Embed Size (px)
Citation preview
ExampleA spring (彈簧 )was loaded with weights (W) in g. The length of the spring (L) is measured for each different load.
Load, W (g) 20 40 60 80 100
Length of Spring, L (cm) 16.0 20.0 24.5 28.0 31.5
Objective : To find an equationequation to describe the relationship between W (load) and L (length of spring).
Graphical Analysis
Since we need to find the relationship between W and L, therefore, the name of the graph should be The graph of L against W.
L will be the vertical axis and W will be the horizontal axis.
On a graph paper, following your steps of plotting graphIn mathematics, draw the vertical and horizontal axes and labelled them properly. Then select suitable scale for the two axes.
Graphical Analysis
The largest number of each scale should cover the maximum data for that axis.
In this question, maximum scale should be more than 100 (say 110 or 120) for the load (horizontal), and more than 31.5 (say 32) for the length (vertical).
Your scale should be very easily scaled. For example, for each largest division (5 small sub-divisions) should represent 1 or 2, or 5 or 10 or the multiples and NEVER represent 3 or 7.
The graph of L against W
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
W /g
L /
cm
(20, 16.0)
(40, 20.0)
(60, 24.5)
(80, 28.0)
(100,31.5)
The graph of L against W
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
W / g
L /
cm
The y-intercept,c is about _____cm 12.3
The slope,m :
496
13310.195
The equation : y = m x +c 12.3
(96,31)
(4,13)
In maths, x and y to for the two axes, however, in this example, the two axes are W and L
The graph of L against W
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
W/g
L
L /
cm
The y-intercept,c is about _____cm 12.3
The slope,m :
496
13310.195
The equation : LL = m x +c
So, L replace y
The graph of L against W
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
WW/g
L
L /
cm
The y-intercept,c is about _____cm 12.3
The slope,m :
496
13310.195
The equation : LL = m WW +c
and W replace x
The graph of L against W
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
WW/g
L
L /
cm
The y-intercept,c is about _____cm 12.3
The slope, m :
496
13310.195
The equation : LL = m WW + c
The graph of L against W
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
WW/g
L
L /
cm
The y-intercept,cc is about _____cm 12.3
The slope, mm :
496
13310.195
The equation : LL = 0.1950.195WW+cc
When W=0, L = c (or 12.3 in this case), so c=12.3
The graph of L against W
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
WW/g
L
L /
cm
The y-intercept,cc is about _____cm 12.3
The slope, mm :
496
13310.195
The equation : LL = 0.1950.195WW+12.312.3
