Newton's Discovery of f ∝ Δp/Δt

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SUMMARY

Newton's formulation of the relationship between force and momentum is expressed as F ∝ Δp/Δt, derived from Galileo's equation for uniformly accelerated motion, v = at. By multiplying both sides of this equation by mass (m), Newton establishes that mv = ma(t), which leads to the conclusion that force (F) can be represented as F = (mv)/t. This derivation raises the question of whether Torricelli, a student of Galileo, had previously articulated this relationship.

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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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