In the event of dropping the same object at two different heights (let's say 1.0m and 2.0m) which will still have the same mass (let's say 1.0kg), why is the force exerted from the ground when the object collides with it not the same when at different heights?
Considering how the acceleration (~9.8) and the mass(1.0kg) are the same with each scenario, shouldn't the force be the same?
The force is the same.
Not sure why you think it isn't.
>>7948787
It doesn't.
>>7948787
g isnt constant
Now go back to high school
>>7948841
That's not why, child.
>>7948841
not sure if serious
>>7948866
but what does momentum have to do with force
>>7948871
d/dx F = p
>>7948871
What happens to the velocity when it hits the ground?
>>7948873
You should be differentiating p, and assuming constant mass.
>>7948876
fugg, you're right
as d/dt v = a and m -> consf
>>7948877
Sorry for sounding stupid, but what is d exactly?
Haven't seen that notation before.
>>7948897
How about you finish high school then
>>7948871
Force is the rate of change of momentum.
>>7948897
why do they even bother trying to teach physics to people who don't understand derivatives?
>>7949080
>You don't need to know derivatives to learn basic physics
You can't understand fundamental concepts without derivatives.
How do you explain acceleration to someone who doesn't know calculus?
The mathematical side, trivial as it is, is very important to make sense of things.
>>7949087
>You can't understand fundamental concepts without derivatives.
Only you because you're shit at physics. Stop projecting.
>How do you explain acceleration to someone who doesn't know calculus?
Are you serious? You can't understand the concept of increasing your velocity over a certain time period? Calculus is only relevant for instantaneous acceleration. Average acceleration the concept is exactly the same and you don't need to know a thing about limits.
The problem with /sci/ is that no-one here understands anything intuitively, they just memorized the equation to plug and chug in an exam.
>>7949096
No.. that's not the problem dude. You just get used to assumptions and shortcuts, and if you're not used to teaching it can be slightly jarring. That's all.
>>7949096
Now express this change of velocity in mathematical terms and why it is that way without using derivatives.
Hell, define "velocity" without using derivatives.
>>7949096
>The problem with /sci/ is that no-one here understands anything intuitively, they just memorized the equation to plug and chug in an exam.
Intuitive understanding is not rigorous.
Going "dude I think this is this way" is not good enough.
Also, asserting that you need to understand calculus to get a grasp of even basic physics is the opposite of plugging and chugging.
>>7949126
>Now express this change of velocity in mathematical terms
final velocity minus initial velocity divided by time passed
>Hell, define "velocity" without using derivatives
rate of change of displacement with respect to time
Being able to speak in only maths, not words is a sign of autism.
>>7949136
>rate of change of displacement with respect to time
You mean like ds/dt/dt?
Sounds a lot like a derivative to me.
>>7949136
>final velocity minus initial velocity divided by time passed
So dv/dt?
I said without derivatives, writing it out in words doesn't change that you are using derivatives.
>rate of change of displacement with respect to time
That's acceleration, though.
>Being able to speak in only maths, not words is a sign of autism.
You speak in maths because it is a far more stripped-down language with less opportunities to misunderstand things.
>>7949146
Rate of change of displacement with respect to time is velocity. You need to step up your English skills. Let me hold your hand, If you travel at 60 miles per hour you are changing your displacement in miles at a rate of 60 miles every hour. Get it now?
You have proved perfectly my point, You can plug and chug equations all the way into undergrad or wherever you are yet you can't even understand the word "rate". Are you really as clever as you think you are?
>>7949181
>You have proved perfectly my point
Not at all.
In fact, you have proven mine. This is why you speak in mathematics, so misunderstandings like this can't happen.
>You can plug and chug equations all the way into undergrad or wherever you are
How many more times do I repeat myself, it's almost as if you didn't know what "plug and chug" means.
>yet you can't even understand the word "rate". Are you really as clever as you think you are?
You can't even get the preterite form of "prove" right.
And you think you can lecture people on the English language?
>>7949126
>Hell, define "velocity" without using derivatives.
Let me have a go at it.
The instantaneous velocity of an object is the distance traveled per unit time by that object if ALL forces on the object were removed at that instant.
>>7949206
>The instantaneous velocity of an object is the distance traveled per unit time by that object if ALL forces on the object were removed at that instant.
Define "force", same rules apply.
Also isn't that just ds/dt?
Okay you fucking sperglords, Johnny travelled one meter in one second and his speed was constant, what was it? You don't need derivatives for that shit you fucking retards. Yeah, derivatives are essential later on, but you can obviously talk about the topic without them.
