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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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>>7642807
Velocity.
I know roughly what this graph should look like, and I know the sequence of events that this is part of, but I don't know how to equate it

>>7642838
Where is your term for the normal force?
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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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>>7643685
Normal contact force.

>>7643760
Yeah, so how do I write this down in an equation?
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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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>>7644290
you're being an autist about this, >>7644266 refers to a formal expression but it's ugly and no one would use it, when you write it like that it's understood that it's a valid way. i promise you do many things like this without noticing
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>>7644306
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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
$\frac{d^{2}x}{dt^{2}}=(F-\mu R)H(F-\mu R)$
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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