Let be the time for one revolution squared (s), g be acceleration due to gravity (ms-1), l be distance between centre of circle (cm), be mass of hanging grams (kg) and be mass of bung (kg).
Now I will show how Tavg2 and ΔT2 was calculated:
First we calculate in kilograms, which is: . For example, =0.551s
Then we have to find Tavg2 and to do that we find Tavg first, and the average is divided by 50 because the time is in 10 revolutions and I need find Tavg for 1 revolution:
Tavg= , for example, =0.742s, then
Tavg2= , for example, 2=0.551 s2.
Then lastly to calculate ΔT2:
ΔT2= (T2
= (T (T
= T2xTavg2
= T2)
For example: ΔT2 =0.5512) = 0.01
Processed Data Table:
Conclusion:
From the graphs above we can see that the relationship between the T2 and 1/mb is linear with the equation of y=0.0262x+0.0492. However, according to the equation , we can see that the relationship should demonstrate a directly proportional relationship, which shows that there are systematic errors in our experiment.
To find the percentage error of the experiment we need to find the experimental slope and the theoretical slope obtained from experiment. The experimental slope was found by using the graph which = 0.0262, and to find the theoretical slope weed need to substitute mb=0.0107kg and l=0.4m and g=9.81ms-2 into = 0.0261, which is not the same with the experimental value, proving there is systematic error in or experiment. Then, the percentage error =
=
= -0.38%
As we can see the experiment has a percentage error of 0.38, and therefore 100-0.38= 99.62% of the experiment was accurate. The results of this experiment are reliable therefore we can verify that the relationship between T2 and 1/mh is directly proportional.
Evaluation:
Weaknesses and limitations:
First there is a systematic error because of friction between the string and the tube when it slides in and out. In the system of the hanging mass, T=f+mhg, hence T= mhg-f. Then we derive the equation with friction taken into account:
Fc = TsinΘ= (mhg-F) sinΘ
Fc =
(mhg-F) sinΘ=
(mhg-F) sinΘ=
(mhg-F) sinΘ=
T2=
As we can see all other variables remain constant except that the denominator is changed with the subtraction of F, and that causes the experimental value to increase, which proves that there is error because the slope of experimental value is greater than the slope of theoretical value.
Secondly the mass of the string will affect the experiment because it adds on more mass to the system.
Improvements:
For friction that occurs between string and tube we should add some lubricants and for the mass of the string that effects the system we should use a thinner and lighter string to minimize the error.