>>7949208
I don't know how to define force without derivatives.
And of course it's ds/dt, the point is that I defined velocity without using derivatives.
>>7949223
You didn't define it without derivatives, you wrote ds/dt in words.
Which is nice, but not what we are trying to do here.
>>7949235
Debatable. Regardless, I think someone with zero knowledge of calculus would have no trouble understanding what I said.
>>7949198
>This is why you speak in mathematics, so misunderstandings like this can't happen.
There is nothing to misunderstand, you just suck at English. And last time I checked more people were proficient in English than maths.
>You can't even get the preterite form of "prove" right.
So you took the time to analyze my post for whatever tiny grammatical mistake you could find in order to get back at me for calling you out on having shit comprehension skills? How pathetic.
>>7949281
>analyze
No need, it's in the very first line and impossible to overlook.
The word order is terrible too.
>whatever tiny grammatical mistake
"whichever" and you really should know your irregular verbs, it's not a tiny mistake at all.
Why should I let someone like you lecture me on the use of the English language?
You still haven't addressed my point either, you prefer insulting me over your own, possibly purposefully, vague"rate of change of displacement".
>>7949239
>someone with zero knowledge of calculus would have no trouble understanding what I said.
True, but where do we go from here?
Velocity is just the most basic thing you need to teach.
Acceleration would be next.
>>7949303
>where do we go from here?
Nowhere, you need a mathematical foundation to study and understand anything beyond pleb level physics. I was responding to a guy who said you couldn't define velocity without derivatives.
>>7949321
No, I was saying that you need this mathematical foundation to learn physics.
The velocity was just a simple, if badly chosen example.
>>7948781
That's because that's the gravitational force the object experiences. What you're talking about is impact, which is a function of momentum. Momentum is reliant on velocity, which is different between two objects which have fallen for different lengths of time.
>>7949330
The post that started all this asked why teach physics to someone who doesn't know derivatives, and you can obviously do plenty of physics without it.
>>7948873
Incorrect,
[math]
F_net = \frac{d \vec{p}}{dt}
[/math]
Which is simply N2L. It should make sense; if velocity is constant, it requires a force to maintain that if the mass of the system is changing. If the velocity is changing, a force is required to maintain that if mass is constant. This sort of understanding is important to dealing with variable mass systems, as well.
>>7949219
[math]
v_{Johnny} = \frac{\Delta x}{\Delta t} \\
v_{Johnny, instantaneous} = \frac{d x}{dt} = lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}
[/math]
Jee, what do you know? It is a derivative, but one just notices that it is invariant with time!
>>7949292
You are just making yourself look like a neckbeard now, stop arguing and accept that you fucked up. Pointing out grammatical mistakes on an anonymous imageboard is not a valid counter argument. Your failure at comprehension was relevant to the discussion, my grammar errors are not. You are just being butthurt and desperate to save face in an argument that you clearly lost.
>>7949556
this. thread over now please
>>7949570
Yeah, but you still don't need derivatives you raging aspie.
>>7949087
My high school physics class was algebra-based and we were perfectly capable of doing all basic stuff. You certainly don't NEED derivatives to understand or calculate acceleration, although I do agree it's the more elegant method.
>>7949582
You understand there's a reason why Newton defined the differentiation operator when describing physics, right?
If you do not understand continuous change over time, you cannot do anything but plug and chug, as you are so fond of dismissing. Intuition is still important, even with mathematical operators such as the derivative. Insult me all you want, it won't make you right, nor will it make me want to agree with you any more.
>>7949589
>I was taught kinematic equations for constant acceleration and had toy problems to calculate acceleration
>Obviously calculus isn't necessary for physics
>>7949595
If you're doing basic stuff you really don't. If you're doing more advanced problems and want to understand physics then yes you do need to know physics.
>>7949570
He didn't say you couldn't use derivatives, he just said they weren't necessary. Nobody is impressed with your ability to write down neat little functions on a Laotian card trading forum
>>7949593
I don't want you to agree with me. I want you to realize how fucking retarded what you said is. And I'm right regardless of how stupid you are.
>>7949595
That's why I used the word "basic" you fucking simpleton. Does everything need to be clearly outlined for you lest you sperg all over your keyboard again? I mean for fuck's sake
>>7949595
Show me one real-life problem that you think needs calculus and I'll try to do it in words.
