[Physics] Proportionality?
Good day,
Unfortunately, I don't yet understand proportionality in physics very well.
[TASK]
[SOLUTION]
- I have understood part a) of the task.
- Unfortunately, part b) is not yet available.
What does “h ~ v^2” mean here?
I just don't understand how one can solve such problems as easily as in the solution sentence of the problem.
Perhaps someone can explain proportionality to me in detail using as many examples as possible. Ideally, with a solution as simple as the one in the problem.
It's probably really simple, but I can't seem to understand it.
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Proportionalities are made from the middle stage, partly from 6/7. Class (proportional assignment).
For loose food, the price is calculated by mass…10 kg of potatoes for 3 €. DAS is the proportionality constant! 3 €/kg
Double mass (20 kg) => double price (6 €)
triple mass (30 kg) => triple price (9 €)
half mass (5 kg) => half price (1.50 €)
The price is proportional to the mass (price ~ m)
This principle applies, for example, to density, speed, resistance, work, performance, …
Later, other dependencies occur, e.g. square dependence.
In the case of uniform acceleration, the distance covered is proportional to the QUADRAT of time, i.e. s~t2. that can be recognized by the formula s=1⁄2×a×t2.
In the case for double time to four times the distance, three times the time to 9 times the distance, but half the time only to one 1⁄4 of the distance.
HERE is now only proportional to the root of height (v~h^1⁄2).
A doubling of the height changes the speed only by a factor of 21⁄2 (1,41)! Only a quadrupling doubles the speed, a quadrupling of the height only triples the speed.
“In the case for double time to four times the distance, three times the time to 9 times the distance, but half the time only to one 1⁄4 of the distance. ‘
I understand how that means, but not why it is.
It is given in your example s~t^2. Then why don’t you use the time, e.g. starting time 10 seconds, so do I use 10s * 2 = 20s?
Why can I just use a two here?
I think I’m wrong.
Well, it’s time to start, but then it’s time to square it!
So (10 s)2=(10 s)×(10 s)=100 s2
Not every connection is a proportional one!
And when falling, the speed does not double when you double the height, but only by a factor of 1.41 (Wurzel 2, 21⁄2)
But one can immediately make an equation from a proportionality by introducing the proportionality factor! Generally this would be k, in math it is the slope, e.g. m. In the case of known relationships, it is itself a known size!
U~I => U=R×I
m~V => m=ρ×V
F~s => F=D×s
W~t => W=P×t
v~√h => v=k×√h …. Then the equation would be. But you can also save the step! By the way, k=√(2g), which is a constant (on the earth). The result is:
v=√(2g)×√(h) or v=√(2gh)
THAT would result from the equation of your bill if you were to re-form v2=2gh…In my eyes, incomprehensible that in the pattern solution you have not completely dissolved to v before h is used!
I thought that one can only change equations with “=” with “|” (e.g. as above “|Wurzel” and not equations with “~”.
Yeah, that’s like an equation.
MMn is even more correct!
For ‘h~v2’ actually means that ‘the height is squarely proportional to the speed’, which is actually only true when you shoot something perpendicular in the sky!
Here, however, the speed is rooted from the height, which is why the formula should be written differently:
So in an exam, I can also make this bill:
‘h ~ v^2 |
v = root h
Root 5 * 10 km/h = 22.36 km/h?
Then I would have understood it!
Yes, it does. It’s like a three-set, but it’s just as easy to work with proportionalities!
With potatoes, you would also take the factor “simple”…50 kg instead of 10 kg…Only that one has to consider the root here!
v2~h | √x
√(v2)~√(h)
v~√(h)
increases h by factor 5, increases v only by √(5)!
v=10 km/h at h1, => √(5×h1) ~ √(5)×10 km/h
At the time of Newton, you’ve only been so excited! Today we have formulas, can either calculate intermediate values (potential E) and then use them in the next formula (kinetic E), OR you both conceive and create a new general formula.
Why is it enough to use only the factor for v (speed) in “h ~ v^2” to find out which factor the speed changes?
And if the task is:
“How fast is maximum speed when the height is open? The speed at a simple height is 10 km/h.’
I have to do this:
h ~ v^2 |Wurzel
v = root h
Root 5 * 10 km/h = 22.36 km/h?
Can you even change “h ~ v^2” with “|Wurzel”?
Actually, it’s quite simple if it makes it quite general:
‘h ~ v^2’ (h proportional to v2) means nothing other than
and it doesn’t matter exactly what “α” is for the question. It can be a completely complicated break from constants and Other Being variables or a simple number – does not matter for the following.
Now v is to be doubled:
So: doubling of “v” leads to factor 4. The game can always be done and it always turns out that the factor is also subject to the potency law. A 3 times large ball has 33=27 times the volume; a sphere with half radius the 1/23=1/8 of the volume, since VK ~ r3 (and “α” would be here 4π/3 to stay in the example)
And at some point, it’s enough to have counted it forty times. You know what the bill will make.
energy conservation,
1/2*m*v^2 = m*g*h, so
v^2/2 = g/h
So v^2 ~ h (~ means proportional to), with proportionality factor 2*g, since v^2 = 2*g*h.
You solve the tasks with exactly this energy conservation.
In the solution they somehow simply calculated it, simply 2 used in v^2 and then wrote that the double speed belongs to four times the height. I don’t understand how to calculate it in this way. Why did they use only 2 in v^2 and not the (old speed * 2)^2?
Yeah, it’s right. Double speed is the original speed twice.
Because the proportionality is sufficient to get to the “fourfold”.
Edited the comment
What you can’t understand will mean Knowledge denotes.
If two things clearly depend on each other, it is also called Function! The speed depends on the height of the fall! And as she is, tell you a series of experiments. No matter how many attempts you set, the equally tracked dependence on daylight => is the proportionality. Mathematically you can say: to each y belongs an a*x
y=a*x
What would the function that is needed to answer the task in my question look like? What would be the solution you can write in an exam?
“y = a*x” in physics you must always use v for speed and h for height. In addition, “h ~ v^2” applies – where is this high 2 in your function?
x and y are so-called parameters or arguments, select one, then the other element is automatically determined (it works!). As they are destined, nature hides behind it. Read that a. so: “the one element (v) rise into the square!” The Tlde ~ stands for proportionality.
if B doubles, A also doubles. Thus A is proportional to B.