Fuck me /sci/ i'm having some troubles

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Fuck me /sci/ i'm having some troubles

Basically i have a situation with a constant force being applied to a particle in contact with a rough plane. The normal contact force varies, so the frictional force increases. However, with the equation i've put in the image, this would result in the particle reversing directions. How do I fix this?

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bump for mechanics

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Are you trying to find the equation for the movement or the velocity? I think it's not possible in this case

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>>7642746

The frictional force will never be greater than the force applied to the object that it is opposing, it increases as the opposing force does until it caps out at F(max). The way of calculating it is V(object)*mu(static or kinetic). As you know, mu only varies with object material.

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>>7643601

No matter how much the normal/contact force is, the friction will remain the same. Plot the graph as velocity against time, and you'll have a straight line graph of gradient (F(pushing)-F(kinetic, max))/m

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>>7643622

This is objectively false

F=uR

as R increases, limiting friction therefore increases

If limiting friction surpasses the force acting on the object, the object will stop moving.

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>>7643623

Gonna define R?

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>>7643685

Ah ok nvm I was mistakenly using static friction while the particle was moving

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>>7643623

Yet what I said still holds true, friction will only ever be equal to the force it opposes as it is generated by the opposing force, were friction to become greater than the opposing force, there would no longer be any movement to generate friction

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>>7643780

There is no good way, other than saying 'for values (original velocity)-Ff*t > 0' you can plug in some arbitrary values for V, M and increase in Fn/t to plot some basic graphs

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>>7643962

fugg >:DD

is there a mathematical way to write an IF statement?

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Bump of desperation

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>>7643970

>is there a mathematical way to write an IF statement?

Yes.

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>>7644250

w-what is it?

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>>7644255

depends on what you wanna do. in general you can just write it as "P, if x ... Q, if ~x" and ignore the formality - you already do all of that for a lot of things without realizing anyway

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>>7644257

I want to say:

If uR >= F, v=0

in an equation

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>>7644260

Then do just that?

v = { 0, if uR >= F x, otherwise }

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>>7644266

That's not an equation though

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>>7644268

Says who, you?

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>>7644271

y-yes

i'm looking for a way to write it like

v=

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>>7644306

how am i being an autist about this? I asked how to write a function in a specific way

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>>7644348

This may help:

https://en.wikipedia.org/wiki/Heaviside_step_function

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>>7644413

Alright, I think that might help, thanks

If that uses 1 as true, and 0 as false, I can use it as a multiplier for velocity

I'm trying to work out how to add F <= uR into that though

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I just don't like how I have to make a manual choice as to whether it's true or false, instead of letting the numbers handle themselves

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>>7644465

Your equation of motion would be

[math]\frac{d^{2}x}{dt^{2}}=(F-\mu R)H(F-\mu R)[/math]

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>>7644260

I'm confused, wouldn't you want to say that a = 0 if both uR>=F and v=0? Otherwise you have it stopping on a dime the moment friction exceeds your force no matter what its velocity is.

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>>7644588

Yeah, you're right

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bump again

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