>>7949615
If you want to answer a question like the OP it's necessary to bring in concepts like impulse and relate them to force. In order to do that, especially on timescales similar to a ball hitting the ground, it's necessary to introduce instantaneous change. I also took a high school physics class which did not utilize differentiation explicitly, but it would be remiss- and in fact, my teacher mentioned this on multiple occasions- to not ensure the understanding that in fact, what we were doing did rely on calculus, and we were using simplification by insightful observations to solve them.
>>7949628
Orbital trajectory of a satellite with a specific mechanical energy of -1/200,000 (mu) + 1000 J/kg
>>7949649
Neglected to mention, r = 100,000 m
>>7949649
An ellipse.
>>7949661
Exact trajectory.
>>7949649
Fair enough, I agree that calculus provides a more fundamental grasp of understanding, I just find it annoying when people say shit like "if you didn't ace calc don't bother even doing anything with physics" because that's bullshit. People should be encouraged to learn no matter what, and if they can get a reasonably decent amount of experience working on problems without calculus, then they should go for it. Nothing wrong with suggesting calculus as the more fundamental and ultimately necessary method for more advanced stuff, but fuck elitist douche bagels who dismiss everyone who doesn't have all the knowledge they do
>>7949666
Absolutely, that wasn't actually my intention (I posted quite a bit later on than the other people)- I was simply staying that inherent to the knowledge people had was calculus applied in special cases which resulted in a more easily understood answer
>>7949666
It's not "if you didn't ace calc don't bother even doing anything with physics", but rather "make sure you understand calc, so you can understand why the formulas you're using to plug and chug are the way they are and what they are describing".
>>7949572
You are still dodging the point and insulting me because my statements don't fit your narrative.
And you still haven't addressed my argument.
>>7949080
>"dt" is a "tiny miniscule change in time"
IT BEGINS
another person's understanding of calculus and differential forms ruined by the memes of infinitesimals and handwaving, you're doing god's work anon
>>7948781
With basic understanding of physics
[math]v_t=g t[/math]
[math]h=\frac{1}{2} t \left(v_t+v_0\right)\Rightarrow t=\frac{2 h}{v_t}[/math]
[math]v_t=\frac{2 g h}{v_t}\Rightarrow v_t=\sqrt{2 g h}[/math]
[math]\frac{v_{t,1}}{v_{t,2}}=\frac{\sqrt{2 g h_1}}{\sqrt{2 g h_2}}=\sqrt{\frac{h_1}{h_2}}\Rightarrow v_{t,1}=\sqrt{\frac{h_1}{h_2}} v_{t,2}[/math]
[math]m_1=m_2\Rightarrow \frac{F_1}{F_2}=\frac{\sqrt{\frac{h_1}{h_2}} m_1 v_{t,2}}{\frac{t_1 \left(m_2 v_{t,2}\right)}{t_2}}=\frac{\sqrt{\frac{h_1}{h_2}} t_1}{t_2}\Rightarrow F_1=\frac{F_2 \sqrt{\frac{h_1}{h_2}} t_1}{t_2}[/math]
So, as you can obviously see, it depends on the height you drop the object from, as well as how the surface reacts to the impact.
Not that I know what I'm actually talking about, if someone cares enough they can probably correct my nonsense.
>>7949777
How do you explain calculus without limits then?
IT is nearly the same
F~Mm/R^2
Now the R doesn't change that much it would make huge difference
>>7948781
The force is the same, but spans different lengths of time.
The energy is different, which is why one will bounce higher. Look up impulse of force.
>>7949885
Calculus doesn't have anything to do with miniscule change, dy/dx is not a fraction.
>>7950077
It's a limit, if it's a fraction, it's a coincidence.
>>7950211
This specific limit, the limit that describes the derivative of a function is a fraction, isn't it?
Isn't dy/dx is just shorthand for that specific limit of a function y(x)?
>>7950218
It's the limit of a fraction, but the limit usually isn't a fraction and yes, dy/dx is just notation, although it behaves like a fraction in many ways.
>>7948781
Why do you think it would be? Those are two different forces. Force #1 is the gravitational force from the earth on the object. Force #2 is the force from the object on the ground.
The connection between the two forces is that force #1 speeds the object up to a certain speed, and the reaction force to force #2 (from the ground on the object, call this force #3) slows the object down from that speed to rest. You just have to look at F = ma to see why force #3 is greater than force #1. The mass is the same, and the velocity change is the same, but the time force #3 spends accelerating the object is much smaller, which makes the acceleration much larger. And force #2 is equal in magnitude to force #3 because of Newton's 3rd law.
