Pendulum Experiment PDF

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Summary

This is an experiment that uses a pendulum to calculate the value of acceleration due to gravity...

Description

EXPERIMENT:*CALCULATING*“G”*WITH*A*PENDULUM* * AIM:*To*determine*a*value*for*acceleration*due*to*gravity*using*pendulum*motion* HYPOTHESIS:*The*value*of*gravity*will*be*9.8ms-2* EQUIPMENT:/

• • • • • •

2m*of*fishing*line* Capstan*Block* Weighted*bob* Retort*stand** Stopwatch* 1m*ruler*

• • • •

3m*of*fishing*line* Light*gate*and*iPad*with* application* Sonic*distance*meter** Weighted*bob

METHOD:/ 1. The*equipment*was*set*up*as*shown*in*Diagram*1* 2. The*fishing*line*was*measured*to*the*nearest*millimetre*-*the*top*of*the*fishing*line*to*the* centre*of*mass-*with*a*metre*ruler* 3. The*bob*was*moved*so*that*the*string*was*less*than*10º*from*the*normal* 4. The*bob*was*let*go*at*the*same*time*a*stopwatch*was*started* 5. 10*oscillations*were*counted*and*the*stopwatch*stopped*at*the*10th*oscillation* 6. The*results*were*recorded*in*a*table* 7. Steps*2-6*were*repeated*5*times* 8. The*fishing*line*length*was*changed*and*steps*2-7*were*repeated*5*times* 9. The*equipment*was*set*up*as*shown*in*Diagram*2* 10. The*fishing*line*was*measured*to*the*nearest*millimetre*-*the*top*of*the*fishing*line*to*the* centre*of*mass*-*with*a*sonic*distance*meter* 11. The*bob*was*moved*so*that*the*string*was*less*than*10º*from*the*normal* 12. The*application*started*recording*and*the*bob*was*let*go** 13. 10*oscillations*were*counted*and*the*application*stopped*after*the*10th*oscillation* 14. The*results*were*recorded*in*a*table* * DIAGRAM:/ Analogue)Measurements)(Diagram)1):)

* Digital)Measurements)(Diagram)2):)

* RISK/ASSESSMENT:/ Hazard* Hair* Bob*and*retort*stand* * * RESULTS:/ Length*(cm)* Length*(m)*

Risk*of*Injury* Caught*in*equipment* Bruising*by*dropping*it*on*foot*

1*

2*

Trial* 3*

4*

5*

Prevention/Treatment* Long*hair*tied*back* Wear*enclosed*leather*shoes**

Average* 1*Period*(T)*(sec)*

T^2*

61.4*

0.614*

30.86*

30.86*

31.03*

31.07*

30.86*

30.936*

1.5468*

2.39259024*

86.8*

0.868*

37.3*

38.65*

37.26*

37.35*

37.45*

37.602*

1.8801*

3.53477601*

101*

1.01*

40.58*

40.58*

40.5*

40.31*

40.73*

40.54*

2.027*

4.108729*

113.5*

1.135*

42.29*

42.52*

42.74*

42.52*

42.52*

42.518*

2.1259*

4.51945081*

135.5*

1.355*

46.47*

46.13*

46.23*

46.3*

46.48*

46.322*

2.3161*

5.36431921*

290*

2.9*

3.40*

*

*

*

*

3.40*

3.4*

11.56*

* * RESULTS/ANALYSED:// The*period*of*the*pendulum*depends*upon*the*length*of*the*string*and*the*rate*of*acceleration*due* to*gravity.* The*formula*is*as*shown:* 𝑇 = 2p Where, T is the period, l is the length of the pendulum, and g)is acceleration due to gravity.

* * *

𝑙 𝑔

To*determine*a*value*for*acceleration*due*to*gravity,*the*equation*was*rearranged*to*isolate*gravity* (g)*from*the*other*variables* 𝑙 𝑔 𝑙 𝑇 * = 4p* 𝑔 * 4 p )𝑙 𝑇* = 𝑔 Using*gradient*intercept*form,*it*can*be*seen*that** y )=)𝑇) 𝑇 = 2p

4 p5 )) 6

gradient)=)

x)=)𝑙) 4 p5 ) 6 5 4p =) = )

Therefore,)𝑚 =) )

))))))𝑔

) Graph of Analogue Data:

Length*vs*Period*Squared 6 y*=*3.9817x*+*0.0166 5

T2 (s)

4 3 2 1 0 0

0.2

0.4

0.6

0.8

Length*(m)

1

1.2

1.4

1.6

Graph of Analogue and Digital Data:

Length*vs*Period*Squared 14 12

y*=*3.98x*+*0.0182

T2 (s)

