pendullum (bandul)

PENDULUM

Helny Lydarisbo*), Andi Lisra Andriani Hasrat, Nurul Angelita, Sitrah Nurdini Irwan

Basic Physic Laboratory, Chemistry Education ICP FMIPA UNM 2015

Abstract. Has done practicum with a title “Pendulum”, with the purpose of the practicum namely, students can understand the factors that influence at all a period of mathematical pendulum swing, determine the acceleration of gravity with the methods swing simple, and can determine the value of the period of mathematical pendulum swing, in practicum this we would determine the acceleration graviatasi through a method of swing simple, with the equation T=2

π√ lg

for pendulum mathematical, of that equation we will get value a period and determine large

the acceleration of gravity. As for tools and material used in this practicum is the balance ohaus 311 grams, plastic bar 30 cm, hanger stative, pendulum mathematical, thread, a protractor, and a stopwatch. In this practicum any 3 activities in the pendulum mathematical namely determine byway relations with a period swing, mass pendulum relations with a period swing, and and relations the length of the rope with a period swing.

Keywords: Acceleration of gravity, pendulum mathematical, period.

FORMULATION OF THE PROBLEM1. What factors that influence at all on the period swing pendulum mathematical ?2. How to determine the acceleration of gravity with the methods swing simple ?3. How to determine the value of a period of mathematical pendulum swing ?

PURPOSE1. Students can understand the factors that influence at all a period of mathematical

pendulum swing.2. Determine the acceleration of gravity with the methods swing simple.3. Students can determine the value of the period of mathematical pendulum swing.

BRIEF THEORI

Pendulum is a thing with attached to a rope and can swing freely and the period of on which to base working from a clock the walls of ancient who have swing. Motion pendulum is motion harmonic simple consisting of a cord with long l and load mass of m. Forces acting on burden is weighs mg and voltage T on a rope. Motion harmonic simple is periodic motion with a traveled always the same are. Motion harmonic simple have equation motion in the form of sinusoidally and used to analyze a certain periodic motion. Periodic motion is motion recurring or oscillates through a point balance in the interval time fixed. [1]

Pendulum Mathematical

l

sinmg

x

cosmgmg

Picture 9.1: Pendulum Mathematical

An object whose mass is considered as a pertikel located in centre the mass, fastened and was hanged with a rope bending in a fixed point. If objects will be given a byway early that a rope forming an angle was small enough to the direction vertical and then objects released, so objects will swinging around point balance on a flat plane vertical with the frequency of the fixed.System that is called pendulum simple or pendulum mathematical.

In mathematical pendulum, mg sin θ referred to as the restoring force. Based on the law of newton to motion rotation, can be rendered;

∑ τ=Iα

-(mg sinθ)l=Id2 θdt2

d2 θdt2 +

mgl sin θI

= 0

Because I is its moment of inertia pendulum, with I = ml2, so that it will obtained:

d2 θdt2 +

mgl sin θml

= 0

where θ<< then sin θ≅ θ so that,

d2 θdt2 +

g l

θ= 0

Of the equation 9.1, obtained that ω2=g/l, so period pendulum simple that is :

T = 2π √lg

With T = oscillation period (s)

l = the length of the rope (m)

g = the acceleration of gravity of the earth (m/s2) [2]

A pendulum simple or a the variety of it, is also the right tools and convincing for the measurement of the acceleration of gravity g , because l and T can be measured easily and right. [3]

EXPERIMENT METHODS

Tools and materials

Tools1. Ohaus Balance 311 grams2. Plastic Bar3. A set hanger stative4. Stopwatch 5. Protractor

Materials1. Thread2. Pendulum mathematical

Identification of variable

1st activity (Byway relations with the period) Control Variable

The length of the rope (cm), mass pendulum (gr), the number of swing Manipulation Variable

Deviation (o/cm) Respon Varible

Period swing

2ndactivity (Mass pendulum relations with a period swing)

Control VariableThe length of the rope (cm), deviation (o/cm), number of swing

Manipulation VariableMass pendulum (gr)

Respon VariblePeriod swing

3rdactivity (Time and Temperature Measurement)

Control VariableMass pendulum (gr), deviation (o/cm), number of swing

Manipulation VariableThe length of the rope (cm)

Respon VariblePeriod swing

Operational Definition of Variables

1st activity

Control VariableThe length of the rope is a long thread used to hang pendulum mathematical in statif , measured from the point hang ( a shaft swing) until in a fastener burden use plastic bar of 30 cm with a unit of cm. Mass pendulum ( gr ) namely burden who was hanged on a rope formerly burden weighed beforehand much value is illegible on the scales that is a mass of the burden. The number of swing is the quantity of motion commuting between done by pendulum caused by a byway given then pendulum released.

