Question

Galileo experimented with balls rolling on inclined planes of various angles. What is the range of accelerations from angles 0 degrees to 90 degrees (from what acceleration to what)?

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

Answer 1

The general formula for acceleration can be written as a = g sin
Where g = 9.81 m/s²
For = 0, a = 0 and for = 90 degrees, a = 9.81 m/s²

The acceleration can be tabulated as,

   a
0   0
1   0.1712081071
2   0.3423640627
3   0.5134157307
4   0.6843110074
5   0.8549978364
6   1.0254242247
7   1.1955382588
8   1.3652881204
9   1.534622102
10   1.7034886229
11   1.8718362446
12   2.0396136869
13   2.2067698431
14   2.3732537958
15   2.5390148325
16   2.7040024606
17   2.8681664233
18   3.0314567148
19   3.1938235952
20   3.355217606
21   3.515589585
22   3.6748906814
23   3.8330723705
24   3.9900864686
25   4.1458851477
26   4.30042095
27   4.4536468024
28   4.6055160309
29   4.7559823746
30   4.905
31   5.0525235149
32   5.1985079821
33   5.3429089335
34   5.485682383
35   5.6267848406
36   5.766173325
37   5.9038053771
38   6.0396390729
39   6.1736330362
40   6.305746451
41   6.4359390744
42   6.5641712484
43   6.6904039122
44   6.8145986142
45   6.9367175234
46   7.0567234413
47   7.1745798129
48   7.2902507379
49   7.403700982
50   7.514895987
51   7.6238018819
52   7.7303854929
53   7.8346143536
54   7.9364567148
55   8.0358815545
56   8.1328585868
57   8.2273582715
58   8.3193518233
59   8.4088112199
60   8.4957092111
61   8.580019327
62   8.6617158859
63   8.7407740023
64   8.8171695942
65   8.8908793908
66   8.9618809395
67   9.0301526124
68   9.0956736133
69   9.1584239839
70   9.2183846099
71   9.2755372266
72   9.3298644249
73   9.381349656
74   9.4299772372
75   9.4757323559
76   9.5186010748
77   9.5585703355
78   9.5956279632
79   9.6297626696
80   9.660964057
81   9.6892226212
82   9.7145297544
83   9.7368777476
84   9.7562597936
85   9.7726699883
86   9.786103333
87   9.7965557359
88   9.8040240131
89   9.8085058895
90   9.81