- #1
prosteve037
- 110
- 3
I was under the impression that, by experiment, Newton deduced
[itex]\textit{F}\propto{m}[/itex] [itex]\rightarrow[/itex] [itex]\textit{F = k}_{1}\textit{m}[/itex]
(where [itex]\textit{k}_{1}[/itex] is some constant)
and
[itex]\textit{F}\propto{a}[/itex] [itex]\rightarrow[/itex] [itex]\textit{F = k}_{2}\textit{a}[/itex]
(where [itex]\textit{k}_{2}[/itex] is some constant)
and then found that either/both
[itex]\textit{k}_{1}\propto{a}[/itex] [itex]\rightarrow[/itex] [itex]\textit{k}_{1}\textit{ = c}_{1}\textit{a}[/itex]
(where [itex]\textit{c}_{1}[/itex] is some constant)
and/or
[itex]\textit{k}_{2}\propto{m}[/itex] [itex]\rightarrow[/itex] [itex]\textit{k}_{2}\textit{ = c}_{2}\textit{m}[/itex]
(where [itex]\textit{c}_{2}[/itex] is some constant)
thus creating
[itex]\textit{F = c}_{1}\textit{ma}[/itex]
and/or
[itex]\textit{F = c}_{2}\textit{ma}[/itex]
where in SI Units they would be in the form
[itex]\textit{F = ma}[/itex]
However, I've read in some other forums how Newton actually meant
[itex]\textit{F}\propto{ma}[/itex] [itex]\rightarrow[/itex] [itex]\textit{F = kma}[/itex]
Which is the case? Did he use the first method or did he simply state the second?
If he did use the first method, how did he resolve that [itex]\textit{k}_{1}[/itex] is dependent on acceleration and/or that [itex]\textit{k}_{2}[/itex] is dependent on mass?
[itex]\textit{F}\propto{m}[/itex] [itex]\rightarrow[/itex] [itex]\textit{F = k}_{1}\textit{m}[/itex]
(where [itex]\textit{k}_{1}[/itex] is some constant)
and
[itex]\textit{F}\propto{a}[/itex] [itex]\rightarrow[/itex] [itex]\textit{F = k}_{2}\textit{a}[/itex]
(where [itex]\textit{k}_{2}[/itex] is some constant)
and then found that either/both
[itex]\textit{k}_{1}\propto{a}[/itex] [itex]\rightarrow[/itex] [itex]\textit{k}_{1}\textit{ = c}_{1}\textit{a}[/itex]
(where [itex]\textit{c}_{1}[/itex] is some constant)
and/or
[itex]\textit{k}_{2}\propto{m}[/itex] [itex]\rightarrow[/itex] [itex]\textit{k}_{2}\textit{ = c}_{2}\textit{m}[/itex]
(where [itex]\textit{c}_{2}[/itex] is some constant)
thus creating
[itex]\textit{F = c}_{1}\textit{ma}[/itex]
and/or
[itex]\textit{F = c}_{2}\textit{ma}[/itex]
where in SI Units they would be in the form
[itex]\textit{F = ma}[/itex]
However, I've read in some other forums how Newton actually meant
[itex]\textit{F}\propto{ma}[/itex] [itex]\rightarrow[/itex] [itex]\textit{F = kma}[/itex]
Which is the case? Did he use the first method or did he simply state the second?
If he did use the first method, how did he resolve that [itex]\textit{k}_{1}[/itex] is dependent on acceleration and/or that [itex]\textit{k}_{2}[/itex] is dependent on mass?