10 8 6 4 2 0 0

0.5

1

1.5

2

2.5

3

3.5

Length*(m)

/ CALCULATIONS: Calculating Gravity: Calculation)with)Analogue)Data)Only:) From)the)graph) y)=)3.9817x)+)0.0166) y)=)mx)+)b) Therefore,)) m)=)3.9817) Substitute)m) 4 p5

Calculation)with)Analogue)and)Digital)Data) From)the)graph) y)=)3.98x)+)0.0166) y)=)mx)+)b) Therefore,)) m)=)3.98) Substitute)m) 4 p5

𝑔 = ) U.VWXY)) ) 𝑔 = )9.914965368) 𝑔 ≈ )9.91)

𝑔 = ) U.VW)) ) 𝑔 = )9.919200403) 𝑔 ≈ )9.91)

Calculating Error: Percentage Error Ruler: Error % = ±0.5mm \.\\] = X ∗ 100 = 0.5% Timing: Error % = ± 0.001s with 0.0012s reaction time \.\\X_\.\X* ∗ 100]^2 =[ X = 1.69 Total: Error % = 0.5% + 1.69% Error % = 2.19% Results Percentage Error V.VXbV.WX

Error % = V.W Error % = 1.02%

∗ 100

DISCUSSION:// Errors:*To*eliminate*errors,*all*variables*were*kept*consistent,*the*results*were*placed*straight*in*an* electronic*table*to*eliminate*copying*errors,*the*string*measurements*were*kept*as*long*as*possible,* and*20*oscillations*were*measured*instead*of*10.*To*reduce*more*error,*using*more*than*20* oscillations*in*recommended.* Reliability:*The*experiment*was*conducted*with*6*different*lengths*of*string,*the*first*five*being* repeated*5*times*to*improve*reliability.*The*known*approximation*for*acceleration*due*to*gravity*is* 9.81ms-2.*Comparing*this*to*the*collected*result,*9.91ms-2,*this*is*very*reliable,*having*1.02%* experimental*error.*To*improve*reliability,*repeating*the*experiment*with*very*long*lengths*and* more*trials*is*recommended.* Accuracy:*The*data*for*the*first*five*lengths*were*collected*by*hand*with*a*stopwatch*correct*to*2* decimal*places*and*a*ruler*correct*to*the*millimetre.*The*data*included*a*data*point*which*was* conducted*using*electronic*equipment*to*be*more*accurate.*To*improve*accuracy,*doing*the*entire* experiment*with*electronic*equipment*as*shown*in*method*2,*is*recommended.* Validity:*The*independent*variable*of*this*experiment*is*the*lengths*of*fishing*line*and*the*dependant* variable*of*the*experiment*is*the*period*of*the*oscillations.*This*was*consistent*though*the*entire* experiment*to*ensure*validity.*The*constant*variables*were*kept*consistent,*e.g.*the*same*fishing* line,*bob,*retort*stand*and*capstan*block*was*used*for*each*experiment*and*the*experiment*was* conducted*indoors*to*eliminate*weather*from*interfering.*This*experiment*was*a*fair*test.* Safety:*This*experiment*was*very*safe*with*very*few*hazards.* Theory:*When*a*pendulum*swings*with*a*small*angle,*the*mass*on*the*end*performs*simple* harmonic*motion,*in*which*the*pendulum*swings*back*and*forth.*The*period*of*the*pendulum*is*the* time*taken*to*complete*one*oscillation.**This*depends*on*two*variables,*length*of*the*string*and*the* rate*of*acceleration*due*to*gravity.*The*mass*has*a*very*minute*or*no*affect*at*all.** Society:*Gravity*is*evident*in*the*entire*world.*Physicists,*engineers*and*scientists*all*use*the*value* for*this*force*to*explore*the*world.*17 th*Century*physicist,*Isaac*Newton,*used*the*force*of*gravity*to* mathematically*derive*Kepler's*three*kinematic*laws*of*planetary*motion,*and*from*him,*many*other* scientists*made*more*discoveries.*

* CONCLUSION:*The*value*for*acceleration*due*to*gravity*using*pendulum*motion*was*found*to*be* 9.91ms-1.*Since*this*is*within*the*2.19%*percentage*error,*this*supports*the*hypothesis.* * BIBLIOGRAPHY:/ - Jacaranda*Physics*Textbook*Chapter*1*‘Space’,*page*11* - http://www.pstcc.edu/departments/natural_behavioral_sciences/Web%20Physics/Experim ent%2004web.htm* - https://en.wikipedia.org/wiki/History_of_gravitational_theory* * *...