Newton's Discovery of f ∝ Δp/Δt

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Newton's discovery that force (F) is proportional to the change in momentum (Δp) over time (Δt) stems from manipulating Galileo's equation for uniformly accelerated motion. By starting with the equation v = at and multiplying by mass (m), it leads to the relationship mv = ma(t), which can be reinterpreted as force. Dividing both sides by time results in F = (mv)/t, establishing the foundational equation F = ma. The discussion also raises the question of whether Torricelli, a student of Galileo, had previously derived similar concepts before Newton. This highlights the evolution of ideas in classical mechanics.
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How did Newton come up with
f ∝ Δp/Δt ??
 
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Galileo's equation for uniform acellerated motion

v=at so multiply both sides by mass m

mv=mat

so
mv=ma(t) and call ma force F

mv=Ft
so
Ft=mv

Divided both sides by t

F=(mv)/t

Didn't Torricelli (Galileo's student) do this before Newton?

Also
F=(mv)/t
so
F=m(v/t) and call v/t acelleration a

F=ma
 
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