Physics Report Samples

The Simple Pendulum

Introduction:
Objective of this experiment was to calculate the acceleration due to gravity after determining the time period. Another purpose of this experiment was to validate the value of acceleration due to gravity i.e. “g”. For validation purpose, the experimental value of “g” was compared with theoretical one. An ideal simple pendulum was used to perform this experiment. To decrease percent error, many measurements of time were taken.

Data:

Data Analysis:
Data analysis for Time period has been shown below-
Average period (s) = (1.80 + 1.78 + 1.80 + 1.78 + 1.79 + 1.78 + 1.78 + 1.78) /8 = 1.784
Standard deviation (s) = ∑ (xi – mean) ^2/ n= 0.009

So, following error can be found out based on average and standard deviation–

Data analysis to calculate propagation of error in determining “g” has been shown below-
Discussion:
After performing the experiment it has been found that the difference between experimental and theoretical value of acceleration due to gravity is about 0.048 which is less than the permissible deviation of the two values i.e. 0.099. So, the experiment was successful. There are some probable source of errors such as error occurred during length of pendulum, error occurred during taking records etc. Percentage error of calculation time period is as high as 47.8% which may affect the experimental value of acceleration due to gravity. This is the largest error in the experiment.

Answers of the questions in lab manual have been written below –

1) Say, the average value is x and square of the average value is x^2 which can be denoted by y
So, y = x^2
or, dy/dx = 2x
or, dy = 2x.dy
or, σy = 2x.σx
so, absolute error can be calculated as 2x.σx , where σx is standard deviation and x is average value.
2) Percentage value = (σy/ y).100%
= [2x.σx / x^2]. 100%
= 2. [(σx/x). 100%
= 2. [Percentage error of x]
= 2. [Standard deviation / average value]. 100%
3) Experimental value = 9.82 ± 0.02 m/s^2; xe = 9.82 and σe = 0.02
Local value = 9.792 ± 0.007 m/s^2 m/s^2; xt = 9.792 and σt = 0.007
So, d = |xe – xt| = |9.82 -9.792| = 0.028
4) σd = ((σe)^2 + (σt)^2)^0.5 = (0.02^2 + 0.007^2)^0.5 = ( 0.0004 + 0.000049 )^0.5 = 0.0212
5) L1 = 76.9 ± 0.5; x1 = 76.9 and σ1 = 0.5;
L2 = 62.4 ± 0.9; x2 = 62.4 and σ2 = 0.9
Propagated error in sum of these two length = ((σ1)^2 + (σ2)^2)^0.5
= (0.5^2 + 0.9^2)^0.5 = ( 0.25 + 0.81 )^0.5 = 1.029.
6) V = 15 volt, % σv = ±3% = ±0.03;
I = 2.7 Amps, % σI = ±3% = ±0.03;
R = V/I , so % error = ((% σv)^2 + (% σI)^2)^0.5 = (0.03^2 + 0.03^2)^0.5 = (0.0018)^0.5 = 0.0424 i.e. 4.24%.

Conclusion:

The lab experiment was carried out safely. The purpose of the experiment, to evaluate the value of acceleration of gravity, was met satisfactorily. Though considerable deviation between experimental and theoretical value has been found out by carrying out this experiment, but the deviation is in permissible limit. Apart from the main objective of the experiment, the knowledge of calculating error and propagation of errors have been gained. So, the objective of the experiment was fully met and it was a successful experiment.