Physics Forums - Classical Physics

Current leading voltage or vice versa concept

Woopydalan — Tue, 21 May 2013 04:45:26 GMT

Hello,

I was wondering if there is a conceptual explanation for when current leads voltage or vice versa for capacitors or inductors with AC voltages, or is it just the way the math pans out?

Angular Frequency of AC voltage

Woopydalan — Tue, 21 May 2013 01:33:06 GMT

Hello,

I am wondering, what is the physical interpretation of the angular frequency of AC voltage? I don't see the physicality of what the angle for which there is a frequency?

I understand that the voltage can switch back and forth at a certain rate, which jives in my mind with the idea of frequency: How quickly the voltage switches back and forth in its magnitude. However, I don't understand what the angular frequency represents?

Modeling Rigid Body - Unsure about Euler angles and angular velocity

jstluise — Tue, 21 May 2013 01:25:03 GMT

I'm modeling a single 3D rigid body in preparation for some more complicated modeling in order to gain a better understanding of Euler angles, the angular velocity vector and the rotating coordinate system.

The body is rotated in inertial frame by an intrinsic ZXZ rotation, with respective state variables ##\alpha##, ##\beta##, and ##\gamma##. Thus, I have the rotation matrix ##R## that will transform points in the body frame coordinates into fixed frame coordinates...and vise versa.

I have composed the angular velocity of the body frame relative to the fixed frame described in fixed frame coordinates, then transformed this into body frame coordinates by ##\vec{\omega}=R^T{\vec{\omega}}_{fixed}##. My moment of inertia tensor for the body is diagonal, and described in body frame coordinates (lets just call it a sphere).

The kinetic energy of the body is then ##T = \frac{1}{2}\vec{\omega}^TI\vec{\omega}##

I formulated the dynamics using Lagrange's equations, and included torque inputs on each of the rotation variables: ##\tau_{\alpha}##, ##\tau_{\beta}##, and ##\tau_{\gamma}## (which can be zeroed during simulation). I simulated and plotted the behavior in Matlab with various initial conditions and inputs. I also plotted angular velocity vector in both frames.

If I mess with one state variable at a time, the model behaves exactly how I would expect. For example, I can set an initial velocity to ##\beta## and it will spin about the X axis. Or apply a torque ##\tau_{\gamma}## and it will spin about the Z axis.

But, if I include two initial velocities (no inputs), say ##\alpha## and ##\beta##, I would expect it to spin about the Z axis while also spinning about the intermediate X axis. And if the speeds were the same, I'd expect them each to complete one rotation at the same time. Well, the body does have an off axis movement, but not like I would expect. Maybe it is just hard to visualize the body moving about two axes.

I would also expect (I think) the angular velocity vector to maintain the same magnitude and direction; it does maintain the magnitude, but not the direction (in the body frame). Is this not right?

Either my modeling is wrong or I do not fully understand Euler angles. As it is right now with my model, there is no intuitive sense to what the model will do given the inputs. For example, if I did a yaw-pitch-roll rotation, it seems like I could control each maneuver independently from each other...like, say make it roll while yawing. Is this not correct?

If you could shed any light on my throught process for the modeling, that would be great! One thing I was unsure of was what coordinate system (fixed or body) to calculate the rotational KE. I did it in the body frame, but didn't know if I was suppose to transform everything to the fixed frame.

Function for a bullet's path

lss1 — Mon, 20 May 2013 23:56:42 GMT

I've been mulling this over all weekend, and I've decided to get some help on this. The problem is writing a function to describe a bullet's path. I've asked two people about it my Physics teacher (who said he didn't know how) and my French teacher, who was a nuclear engineer for the US Navy (who said it was impossible). I don't know much about ballistics, but I am very willing to learn.

My Physics teacher started out with the equation $$y = v_y t + \frac{1}{2} a t^2$$ and the equation $$x = v_x t.$$ So I've been looking for a way to combine these two functions. I asked my French teacher about it and he said it was impossible because at the beginning of the travel-path, the motion is dominated by the x-component, and as it goes on the velocity in the x-direction slows down, and the y-acceleration becomes more dominant. He said that as the motion changes from x-dominated to y-dominated, the variable, t, becomes two different variables, and therefore cannot be written in the same function. I've been thinking it could work as a multivariable function, but I'm not sure.

Any help would be gratefully appreciated.

Elementary questions relating to Newton's laws of motion

chipotleaway — Mon, 20 May 2013 22:31:11 GMT

i) If a wall breaks when it gets hit by a cannonball, did the wall exert an equal and opposite force on the cannonball?

ii) Would the force exerted by the cannonball on the wall only be the amount that was needed to break it?

iii) Hypothetically, is it possible for the wall to break but also cause the cannonball to rebound?

Magnetic Energy of Solenoid With/Without Core

dgreenheck — Mon, 20 May 2013 22:25:18 GMT

I have a question about solenoids.

The formula for the magnetic field energy density is:

[itex]\frac{1}{2}\frac{B^{2}}{μ}[/itex]

If I have an air-filled core, then μ=μ₀. If I have a steel core, then μ will be ~ 100μ₀. This implies that an air-filled core solenoid stores more energy than a steel core solenoid since the denominator for the air-core case is smaller.

Doesn't this contradict the fact that solenoids with a ferromagnetic core produce stronger magnetic fields than a solenoids with no core?

