Comment on xkcd #3084: Unstoppable Force and Immovable Object

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Snazz@lemmy.world ⁨4⁩ ⁨weeks⁩ ago

It may be worth it to decide how we define ‘unstoppable force’ and ‘immovable object’.

An Immovable Object has 0 velocity:

v = 0

Acceleration is the time derivative of velocity:

a = d/dt(v(t))

a = d/dt(0)

a = 0

And we know that

a = F~net~ / m

An object with infinite mass would satisfy this equation, but an object with no net force would too. We could add a correction force that will satisfy the constraint of 0 net force.

|F~net~| = 0

∑F~i~ = 0

F~correction~ + … = 0

To satisfy Newton’s 3rd law, we would need a reaction force to our correction force somewhere, but let’s not worry about that for now.

A physics definition of ‘Unstoppable Force’ is:

|F~unstoppable~| =/= 0

In this case the gravitational force fits this description, given a few constraints

F~g~ = Gm∑ M~i~ / x~i~^2^

As long as the gravitational constant G is not 0, our object has mass, and

∑ M~i~ / x~i~^2^ =/= 0, then

|F~g~| > 0

But this does feel kinda like cheating because it’s not really what people mean by ‘unstoppable force’. the other way to define it is just immovable object in a different reference frame.

a = 0, |v| > 0

I’m gonna stop here because this is annoying to type out on mobile

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