Sagar Sood IB Physics Yr. 1 IB Lab Report Due: 5th Jan, 09
Introduction / Purpose
An object tends to be in motion when there is a change in its locati location on due to its moveme movement nt. This This change change occurs occurs because because of a force force applie applied d on it. Motion Motion is typica typically lly describe described d in terms terms of veloci velocity ty, accel accelera eratio tion n, dis displa placem cement ent, and time time. An object object's velocit velocity y (in other other word words s its its moti motion on) cann cannot ot chang change e unless unless it is acted acted upon upon by a forc force e, as desc descri ribe bed d by Newto Newton n's firs firstt law law. In this lab, the the type type of moti motion on that is deal dealtt with with is line linear ar motion motion. Line Linear ar motion motion is the the moti motion on of an obje object ct in a straight line. All objects objects possess possess energy energy. Energy Energy is the stored stored form of work work in an objec objectt. In this this case case, the the cart cart also also stores stores energ energy y in it when it is at rest rest in the form of potent potential ial energy energy. Pote Potenti ntial al energ energy y is the energy energy stored by an object by the virtue of its position at different heights . More More the height height, more more the potentia potentiall energy energy. The energ energy y posses possessed sed by an object object in moti motion on is know known n as kineti kinetic c ener energy gy. In this this case case, the the cart cart posses possesses ses kinetic kinetic energy energy while while moving moving down the plane plane. It is related related by the the velo veloci city ty of an obje object ct as well well as its its mass mass. If eithe eitherr one one of these these incre increase ases s, the kinetic kinetic energy energy also incre increase ases s. The relatio relationsh nship ip betwee between n kinetic energy and potential energy is that as the potential energy decre decrease ases s (the hori horizon zontal tal posit position ioning ing of an object object), the kinet kinetic ic ener energy gy increases. In this this invest investiga igatio tion n, the cart will will be placed placed at differe different nt angles angles of the incline inclined d plane plane. As the height height would incre increase ase the cart will be
dropped without any applied force on it and a photogate on the plane will measure the time taken for the 0.050m±0.001m side of the car. In this this lab lab, the the angle angle of the the incl inclin ined ed plane plane woul would d be incre increase ased d, henc hence e being being the indepe independe ndent nt/manipula manipulated ted variable variable. The veloc velocity ity of the cart will will depend depend on the height height, hence hence being being the dependan dependantt/respondi responding ng vari variab able le. A numb number er of fac facto tors rs li like the the app appli lied ed for force ce on on the the cart cart (0 N), mass mass of the cart, fric fricti tion on on the the incl inclin ined ed plane plane, dist distanc ance e of the ramp and distance at which the photogate will be placed will be kept constan constantt, hence hence being being the controll controlled ed variab variables les. These These contr controll olled ed vari variabl ables es, if chang changed ed, can can dire direct ctly ly affect affect the motio motion n of the cart cart, henc hence e changing the velocity. The main purpose of this experiment is to find the one factor that that affec affects ts the moti motion on of the cart cart on the the inclin inclined ed plane plane.
In this this lab lab,
the angle of the inclined plane will be the one factor that will be change changed d, hence hence affectin affecting g the motion motion of the cart.
Hypothesis As the angle angle of the incline inclined d plane plane will be incre increase ased d, the height height would would also also incre increase ase. This This would would incre increase ase the veloci velocity ty of the cart moving moving down down the plane plane. This This would would happen happen because because as the height height would would increase the potential energy of the cart would also increase . As the potenti potential al ener energy gy would would incre increase ase, the cart would have more energy stored in it which would be converted in the form of kinetic energ energy y. As kinetic kinetic energy energy is relat related ed by the mass and the veloci velocity ty of an object object, the time time taken taken for the cart’s cart’s motion motion would decreas decrease e, hence hence incr increasing easing the velocit velocity y of the cart (mass mass of the cart is kept kept constant constant).
Design
Materials Required
Photogate(±0.0001s)
Meter stick ( ±0.001m)
Cart
Inclined Plane(1m± m±0.01m)
Stand
Protractor Protractor(±1°)
Procedure 1.
