Uniform Acceleration

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Uniform Acceleration Salvacion, Jozel John P.  Physics Department, De La Salle University, 2401 Taft Taft Avenue, Avenue, Manila [email protected]

 Abstract - A cart was used to slide down a ramp inclined at different angles. The angle of displacement is determined by the height of elevation of one end of the ramp while the other end was placed on a flat surface. We We then determined the starting point and end point of the track to serve as distance travelled (d) needed for the experiment. As the cart is released from the inclined part of the ramp the same person who releases the cart also uses a stopwatch to time how long it takes the cart to get from the starting point to the end point of  the track. This process is recorded and repeated !" times (to get a more specific average value) for a specific height of elevation and we used # different heights of elevation to get # different average values for acceleration. We got the value for acceleration by multiplying the distance travelled (d) by $ and then divided the product to the s%uare of the time (t) the cart travelled the whole distance of the track. &n short the e%uation we used is $d't$ to get the acceleration.  Keywords- Angle of isplacement *eight of +levation istance Time Acceleration

I. INTRODUCTION Acceleration is the rate of change of velocit of an !o" in a given #erio" of time. Accel Acceleration eration can ha##en "$e to the change of velocit or tthe he change of "irection of an !o". Uniform Acceleration is the constant rate of change of velocit of an o!%ect in a given #erio" of time. An e&am#le of this constant rate of change of velocit or $niform $ niform acceleration 'o$l"  !e the acceleration "$e to gravit (g) 'hich here on earth has a val$e of *.+ms-. If the o!%ect is e&#eriencing constant acceleration it onl means that the o!%ect has its velocit increasing"ecreasing at a constant val$e in a given time. The changing of the angle of "is#lacement is necessar in this e&#eriment !eca$se 'e are here to #rove that as the angle of "is#lacement is nearer to to the angle of */ or 0/ "egrees the nearer the val$e of acceleration to the constant acceleration of gravit (g) 'hich is e1$al to *.+ms-. The #$r#ose of the e&#eriment is to "etermine the val$e of constant acceleration of a falling o!%ect "$e to earth2s gravitational #$ll at a given angle of "is#lacement via a cart

sli"ing "o'n an incline" trac3 'ith "ifferent angles of "is#lacement. II. 45P4RI64NTA7 D4TAI7S 8e first #re#are" the materials nee"e" 'hich are the Dnamics Cart, Dnamics Trac3 'ith 4n" Sto#, 9ase an" S$##ort Ro" 'ith #ivot Clam# com#ati!le 'ith the Dnamics Trac3, R$ler, an" Sto#'atch. After the #re#aration, 'e elevate" one en" the trac3 'ith the $se of the Pivot Clam# an" 9ase an" S$##ort Ro" at a height of :;cm. 8e $se" a R$ler to "etermine the height of one en" of the trac3. 8hile one en" of the trac3 is incline", the other en" 'ill !e #lace" on a flat s$rface. s$ rface. Then 'e #lace" the sto##er of the trac3 near the en" that is #lace" on the flat s$rface. After  #lacing the sto##er, 'e #$t the cart on the incline" #art of the trac3 then $se" one en" of the cart to serve as !asis for the starting #oint. The starting #oint 'ill !e one en" of the cart an" this is "etermine" ! the n$merical val$e #lace" at the !esi"e the cart an" on si"e of the trac3. The si"es of a trac3 has n$merical val$es an" has a $nit in centimeters. The trac3 is :/cm or :.m long. 8ith the starting #oint esta!lishe", 'e #lace" the cart at the si"e of the trac3 'here there is the sto##er. 8e then $se" the same en" of the cart $se" to "etermine the starting #oint to "etermine the en" #oint. 8e "i" the same #rocess in "etermining the en" #oint as 'e $se" to "etermine the starting #oint. No' 'e have !oth starting an" en" #oints, to get the "istance (") the cart 'ill travel 'e have to s$!tract the starting #oint from the en"  #oint. The ne&t thing 'e "i" is the e&ec$tion of the e&#eriment 'hich is to #lace the cart at the starting #oint, release the cart, an" $se the sto#'atch to "etermine "etermine an" recor" the time the cart too3 to get from the starting #oint to the en" #oint of the trac3. 8e 8e re#eate" the same #rocess ten(:/) times an" got tthe he average time of these ten(:/) trials. After trial :/, 'e "ecrease" the height of the incline ! :cm then 'e $se" the same #rocess an" got the average. 8e "ecrease" the height of the incline $n $ntil til 'e 'ere on *cm mar3. The *cm mar3 'as the last height 'here 'e e&ec$te" the e&#eriment.

