Caribbean School of Medical Sciences, Jamaica
Pre Med Year 2
Physics Lab # 1
Date: February 6 2023
Name: Ryan McLeod
ID#: 217002
Title: Graphical analysis and errors in measurement.
Aim: To determine the acceleration due to gravity using a simple pendulum bob swinging from
non-rigid support.
The following set of results was obtained from an experiment to determine the acceleration due
to gravity g using a simple pendulum bob swinging from non-rigid support. The length of the
string is represented by l and is measured in meters, and t represents the time for 10oscillations in
seconds.
t/s
13
15.9
22
31.6
39.8
56.1
63.1
l/cm
10
20
30
40
50
60
70
RESULTS:
t/s
13.0
15.9
22.0
31.6
39.8
56.1
63.1
l/cm
10
20
30
40
50
60
70
T/s
1.30
1.59
2.20
3.16
3.98
5.61
6.31
Graph:
Plot a suitable graph from which g can be calculated.
T2/s2
1.69
2.53
4.84
9.99
15.8
31.5
39.8
l/m
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Analysis questions:
It is known that the relation between (T) the periodic time and (l) the length of the string is of the
form:𝑇 = 2𝜋 √𝑙/𝑔
a) Arrange equation 1 in the form y = mx + c so that g can be calculated from drawing
a suitable graph.
2
(𝑇 2 )
=
(2𝜋)2
√𝑙
∙( )
𝑔
𝑇 2 = 4𝜋 2 ∙
𝑙
𝑔
𝑇 2 = 4𝜋 2 ∙ 𝑙 ∙
1
𝑔
4𝜋 2
𝑇 =
∙𝑙+𝑐
𝑔
2
b) Calculate the value of g.
Slope = T2 / l
= T22– T12 / l2 – l1
= 36 - 12 / 0.85 – 0.38
= 24/0.47
=51.0
Therefore, g is S = 4π2/g
g = 4π2/S
g = 39.5/51.0
g = 0.77
c) Calculate the error in the slope.
Slope = maximum slope – minimum slope/ 2√n
Maximum slope = 34 – 6/ 0.72 – 0.36 = 78
Minimum slope = 32 – 16 / 0.87 – 0.46 = 40
Δs= 38/ 2√7
=38 / 5.30
=7.17
d) Calculate the error in the intercept.
Intercept = maximum intercept – minimum intercept/ 2√n
ΔI =1.2 – 0 / 2√7
=-1.2/ 5.30
=-0.226
e) Calculate the error in g.
g=
𝛥𝑠
𝑠
=
𝛥𝑔
𝑔
𝛥𝑔 =
Δg = 7.17/ 51.0 x 0.77
Δg = 0.140 x 0.77
Δg = 0.1078
𝛥𝑠
∙𝑔
𝑠𝑙𝑜𝑝𝑒