ill #ecome an incline #y rising one

si)e o it; use the hol)ing magnet to hol) the trolley still.Connect the sto! cloc4 ith a light #arrier an) !ut the light

#arrier at a certain )istance an) recor) the )istance that thetrolley shoul) travel.

easure the height at the #eginning an) at the en) o themotion o the trolley.

elease the trolley an) in) the time it nee)s to travel the)istance three times an) in) the average time o traveling.

Use the equation 5.5 an) 5.6 to in) the inal velocity. 3het o values shoul) #e equal.

Fin) the !ercentage error.Calculate the initial an) inal P( an) Q(.

e!eat the !revious ste!s #y changing the height; the mass

an) the )istance an) conclu)e their e ect on energy.


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Theory:-n o#>ect is sai) to #e in equili#rium i the the resultant orceacting on the o#>ect is ect then that o#>ect can #e #rought into equili#rium #y a!!lying an a))itional orce thate,actly #alances this resultant. Such a orce is calle) theequili#rant an) is equal in magnitu)e #ut o!!osite in )irectionto the original resultant orce acting on the o#>ect.

$%uilibrant *orce$ ( p e rime n

t ) 4

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t ) 4

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Objective:3o in) the resultant orce o t o orces; then in) the

equili#rant orce.

Equipment:agnet #oar) G )egree scale G !ulleys G masses G mass

hangers G s!ring #alance G orce ring G string.


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t ) 4

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Procedure:Use the magnet #oar) to attach the )egree scale.3ie three strings to the orce ring an) attach t o strings ith

t o mass hol)ers ith )i erent slotte) masses.Set the hangers as !ulling orces #y using !ulleys an) ma4e

the orces act in )i erent angles ith res!ect to the ust the s!ring #alance until the orce ring is in

equili#rium.

ra the t o orces F 1 an) F $ an) in) gra!hically their

resultant.3he resultant orce you oun) shoul) #e equal to the orce

a!!lie) #y the s!ring Dmagnitu)e an) )irection ; chec4 yourresults.


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Theory:Ahen a orce F acts on a !oint hich is )is!lace) rom thea,is o rotation a )istance ); the torque #y this orce is

B F) sinM (quation 6.1

here the M is the angle #et een F an) ).

Ahen torque acts on an o#>ect; it rotates. 3here ore; the nettorque must #e


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Tor%ue$ ( p e rime n

t ) 5

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Objective:?alancing an o#>ect ith )i erent torques.

Equipment:agnet #oar) G #alance #eam G !ulleys G masses G mass

hangers G s!ring #alance G string.


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Procedure:Use the magnet #oar) to attach the #alance #eam.Hang t o mass hol)ers ith )i erent slotte) masses.Change the )istance until the #eam is #alance).Calculate the torques an) chec4 your ans er.


t ) 5

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/o remove one o the mass hol)ers an) use the )egreescale an) the s!ring #alance to a!!ly another orces on the

#eam ith an angle o %0 o.-)>ust the s!ring in or)er to #alance the #eam.

ecor) the irst orce a!!lie) #y the hanging mass.3hen ta#ulate your )ata to in) the orce a!!lie) #y the

s!ring an) in) the !ercentage error.Change the angle an) re!eat the !revious ste!s.


t ) 5

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egree F1 BF1) 1sinM (rror: D 17 $ E$ ,100

%0N

'0N+0N

*0N


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Theory:

3he center o mass is an im!ortant conce!t in !hysics. 3hecenter o mass is the !oint at hich an o#>ect can #e #alance).Sometimes in)ing the center o mass o an o#>ect can #echallenging; es!ecially i the o#>ect has an o)) sha!e. 3hise,!eriment illustrates a sim!le ay to in) the center o masso some interesting sha!es.

Center of Mass$ ( p e rime n

t ) 1 0

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t ) 1 0

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Objective:Fin)ing the center o mass o a !lane.