 

To get an i"ea of the e&#eriment set<$#, refer to =ig$re : !elo'.

the en" of the ta!le an" that val$e 'ill !e $se" in the e1$ation a?"t-. The "ifference of val$es in the trials is "$e to either h$man error, s#ecificall refle&es on #ressing the !$tton on the sto#'atch, or "$e to the $ncontrolle" varia!les (i.e. air, friction) in the #lace of e&ec$tion of the e&#eriment.  T  Table able 3 : Acce Acceleration leration of the ca cart rt and Sin Ɵ

*eight !,cm !cm !cm !$cm !!cm !"cm /cm

III. R4SU7TS AND DISCUSSION Ta!le : > Distance Travelle"

Starting Point 4n" Point Distance Travelle" (")

/cm ://c m +/cm

The #$r#ose of ta!le : is to esta!lish an" vis$all  #resent the "istance travelle" an" ho' 'e came $# to s$ch val$e. The "istance travelle" (") 'ill !e $se" in the e1$ation a?"t- later on to "etermine the acceleration of the cart at a s#ecific

Ta!le  > @eight of Incline an" Time Travelle"

!,cm :/+ ::/ :: :/; :: :/; :/ :/0 :/ ::: :/0

!cm :B :/ :: ::0 ::+ :: ::B :; ::/ :/ ::0

*eight of &ncline !cm !$cm !!cm :* :/ :B : :+ :0 :/ :B :B; :+ :BB :B; :: :* :0/ :/ :/ :BB ::0 :B/ :* :/ :; :;: :/ :B0 :B+ :+ :B/ :;/ :B :; :;/

!"cm :+* :+/ :;/ :;B :0 :;: :B :+/ :B :0 :

2in Ɵ /.:; /.::0 /.:/+ /.: /./* /./+ /./0;

Ta!le  sho's the val$e for acceleration of the cart $sing the form$la a?"t- 'here " is the val$e of "istance travelle" in ta!le : an" t is the average time in ta!le . 8e got the val$e for Sin Ɵ ! $sing the height height of the incline an" the length of the trac3 (:/cm) to !e re#resente" as the h#oten$se of the triangle forme" ! !  the trac3 an" the flat s$rface on 'hich the other en" of the trac3 is #lace". The e1$ation 'e $se" to "etermine the Sin Ɵ is @eight over :/). @#oten$se(:/). @#oten$se(

height of incline

Time Trial ! Trial $ Trial  Trial  Trial , Trial 0 Trial # Trial 1 Trial / Trial !" Average

Acceleration :.+0 ms- :.:+ ms- :./B; ms- /.++ ms- /.0:+ ms- /.;+ ms- /.B ms-

/cm :* :* :+/ :0* :+0 :+ :*; :+: : :0 :+

IE. CONC7USION After the e&#eriment, it 'as #roven that as the height of  the incline increases, the acceleration of the cart also increases along 'ith the angle of the trac3. The higher the angle of the trac3, the higher the val$e for the acceleration of the cart. R4=4R4NC4S F:G De 7a Salle Universit P7a!6an$al:HA::<: #ages 0<0/ FG Dnamics Trac3 Sstem information in Paasco in Paasco FOnlineG  FOnlineG availa!le at >

Ta!le Ta!le  sho's the time the cart travelle" from the starting #oint to the en" #oint. The average time is in"icate" at

http://www.pasco.com/physuniv/kinematics/dynamics-trackhttp://www.pasco.com/physuniv/ki nematics/dynamics-tracksystems/inde.cfm! "3# Theta symbol from Wikipedia "$nline# available at : http://en.wikipedia.or%/wiki/&'(&)*

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