When When all the material materials s are are acquir acquired ed, set up the apparatu apparatus s as the figure below. Measure
2.
the angle of
the inclined plane with the help of the protractor.
(In
our case, the first angle is
12°±1°) 3.
Measu Measurre the the leng length th of the side side of the car car.(in our our case case it was was
0.050±0.001m) 4.
Set the photogate at almost 2/3 rd the way down the ramp and note note the the poin pointt at whic which h it is set.(in our our case case, it was was set set at
0.50m±0.01m)
5. Put the car at the top of the inclined plane and set the photogate at zero. Without ut any applie applied d force force, rele release ase the cart and let it move move all the 6. Witho way down the ramp. 7.
Record the time in the timer of the photogate and set the photogate to zero again.
8.
Without changing the position of the photogate on the ramp, repeat the steps 4, 5 and 6 two more times in order to get 3 trials.
9.
After fter mea measu suri ring ng 3 tria trials ls for for the firs firstt data data point point move move on to the the next by changing the angle of the ramp( fix the ramp in the next possi possibl ble e hole hole of the the stand stand, in our case the next next data data poin pointt was was
17°±1°) 10. In total otal measur asure e dow down n 6 data data poi points nts wit with h 3 tria trialls eac each h.
Data collection
The The tab table le be below low show shows s the the tim time e tak taken en for for the the 0.05 cm side side of of the the car to pass through the photogate at different angles of the inclined plane.
Angle of the
Time elapsed( s)
Average time(s)
Uncertaint y
(±
ramp(°) s)
0.002 0.002
0.002 0.001 0.002 0.001 ± 1°
± 0.0001 Average
Velocity
time
(ms )
Uncertainty
-1
-1
(±ms )
±0.002
Instantaneous
Uncertainty
Velocity
(±ms )
-1
(s)
(ms )
0.0407
1.2
0.03
2.5
0.0332
1 .5
0.04
3.0
0.0285
1 .7
0.04
3.5
0.0243
2.0
0.05
4.1
0.0222
2. 3
0.05
4.5
0.0207
2 .4
0.06
4.8
With With help help of the aver average age time time, the the velo veloci city ty of the the cart cart is found found and shown below in the table.
Data processing
Average Time=
Sum of trials / Number of trials
=
(0.0405+0.0407+0.0408) (0.0405+0.0407+0.04 08) / 3
-1
=
0.0406666667
=
0.0407s
Unce Uncert rtai aint nty y of aver averag age e = (Lar Largest gest numb number er. – Smal Smalle lest st numb number er) / 2
= (0.0408 – 0.0405) / 2 = 0.00015 = ±0.0002 = 0.04 0.0407 07s ± 0.00 0.0002 02s As sh shown in in th the da data tab tablle, the un uncertain ainty iis s ta taken to be be 0.002 s. This is calculated my taking out the average of all the trials and data points.
(0.002 + 0.002 + 0.002 + 0.001 + 0.002 + 0.001) / 6 =
0.002s
Velocity = Dista stance / Time
= (Side of car) / (Time) = (0.050m) / (0.0407 s) = 1.2 ms
-1
Instantaneous Velocity Velocity = Distan ance ce of the the car car side side / Time ime ela elaps psed ed) / Dist Distan ance ce of the the pos posit itio ion n of of [(Dist the photogate photogate]
= (0.050m / 0.0407s) / (0.50 m) OR
= (0.050m / 0.0407s) X (Velocity X 2 = Inst. ve velocity )
= 2.457002487 -1
= 2.5 ms
Uncertainty = [(±0.001m) (±0.0002s)] / ( ±0.01)
=> [(±0.001m) (±0.0002 s)] = (Uncertainty #1) +
(Uncertainty #2)
(Value 1) =
(0.001)
X 100
(Value 2) +
(0.0002)
X 100
(0.050m)
(0.0407s)
= 2.49 % = 2.49 % of 1.23ms
-1
= 0.030601 -1
= ±0.03 ms …………………………………………. (Uncertainty for velocity ) -1
Uncertainty for Inst. Velocity = (± 0.03 ms ) /
(±0.01)
= X 100
(0.03)
+
(0.01)
-1
(1.23 ms ) =
4.44 %
=
4.44 % of 2.5ms
=
0.1109756098
=
±0.1
=
2.5 ms
-1
(0.50m)
-1
-1
± 0.1 ms
Uncertainties of other data points = 0.1+ 0.1 + 0.2 + 0.2 + 0.2 + 0.3
6 = 0.1833333 = ±0.2………………………. (Average uncertainty) Slope of the Graph = Rise / Run
= (36.5 – 12) / (4.8 – 2.5) = (24.5 / 2.3) = 10.7 ms
-2
(Value of acceleration due to
-2
gravity = 9.8 ms ) Percent Error = [{The Theoretica ticall Value – Calcu alcullated ated Value} / Theo heoretica ticall Value alue] x 100
= [(9.8 – 10.7) / 9.8] x 100 = 9.2 % Error
CONCLUSION