Manipulation VariableDeviation is the large the angle formed by pendulum mathematical when pendulum in pull laterally and at the base of the rope forming angles it is deviation measured using protractor with a unit of degrees (o).

Respon VariableThe period swing is great the time it takes pendulum to do 10 times swing measured use a stopwatch.

2ndactivity

Control Variable The length of the rope is a long thread used to hang pendulum mathematical in statif , measured from the point hang ( a shaft swing) until in a fastener burden use plastic bar of 30 cm with a unit of cm. Deviation is the large the angle formed by pendulum mathematical when pendulum in pull laterally and at the base of the rope forming angles it is deviation measured using protractor with a unit of degrees (o). The number of swing is the quantity of motion commuting between done by pendulum caused by a byway given then pendulum released.

Manipulation Variable Mass pendulum ( gr ) namely burden who was hanged on a rope formerly burden weighed beforehand much value is illegible on the scales that is a mass of the burden.


3rdactivity

Control VariableMass pendulum ( gr ) namely burden who was hanged on a rope formerly burden weighed beforehand much value is illegible on the scales that is a mass of the burden. Deviation is the large the angle formed by pendulum mathematical when pendulum in pull laterally and at the base of the rope forming angles it is deviation measured using protractor with a unit of degrees (o). The number of swing is the quantity of motion commuting between done by pendulum caused by a byway given then pendulum released.

Manipulation Variable

The length of the rope is a long thread used to hang pendulum mathematical in statif, measured from the point hang ( a shaft swing) until in a fastener burden use plastic bar of 30 cm with a unit of cm.


Work Procedure

1st activity : Pendulum mathematical

Prepared tools and the materials to be used. Then mass pendulum weighed (the load to be suspended in statif), after that pendulum supported by a rope in statif. And then, the length of the rope hanger measured and the results noted in table observation. Next give a byway in pendulum of ± 5 degree (or said deviation in a small (<14o)) then pendulum released. Measuring the time it takes pendulum to swing 10 times by swing and repeating step last as many as 5 times with a byway different and the results noted in table observation. Next to the steps was same by changing mass pendulum as many as 5 times (long rope and byway constant) and the results noted in table observation. Then to the steps was the same again by changing the length of the rope as many as 5 times (mass pendulum and a byway constant) and then the result of the observation noted in table.

EXPERIMENTAL RESULTS AND DATA ANALYSIS

Experimental Result


1st activity : Byway relations with the period

The length of the rope = |50 ± 0,05| cm

Mass pendulum = |98,940 ± 0,05| gram

The number of swing = 10 kali

Table 1. The influence of a byway against the period swing

Deviation (o/cm) Time (s)

|5 ± 0,5| |14,6 ± 1|

|7 ± 0,5| |14,8 ± 1|

|9 ± 0,5| |15,0 ± 1|

|11 ± 0,5| |15,2 ± 1|

|13 ± 0,5| |15,4 ± 1|

2ndactivity : Mass pendulum relations with a period swing

The length of the rope = |50 ± 0,05| cm

Deviation = |5 ± 0,5| (o/cm)


Table 2. The relations between mass pendulum with a period swing

Mass Pendulum (gram) Time (s)

|0,003 ± 0,005| |14,6 ± 1|

|20,003 ± 0,005| |14,8 ± 1|

|50,075 ± 0,005| |15,0 ± 1|

|98,940 ± 0,005| |15,2 ± 1|

|100,004 ± 0,005| |15,4 ± 1|

3rdactivity : The length of the rope relations with a period swing

Mass pendulum = |98,940 ± 0,005| gram

Deviation = |5 ± 0,5| (o/cm)


Table 3. Influence the length of the rope against the period swing

The length of the rope (cm)

Time (s)

|50 ± 0,05| |15,2 ± 1|

|45 ± 0,05| |14,4 ± 1|

|40 ± 0,05| |13,0 ± 1|

|35 ± 0,05| |12,2 ± 1|

|30 ± 0,05| |11,2 ± 1|

Data Analisys


1. Based on table 1, 2 and 3 we can conclude factors affecting the period swing namely the length of the rope, mass pendulum, and a byway. This was seen table 1 changed in the if the given a byway a great so the time it takes pendulum to swing 10 times by also longer. In table 2 when crowds pendulum used the more severe so the time it takes pendulum to swing 10 times by will become long. In table 3 the length of the rope used is also different, when the length of the rope reduced so the time it takes pendulum to swing as many as 10 times will the sooner. So that it can be concluded that that affects the period swing simple is the length of the rope, mass pendulum, and a byway. Continues to be long a rope the large also time used pendulum to do swing so that stretch out the bigger also, including on the other hand. The bigger a byway the large also the time it takes pendulum to do swing and vice versa. The more severe mass pendulum the large also the time it takes pendulum to do swing including on the other hand.