Static Equilibrium and D'Alembert's Principle

Astrum — Mon, 20 May 2013 22:01:26 GMT

Virtual work principle states: [tex] δW = \sum^{N}_{i=1}\vec{F}_{i}\centerdot δ\vec{r}_{i}[/tex]

And from this, we can see that if a system is to be in equilibrium we have

[tex]δW = (\sum^{N}_{i=1}\vec{F}_{1} \centerdot \frac{\partial \vec{r}_{1}}{\partial q_{1}})δq_{1} + \cdots = 0[/tex]

Where did q come from? It's the rate of change of r with respect to a generalized coordinate?

[tex]\sum_{i} (\vec{F}_{i} - m_{i} \vec{a}_i ) \centerdot δ \vec{r}_{i} = 0[/tex]

F_applied-ma = F_constraint

the applied force, subtracted by the total acceleration of the system, doted with the virtual displacement in the r direction equals zero? This would mean that the force applied would have to be equal to zero in the direction of the displacement. What does this equation actually tell us?

What do YOU think the most important FirstYear Phys topic is?

martinlematre — Mon, 20 May 2013 21:56:02 GMT

I'm kind of rushing through first year physics cause im doing it self paced, but I am realizing now that as an engineering i relaly need to internalize and fully understand these lessons. I don't have much time to go over everything again, but what would yo usay the most important lesson/topic/thing to internalize is in first year physics? (in terms of vector decomp, angular speeds or accels, forces, work/energy etc)

I havent started on electromagnetism yet but idont have much time so i may end up rushing through that as well. i looked through some of the formulas and they dont seem complicated at all (parallel/series circuits and whatnot)

Magnetic field and repulsion bewteen wires

gralla55 — Mon, 20 May 2013 18:36:24 GMT

If you place a wire with a running current in a magnetic field, the magnetic field will excert a force on the wire. So, if you place two wires parallel to each other, the current on each will produce a magnetic field, which in turn will attract or repulse the other wire depending on the direction of the current.

What I don't get, is how the magnetic field from wire a reaches wire b. If you look at drawings of magnetic field lines between wires, the total field does not seem to run through the wires at all, as the magnetic field generated from wire a, "deflects" the field generated by wire b.

This is what I'm talking about:

What am I missing?

Enthalpy of reaction

susdu — Mon, 20 May 2013 12:44:37 GMT

Given some chemical reaction, A+B -> C+D (all are ideal gases) that occures in 298K and 1 atm.
why can't I automatically say that ΔH=0 for this reaction?

I know that enthalpy is a state function that is dependant on temperature alone (for an ideal gas),
and the final and initial temperature are the same.

Harmonic oscillation problem -Dancing pot

ROBwithaB — Mon, 20 May 2013 12:02:56 GMT

http://youtu.be/FZiBezCMUck
Can anyone help to explain what is going on here?
What are all the variables that might influence the frequency of this oscillation?
Thanks

Ultracapacitor to power electromagnet?

Pharrahnox — Mon, 20 May 2013 11:25:28 GMT

I have been looking for a better way to power my electromagnet than a bunch of AA batteries, and am now thinking of using ultracapacitors.

I have a few questions.

I have been looking on ebay for them, I don't know of better options, and I have seen mostly 2.7V with >1F, up to 1500F. One in particular has grabbed my attention 10X 2.7V 10F ultracapacitors, for < $25, and they are stated to have: ESR (mΩ, 1KHz, 25℃) : 60

Does that mean that it has 60mΩ of resistance, therefore a maximum current of 2.7/0.06 = 45A?

What are the pros and cons of using capacitors as the power source for an electromagnet?

I think the resistance of my magnet is about 6-7Ω, so 2.7/6.5+0.06 = 0.41A. So I don't think the current would be too much, and I can always add more turns of wire (I have about 2500).

How could I connect the capacitors so that I can get more amperage? I know that connecting them in series adds their voltages, and decreases capacitance, but would that then also increase the resistance, rendering it useless?

Also, since the capacitors are rated at 2.7V, how do I charge them? I don't know of any 2.7V power sources... Also, is it possible to safely charge them off mains power, using a step down transformer?

Are there many dangers of what I am trying to do with these capacitors? If so, I would like to know, so I can prevent any injury or damage to myself or to the electrical circuits involved.

Thanks for any responses. Sorry about all the questions.

Confusion in Electro Statics

Sandi Gokul — Mon, 20 May 2013 10:57:11 GMT

During electrostatic induction,a posivitiely charged body is brought near to a uncharged body.During this uncharged body gets bound negative change toward the end of the body near to charged body.
My question is in reality what happens to the electron and proton of uncharged body.Do the all electron of far end comes to near end or what???????????????

simple gravity question

joshmccraney — Mon, 20 May 2013 09:45:43 GMT

hey all!

can anyone please explain where the equation [itex]{Gmm_e}/{r^2}={mgR^2/r^2}[/itex] comes from given $$ma=Gmm_e/r^2$$ where [itex]G,m,m_e[/itex] are the universal gravity constant, mass of object, earth's mass and [itex]r[/itex] is the distance from center of earths mass and [itex]R[/itex] is radius of earth

thanks!

I need help understanding the Fourier components of a square wave

jeff.berhow — Mon, 20 May 2013 07:57:54 GMT

In my physics book there is an example of making a square wave by "simply" summing up a few cosine waves. The book says these first three waves are the first three Fourier components of a square wave, yet when I sum the three wave functions up, I get something way off; as does my calculator.

For example, if we take the easiest case of x = 0, we get the sum of 1, 1/3, and 1/5 equals 1.53m. However, when I look at the plot for the sums, the amplitude seems to be at about 0.9m. That is nowhere near the sum of the three wave functions at zero. This means that I am missing something fundamentally important here. What is it?

Here's a link to the graphs and the example problem. Thanks for your help.

http://i.imgur.com/DrjU0VE.jpg?1