So this might not be the realm of 5-year-olds but I was curious from a mathematical standpoint how Newton came to discover specifically that [F]orce was [m]ass multiplied by [a]cceleration and not some other mathematical operation like some logarithm or polynomial or something (not sure what those are either but that’s another eli5 entirely).
In: Physics
You can come up with the law if you can measure position and time. Changes in position over time give velocity. Changes in velocity over time give acceleration .
Set up a cart pulled by a string attached over a pulley. Hang a weight over the pulley to supply a set amount of gravitational force and vary the mass of the cart by adding weights to it. You will quickly discover that the cart’s acceleration varies inversely with its mass. (Twice the mass is half the acceleration, 3x mass is 1/3 the acceleration).
Next leave the cart alone and instead add weight a to the string over the pulley. You will find that the cart’s acceleration varies directly with the weight pulling it. (Twice the weight, twice the acceleration, 3x the weight, 3x the acceleration).
Putting those observations together, a=f/m, which we normally rearrange to F=ma.
Newton didn’t come up with the relationship, it was known since Galileo. Newton combined it with other observations and equations and gave a complete and cohesive description of the laws of motion, so the equation is known as Newton’s second law.
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