2. Analysis dimension for equation T to pendulum mathematical

T=2π √ lg

T is unit of sekon (s) with dimension of T

T = 2π √lg

s = 2π √mm/s²

2π is constant and don’t having a unit.

[T ]=√ [L]

[ L ] [T ]−2

[T ]=√ 1[T ]−2

[T ]=√[T ]2

[ T ]=[T ]From the analysis dimensions can be expressed that the equation T to mathematical

pendulum is true.3. The Period swings on the activities 3

Analysis uncertainty period swing according to the theory :

T= 2π √ lg

T=2 π l12 . g

−12

∂ T=|δTδl |∆ l

∂ T=¿

∆ T=|π l−1

2 . g−12 |∆l

∆ TT

=| π l−1

2 . g−12

2 π l12 . g

−12 |∆ l

∆ TT

= ∆l2 l

∆ T=|∆l2l |T

Analysis uncertainty period swing according to the practicum :

T = t.n-1

∂ T =|δTδt | ∆ t

∂ T=|δ t .n−1

δt |∆ t

∂ T = n−1 ∆ t

∂ TT

=|n-1

t.n−1| ∆ t

∆TT

=|∆tt |

∆T =|∆tt | T

a. The oscillation period for the length of rope 1The length of rope = 50 cm = 0.5 mg = 9.8 m/s2

1) According to the theory

T 1 = 2π √ l1

g

T 1 = 2 ×227 √0,5 m

9,8 m/s²

T 1 = 6,2857 × 0,2258 s

T1 = 1,4193 s

∆T1 = |∆l1

2 l1|T1

∆T1 =|0,00052 × 0,5 |1,419 3

∆T1= 0,0005 × 1,4193

∆T1 = 0,0071 s

KR = ∆T1

T1

×100%

KR = 0,00711,4193

×100%

KR = 0,005 × 100 %

KR = 0,05 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,05 %

DK = 99,95 %

PF = |T1 ± ∆T1| s

= |14 ,19 ± 0,007 |10-1 s

= |14 ,19 ± 0,01 |10-1 s

2) According to practicumt1= 15,2 sn = 10 kali

T1 = t1

n =

15,210

= 1,52 s

∆T1 = |∆t1

t1|T1

∆T1 =|0,115,2 | 1,52

∆T1 = 0,0066 × 1,52

∆T1 = 0,01 s

KR = ∆T 1

T1

×100%

KR = 0 ,011,52

×100%

KR = 0,66 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,66%

DK = 99,34 %

PF = |T1 ± ∆T1| s

= | 15 ,2 ± 0,1 |10-1 s

b. The oscillation period for the length of string 2The length of string = 45cm = 0,45 mg = 9,8 m/s2

1) According to theory

T 2 = 2π √ l2

g

T 2 = 2 ×227 √0,45 m

9,8 m/s²

T 2 = 6,286 ×0,2143 s

T2 = 1,347 s

∆T2 = |∆l2

2 l2|T2

∆T2 = |0,00052 × 0,45 |1,347

∆T2= 0,00055 × 1,347

∆T2 = 0,00074 s

KR = ∆T2

T2

×100%

KR = 0 ,000741,347

×100%

KR = 0,00055 × 100 %

KR = 0,05 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,05%

DK = 99,95 %

PF = |T2 ± ∆T2| s

= |13 ,47 ± 0,007 |10-1 s

= |13 ,47 ± 0,01 |10-1 s


T2 = t2

n =

14 ,410

= 1,44 s

∆T2 = |∆t2

t2|T2

∆T2 =|0 ,114,4 | 1,44

∆T2 = 0,0069 × 1,44

∆T2 = 0,01 s

KR = ∆T2

T2

×100%

KR = 0 ,011,44

×100%

KR = 0,69 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,69%

DK = 99,31 %

PF = |T2 ± ∆T 2| s

= |14 ,4 ± 0,1 |10-1 s

c. The oscillation period for the length of string 3The length of string = 40 cm = 0,40 mg = 9,8 m/s2


