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An experiment to measure the acceleration due to gravity g of a pendulum is done. The...

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syedajmain | Student | eNoter

Posted October 5, 2010 at 2:59 AM via web

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An experiment to measure the acceleration due to gravity g of a pendulum is done. The length of threads l/m are 0.35, 0.65, 1.00, 1.45, 1.95 & ...

time for 20 oscillation t/s are 24.1, 32.4, 40.1, 47.5, 56.3 respectively. Given that the relation between the period T, the length of the pendulum l and the acceleration due to gravity g is T=2pi x sq. rt. of l/g. Find the value of g.

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william1941 | College Teacher | Valedictorian

Posted October 5, 2010 at 3:17 AM (Answer #1)

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The time period T of a pendulum is given as T = 2*pi*sqrt [ l / g ], where l is the length of the pendulum and g is the acceleration due to gravity.

Now for the pendulum of length:

0.35 m,  T= 24.1 / 20 = 1.205

0.65 m, T = 32.4 / 20 =1.62

1.00 m,  T= 40.1/20 = 2.00

1.45 m , T = 47.5 / 20 = 2.375

1.95 m , T = 56.3 /20 = 2.815

Now T = 2 pi sqrt [ l /g ]

So 2 = 2 pi sqrt [ 1 / g]

=> pi sqrt [ 1/g ] = 1

=> 1/g = (1/ pi )^2

=> g = pi ^2 m/s^2

Therefore the value of g is pi^2 m/s^2

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mike-krupp | (Level 2) Adjunct Educator

Posted October 5, 2010 at 7:52 AM (Answer #2)

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I like to do this a different way, although we get the same result.

Start with T = 2 * pi * sqrt(L/g)

Solve for g:  g = (4 * pi^2 * L)/(T/20)^2

I hope you can read my notation.  The factor of T/20 is because we are given the period of 20 oscillations.

Substituting our data for L and T, we get

L           T           g

0.35      24.1      9.52

0.65      32.4      9.78

1.00      40.1      9.82

1.45      47.5      10.15

1.95      56.3      9.71

The value of 10.15 is probably an outlier that we could discard, but what the hey.  The average value for g is

g = 9.80 m/s^2, in good agreement with the textbooks.

Comparing with the previous response:

His value for g = pi^2 = 9.87.  I think his answer is different because he simplified, considering only the data for L= 1 and T/20 = 2.

Incidentally, I did all the arithmetic with Excel, the poor man's mathematical analyser.

 

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