Equipment:agnet #oar) G Planar mass G masses G mass hangers Gegree !late G string.


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Procedure:Hang the !lanar mass rom the hol)ing !in o the )egree

!late.Since the orce o the !in acting on the mass is equili#rant

to the sum o the gravitational orces acting on the mass; theline o the orce e,erte) #y the !in must !ass through thecenter o mass o the !lanar mass.

Hang a !iece o string ith a hanging mass rom thehol)ing !in.

3a!e a !iece o !a!er to the Planar ass as sho n.ar4 the !a!er to in)icate the line o the string across the

Planar ass. /o hang the !lanar mass rom a )i erent !oint. -gain;

mar4 the line o the string.?y in)ing the intersection o the t o lines; locate the

center o mass o the !lanar mass.Hang the Planar ass rom a thir) !oint. oes the line o

the string !ass through the center o massT


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6asic SI Units andPre7(

' p p e n d i('

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ulti!le Pre i, Sym#ol10 1$ 3era 3

10 6 &iga &

16 * ega

10% Qilo Q

10$

Hector H10 eca a

10 71 eci )

10 7$ Centi c

10 7% illi m

107*

icro L10 76 /ano n

10 71$ Pico !

SI Pre i,

Unit /ame Unit Sym#ol uantity

eter m "ength

Qilogram 4 ass

Secon) s 3imeRoule R (nergy

Aatt A Po er

SI Units ?asic


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*ractions' p p e n di(

6

Physics011

- raction is e,!resse) as ; here a is calle) the numeratoran) # the )enominator.

3he a))ition or su#traction o ractions:

3he !ro)uct o ractions:

ba

dbcbad

d c

ba +

=+

dbcbad

d c

ba −

=−

db

ac

d

c

xb

a=


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8ectors' p p e n di(

C

Physics011

Scalars: are quantities hich are ully )escri#e) #y amagnitu)e alone.

Jectors: are quantities hich are ully )escri#e) #y #oth amagnitu)e an) a )irection.- vector in the ,7y !lane has t o com!onents; - , an) - y.

3he sum o t o vectors; an) ; is a vector ; hich iso#taine) #y !lacing the initial !oint o on the inal !oint o

; an) then )ra ing a line rom the initial !oint o tothe inal !oint o .3hen

-

- ? C?

- -?

y y y

x x x

C B A

C B A

=+

=+

=+ C?-


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8ectors' p p e n di(

C

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3he su#traction o t o vectors; an) ; is a vector ; 3hen- ? C

y y y

x x x

C B A

C B A=−

=−

=− C?-


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*ree 6ody 9ia"ram' p p e n di(

9

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Free #o)y )iagrams are sim!li ie) re!resentations in a !ro#lem o an o#>ect; an) the orce vectors acting on it. 3his

#o)y is ree #ecause the )iagram ill sho it ithout itssurroun)ings.some o the main orces:

&ravity: 3he irst is that )ue to gravity; hich is calle) thegravitational orce. 3he acceleration )ue to gravity o (arth isa!!ro,imately g B 6.2 mEs $. 3he orce; #y /e ton=s Secon)"a is:

F g B m g /ormal: 3he normal orce is one hich !revents o#>ectsrom alling into hatever it is they are sitting u!on. It is

al ays !er!en)icular to the sur ace ith hich an o#>ect is incontact.

Friction: elate) to the normal orce is the rictional orce.3he t o are relate) #ecause they are #oth )ue to the act thatthe #o)y is in contact ith the sur ace. Friction is )ivi)e) intot o ty!es7static an) 4inetic.Push an) Pull: -nother orce hich may act on an o#>ectcoul) #e any !hysical !ush or !ull.

3ension: 3ension in an o#>ect results i the !ulling orce acts

on its en)s; such as in a ro!e use) to !ull an o#>ect.


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Mechanics Lab Experiments

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Transcript of Mechanics Lab Experiments