T3 = 2π √ l3

g

T3= 2 ×227 √0 ,40 m

9,8 m/s²

T3 = 6,286 × 0 ,2020 s

T3 = 1,2699 s

∆T3 =|∆l3

2 l3|T3

∆T3=|0,00052 × 0,40 |1,2699

∆T 3 = 0,000625 × 1,2699

∆T3 = 0,00079 s

KR = ∆T3

T3

×100%

KR = 0 ,000791,2699

×100%

KR = 0,00062 × 100 %

KR = 0,062 % (4 AB)

DK= 100 % - KR

DK = 100 % - 0,062 %

DK = 99,94 %

PF = |T3 ± ∆T3| s

= | 12 ,69 ± 0,01 |10-1 s

2) According to practicumt3= 13 s

n = 10 kali

T3= t3

n =

1310

= 1,30 s

∆T3 = |∆t3

t3|T3

∆T3 =|0,113 | 1,30

∆T3 = 0,0077 × 1,30

∆T3 = 0,01 s

KR = ∆T3

T3

×100%

KR = 0 ,011,30

×100%

KR = 0,77 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,77 %

DK = 99,23 %

PF = |T3 ± ∆T3| s = |13 ,00 ± 0,1|10 -1 s

d. The oscillation for the length of string 4The length of string = 35 cm = 0,35 mg = 9,8 m/s2

1) According to the theory

T4 = 2π √ l4

g

T4 = 2 ×227 √0 ,35 m

9,8 m/s²

T4 = 6,286 × 0 ,1889 s

T4 = 1,1874 s

∆T4 =|∆l4

2 l 4|T4

∆T 4 =|0,00052 × 0,35 |1,1874

∆T4 = 0,000714 × 1,1874

∆T4 = 0,00085 s

KR = ∆T4

T4

×100%

KR = 0 ,000851,1874

×100%

KR = 0,000715 × 100 %

KR = 0,0715 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,0715%

DK = 99,93 %

PF = |T4 ± ∆T 4| s

= | 11,87 ± 0,01 |10-1 s


T4 =t4

n =

12 ,210

= 1,22 s

∆T4 = |∆t4

t4|T4

∆T 4 =|0,112,2 | 1,22

∆T4 = 0,0082× 1,22

∆T4= 0,0100 s

KR = ∆T4

T4

×100%

KR = 0 ,011,22

×100%

KR = 0,82 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,82%

DK = 99,18 %

PF = |T4 ± ∆T 4| s

= | 12 ,2 ± 0,1 |10-1 s

e. The oscillation period for the length of string 5 The length of string = 30 cm = 0,30 mg = 9,8 m/s2


T5 = 2π √ l5

g

T5 = 2 ×227 √0 ,30 m

9,8 m/s²

T5 = 6,286 × 0 ,1749 s

T5 = 1,0998 s

∆T5 =|∆l5

2 l5|T5

∆T5=|0,00052 × 0,30 |1,0998

∆T5 = 0,00083 × 1,0998

∆T5 = 0,00092 s

KR = ∆T5

T5

×100%

KR = 0 ,000921,0998

×100%

KR = 0,000836× 100 %

KR = 0,084 % (4 AB)

DK = 100 % - KR

DK = 100 % - 0,0845%

DK = 99,92 %

PF = |T5 ± ∆T5| s

= | 10 ,99 ± 0,01 |10-1 s


T5 =t5

n =

11,210

= 1,12 s

∆T5 = |∆t5

t5|T5

∆T5 =|0,111,2 | 1,12

∆T5 = 0,0089 × 1,12

∆T5 = 0,01 s

KR = ∆T5

T5

×100%

KR = 0 ,011,12

×100%

KR = 0,89% (4 AB)

DK = 100 % - KR

DK = 100 % - 0,89%

DK = 99,11 %

PF = |T5 ± ∆T5| s

= | 11,20 ± 0,1 |10 -1 s

Table 4. relation the period of pendulum mathematical on the activity 3

The length of rope (m)

