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PHYSICS LABORATORY: The Simple Pendulum, Slides of Physics

University College Bahrain (UCB)Physics

The purpose of this lab was to experimentally determine a value for g, the acceleration of Earth's gravity, by using the given 'pendulum ...

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Madeline Smith
IB Physics SL
November 18, 2013
PHYSICS LABORATORY: The Simple Pendulum
The purpose of this lab was to experimentally determine a value for g, the acceleration of Earth’s
gravity, by using the given ‘pendulum equation’ and experimental data for the period of a pendulum and
the length of a pendulum string. Additionally, we were to consider how the period of a pendulum is
affected by its length.
HYPOTHESIS: I think that as the string length gets shorter, the period of the pendulum will decrease.
I am basing this hypothesis on a game that I play with my little brother on the swingset at the
playground. We like to flip the swing over the top bar and make the seat higher. When we do this, it
seems like the swing moves back and forth faster.
DATA COLLECTION AND PROCESSING (DCP)
Data collected on 12 November 2013 with Scarlett Gemmer. The mass on the pendulum was 200 g.
Table&1:&RAW&DATA&&&
&
&
String'
Length'''''''''
(±'0.001'm)'
10T'''TRIAL'1''''
(±0.30's)'
10T'''TRIAL'
2''''(±0.30's)'
0.600!
15.54!
15.56!
0.486!
14.09!
14.10!
0.435!
13.31!
13.22!
0.371!
12.25!
12.66!
0.273!
10.66!
10.81!
0.198!
9.09!
9.03!
0.106!
6.69!
6.47!
&
&
&
&
&
&
Table&2:&PROCESSED&DATA&
&
&
&
&
10T'''''''''''''
Ave'''(s)'
Unc'in'10T'''
(s)'
T''Ave''(s)'
15.46!
0.14!
1.55!
14.07!
0.04!
1.41!
13.29!
0.06!
1.33!
12.51!
0.21!
1.25!
10.74!
0.08!
1.07!
9.12!
0.11!
0.91!
6.60!
0.11!
0.66!
I decided to measure the time taken for 10 full swings of the pendulum for each length.
The uncertainty in 10 swings was calculated by ((max trial value) – (min trial value))/2. For example, for
the first data point:
15.56!s!−15.28!s
2
=0.14!s
pf3

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Download PHYSICS LABORATORY: The Simple Pendulum and more Slides Physics in PDF only on Docsity!

Madeline Smith IB Physics SL November 18, 2013

PHYSICS LABORATORY: The Simple Pendulum

The purpose of this lab was to experimentally determine a value for g, the acceleration of Earth’s gravity, by using the given ‘pendulum equation’ and experimental data for the period of a pendulum and the length of a pendulum string. Additionally, we were to consider how the period of a pendulum is affected by its length. HYPOTHESIS: I think that as the string length gets shorter, the period of the pendulum will decrease. I am basing this hypothesis on a game that I play with my little brother on the swingset at the playground. We like to flip the swing over the top bar and make the seat higher. When we do this, it seems like the swing moves back and forth faster. DATA COLLECTION AND PROCESSING (DCP) Data collected on 12 November 2013 with Scarlett Gemmer. The mass on the pendulum was 200 g. Table 1: RAW DATA String Length (± 0.001 m)

10T TRIAL 1

(±0.30 s)

10T TRIAL

2 (±0.30 s)

10T TRIAL 3

(±0.30 s) 0.600 15.54 15.56 15. 0.486 14.09 14.10 14. 0.435 13.31 13.22 13. 0.371 12.25 12.66 12. 0.273 10.66 10.81 10. 0.198 9.09 9.03 9. 0.106 6.69 6.47 6. Table 2: PROCESSED DATA 10T Ave (s) Unc in 10T (s) T Ave (s) Unc in T (s) T^2 (s^2) Unc in T^ (s^2) 15.46 0.14 1.55 0.01 2.39 0. 14.07 0.04 1.41 0.01 1.98 0. 13.29 0.06 1.33 0.01 1.77 0. 12.51 0.21 1.25 0.02 1.57 0. 10.74 0.08 1.07 0.01 1.15 0. 9.12 0.11 0.91 0.01 0.83 0. 6.60 0.11 0.66 0.01 0.44 0. I decided to measure the time taken for 10 full swings of the pendulum for each length. The uncertainty in 10 swings was calculated by ((max trial value) – (min trial value))/2. For example, for the first data point:

  1. 56 s − 15. 28 s 2 = 0. 14 s

To get the average period and uncertainty, I divided each average and uncertainty for 10T by 10. The simple pendulum equation was given to us as Which means if we graph T against l, we should get a square root function. In order to determine a value for g, however, we had to graph T^2 against l, then consider the gradient of the linear function. Sample calculation for uncertainty in T^2 (first data point): 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝑇 =

𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝑇!^ = 2 × 0. 00645 = 0. 0129

𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑖𝑛 𝑇!^ = 0. 0129 × 1. 55!^ = 0. 04 s These calculations were done in an Excel spreadsheet, which rounded the values to 2 decimal places. When it performed the calculations, therefore, more decimal places were used. This graph is of the form 𝑦 = 𝑚𝑥 + 𝑏 which, from the pendulum equation, is equivalent to: 𝑇!^ = !!! ! 𝑙 Hence, the gradient of this graph should be 𝑚 = !!! !.^ Rearranging gives:^ 𝑔^ =^ !!! ! g l T = 2 π