Overall the experiment was carried out with minimum errors . Ther There e were were six data data points points with three three trials trials each. The investig investigati ation on was carri carried ed out as stated stated in the procedu procedure re. The experi experimen mentt was relate related d to find one factor that affects the motion of a cart on an inclined plane . The factor used in my experiment was the increase in angle of the incl inclin ined ed plan plane e (or the the heigh heightt of the ram ramp p). The The data data and the the graph graph clearly show that as the angle/height of the ramp increases the veloci velocity ty of the cart cart incre increase ases s as well well. This This means means that they they are are direct directly ly proportional. In my experiment the angle of the ramp was increased which incre increase ased d the height height of the ramp ramp. As the height height incre increase ased d the potentia potentiall energy of the cart increased as the main factor in potential energy is the height height. This This energy energy was furthe furtherr transf transfor ormed med into kineti kinetic c energy energy or the the ener energy gy of moti motion on. In othe otherr word words s as the heig height ht increa increase sed d, the the potential energy increased which furthermore increased the kinetic energy energy. As kineti kinetic c energy energy is dire directl ctly y linke linked d to the velocit velocity y of an object object, it is safe safe to say say that that as the the kine kineti tic c ener energy gy incr increa ease sed d, the the velo veloci city ty of the cart cart incre increase ased d. This This prove proves s my hypoth hypothesi esis s corre correct ct.
Evaluation As it can be seen from the graph and the data table that there were were some some erro errors rs in the investig investigati ation on. The percent percent error error that was calc alculate ated to be 9.18 % ass ssu ures the fact act that there were flaws in my exper experim iment ent. One big erro errorr was that the whole whole ramp ramp setup setup was never never flat flat and and stra straig ight ht. Beca Because use of this this, the the car car was was at diff differ eren entt heig height hts s hence having different potential energy and furthermore changing the velo veloci city ty of the the cart cart. Also Also, it was almos almostt neve neverr that that the cart left left the the top top of the ramp ramp without without an applie applied d force force. This This change changed d the velocit velocity y of the cart cart hence hence alteri altering ng the the valu values es in the the data data table table. Also Also, durin during g the the
exper experim iment ent a couple couple of times times, the cart slammed slammed into into the photogat photogate e. This changed the position of the photogate by a centimeter or two. This hence gave different values of the time which later changed the values of the calculated instantaneous velocity.
Self-improvement The above errors can be improved by a number of precautions. Before starting the experiment the ramp should be completely flat and stra straig ight ht, a rule rulerr shoul should d be used to alig align n if necess necessar ary y. Even Even during during the the exper experim iment ent, it should should be made sure that the ramp ramp is aligne aligned d as after after each each tria triall the the high high sp spee eed d of the the cart cart chang changes es the the alig alignm nmen entt. Also Also it should be made sure that the cart leaves the top of the ramp without any applied applied force force. The hand should should be perfec perfectly tly still still befor before e leavin leaving g the cart cart so that that the cart does not experie experience nce exer exerted ted force force. The positio position n of the photogate should always be noted down and even if the cart slams into into the the phot photog ogat ate e, it sh shou ould ld be posi positi tion oned ed back back to the the same same poin pointt and and the trial should be re-done.