Time (s) Periode T = tn

(s) Periode T= 2π √ lg

(s)

| 0,50 ± 0,0005 | | 15,2 ± 1 || 14,19 ± 0, 0 1 |10 -1

s

| 15,2 ± 0,1 |10-1

s

| 0,45 ± 0,0005 | | 14,4 ± 1 || 13,47 ± 0 ,01 |10 -1

s

| 14,4 ± 0,1 |10-1

s

| 0,40 ± 0,0005 | | 13,0 ± 1 || 12,69 ± 0 , 01 |10 -1

s

| 13,0 ± 0,1 |10-1

s

| 0,35 ± 0,0005 | | 12,2 ± 1 || 11,87 ± 0 ,01 |10-1

s

| 12,2 ± 0 ,1 |10-1

s

| 0,30 ± 0,0005 | | 11,2 ± 1 || 10,99 ± 0 , 01 |10 -1

s

| 11,2 ± 0 ,1 |10-1

s

4. The plot charts the relations between T2 and l The period based on theory to equation the period pendulum mathematical

Tabel 5. Relation T2 with l

No. The length of string (m) T2 (s2)

1. 0,50 2,0144

2. 0,45 1,8144

3. 0,40 1,6126

4. 0,35 1,4099

5. 0,30 1,2096

Graph 1. Relation T2 with l

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.10

0.1

0.2

0.3

0.4

0.5

0.6

f(x) = 0.248248610428989 x − 0.000221444761406786R² = 0.999995052530052

Relation T2 with l

Period T2(s2)

Linear (Period T2(s2))

The period T (s)

Th

e le

ngt

h o

f st

rin

g l (

m)

Acceleration of gravity from the graphic plot

T = 2π √lg

T 2 = 4π²lg

g = 4π²lT²

in the graphic we get :

m=∆y∆x

= lT ²

so, the equatioan acceleration of gravity is :

g = m4π²

y = mx + c

y = 0,248x + 0,000

so, m = 0,248, the value of g is :

g = 0,248 × 4 ( 227 )

2

N/m = 0,248 × 193649

N/m = 9,79 m/s 2

find ∆ g by graph :

R2= 1

DK = 100% × R2

DK = 100% × 1 = 100 %

KR = 100% - DK = 100% - 100 % = 0 % (4 AB)

KR = ∆gg

×100%

∆g = KR ×g100%

= 0% ×9,79100%

= 0,00 m/s2

PF = |g ± ∆g | satuan

PF = |9,79 ± 0,0 | m/s2

EXPLANATION

In practicum are 3 activity in pendulum mathematical. The first activity is the influence of a byway to the period swing, to these activities will be done with member a byway in pendulum five times, a byway used small enough because only a multiple 2, and after doing this activity we get that the time needed pendulum to swing 10 times by on each a byway only a distinct 0,2 second that of foreclose on we can conclude that a byway given impact on large the period swings on pendulum mathematical. The work of the second we will prove the influence of mass load against the period swing, to these activities provided 5 load with heavy different starting from 0,003 grams up to 100 grams. After doing practicum in fact burden also affect the period swing in the time every burden namely 0,2 seconds. The activity of the three of which is the influence of the length of the rope to the period swing, to these activities we hung load with a rope converted in length as many as 5 times (mass burdens and a byway constant), after doing practicum this we can identify the effects the length of the rope to the period swing, because the more we add the length of the rope so the period swing pendulum also will be bigger.

On the activities of third can be seen table results obtained data observation where the time it takes to perform 10 times swing with a long rope different having travel time (period) different. And based on the theory says that a length of rope period affecting large swings. Where the results to a length of rope |0,50 ± 0,0005|m large stretch

out |15,2 ± 0,1|10-1s, the length of the rope |0,45 ± 0,0005|m large stretch out

|14,4 ± 0,1|10-1s, the length of the rope |0,40 ± 0,0005|m large stretch out

|13,0 ± 0,1|10-1 s, the length of the rope |0,35 ± 0,0005|m large stretch out

|12,2 ± 0,1|10-1 s, and the length of the rope |0,30 ± 0,0005|m large stretch out

|11,2 ± 0,1|10 -1 s. Of anlisis charts obtained the value of the acceleration of gravity of

9,79 m/s2 .

CONCLUSION

After doing practicum we can conclude that factor that influences large the period swings on pendulum mathematical is the length of the rope, mass pendulum and a byway. Through a method of swing simple we can determine large the acceleration of gravity

using formulas T=2π √ lg

to pendulum mathematical in theory and can also through

formula T= tn

, to find stretch out first in practicum.

REFERENCE

[1] Halliday, Resnick, Walker. 2010. Fisika Dasar Jilid 1. Ciracas: Erlangga

[2] Practice Guidebook 1 Unit Basic Physics Basic Physics Laboratory Department of Physics, State University of Makassar

[3] Serway, Jewett. 2009. Fisika untuk Sains dan Teknik. Jagakarsa, Jakarta : Salemba Teknika

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