Thanks everyone for the explanations.
The problem here was that I expected the function to have a local maximum and when the derivative showed me it had none, I thought I must have done something wrong but now I realize that there is no reason for the function to have a maximum.
We can...
Hi, here is a very simple solution mixing problem that I can't solve which I am really ashamed of.
Problem. A vessel whose capacity is 5 liters contains 2 liters of 15% salt solution. How many liters of 20% salt solution have to be mixed to the 15% solution to produce a solution with as high...
Your advice really simplifies things. Thanks!
I did as you suggested, and solved for i1 (actually I just simplified the system of the three equations and then handed it off for MathCAD to handle - there's too much physics to be bothered by maths here). I got
i_1=-\dfrac{22U_0}{79R},
and...
OK, now I'm trying to solve it using KCL/KVL and expect the same answer. I don't see, however, in what way KCL/KVL should help me determine how the resistors are connected.
First, I redraw the circuit and choose arbitrary currents and loop directions. I also apply a dummy potential U0 across...
Normally I assume the potential to be higher at an input left and lower at an exit right, which gives the overall current direction from left to right. I realize that this may not always be the case but let's just make this assumption for now.
Let me present my reasoning now.
Once we...
Thanks!
I see that in all my excitement I didn't notice that I could simplify the fraction:
3\dfrac{221}{374}=3\dfrac{13}{22}
Follow-up questions:
1. is it correct that in the original problem, potential is higher at 2 than at 3, which makes currwent flow from 2 to 3?
2. is it...
Okay, so this is what I get:
http://o3xn.files.wordpress.com/2012/04/r20120415_12.png
First, I slightly rearranged the circuit to clearly see the delta grouping in it, then I applied the Y-Δ transform, which eliminated node 2 and instead connected nodes 1-3 and 3-4. The equivalent...
I'm having problem trying to calculate total resistance in resistor arrangement like this one:
http://o3xn.files.wordpress.com/2012/04/different.png
Before I go into any more detail with the original problem, I just want to say that whenever I get this "closed" type of circuits, I like...
OK, since there has been no activity here for quite some time, I'll finish this one off just for the fun of it.
Continuing from my previous post, v0 is the initial velocity for the second half of the free fall. It is non-zero and is the same as the final velocity the stone will have...
The general outline of how I would approach this problem is this:
1. calculate acceleration
2. write down Newton's Second Law for this problem (here all the sines and cosines come in)
3. calculate μ (since μ is in R=μN)
Edit: I see that you're asking not about how to solve it but why you can't...
Well you're asked for a ratio, t1/t2. Whenever you're asked for a ratio, chances are that something will cancel from both the numerator and the denominator. And I suspect this may just be the unknown distance/height the rock travels, d.
The equation for d is correct as azizlwl pointed out...
The notion of gravitational and inertial mass arises because there are two different ways to look at mass. First and foremost, mass decides how readily or reluctantly a body will respond to forces that other bodies exert on it. This mass is known as the inertial mass. For example, you can easily...