Physics Help

[!!GC!!]

I need to know how to rearrange this equation for my test on Wednesday.

 

From this equation, i need to rearrange it in order to find t.

 

at² + Vit - d = 0

 

FYI (but you dont actually need it):

a = acceleration

t = time

Vi = Velocity initial

d = distance displacement

 

Thanks to anyone who can help.

Edited April 6, 2009 by !!GameCH33TA!!

[asimov]

Since you do physics I assume you are doing a similar math course. You'll notice this is a quadratic equation, which means you can factorise it. As taken from the first search entry on google for "quadratic solve for x".

 

 

    *  Solve x2 + 5x + 6 = 0.

 

      This equation is already in the form "(quadratic) equals (zero)" but, unlike the previous example, this isn't yet factored. The quadratic must first be factored, because it is only when you MULTIPLY and get zero that you can say anything about the factors and solutions. You can't conclude anything about the individual terms of the unfactored quadratic (like the 5x or the 6), because you can add lots of stuff that totals zero.

 

      So the first thing I have to do is factor:

 

            x2 + 5x + 6 = (x + 2)(x + 3)

 

      Set this equal to zero:

 

            (x + 2)(x + 3) = 0

 

      Solve each factor: Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

 

            x + 2 = 0  or  x + 3 = 0

            x = –2  or  x = – 3

 

      The solution to x2 + 5x + 6 = 0 is x = –3, –2

 

 

source

 

If you can't follow that example don't bother doing physics.

[K^2]

Just use quadratic formula. It's useful to know how to derive it, but for the test, just memorize it.

 

Given: a*x² + b*x + c = 0

 

Solution: x = ( -b ± √(b² - 4*a*c) ) / (2*a)

 

The derivation of this equation comes from generalization of algorithm in asimov's post.

[!!GC!!]

Ah, sh*t. I completely overlooked it as a quadratic.

Ok, so i've just done it as a quadratic using my terms and came up with this:

t = (-Vi + √(Vi² + 4ad)) / 2a

 

EDIT: I see you got the same, K^2. I wasn't sure if it was right.

 

 

Since you do physics I assume you are doing a similar math course.

Good assumption, i am.

 

 

If you can't follow that example don't bother doing physics.

I can follow it fine, and i need Physics for my line of career that i am hoping to do.

 

Ok, thank you both, and thanks asimov for the original quadratic solution.

Edited April 6, 2009 by !!GameCH33TA!!

[K^2]

Keep in mind that it simplifies greatly when Vi = 0, which is often the case. I suggest you work out solution for this special case in advance, because it can save you a lot of time when solving simple projectile motion problems.

 

Edit: By the way, if you need real Physics, I have bad news for you. This doesn't even begin to scratch the surface.

[!!GC!!]

 

Keep in mind that it simplifies greatly when Vi = 0, which is often the case. I suggest you work out solution for this special case in advance, because it can save you a lot of time when solving simple projectile motion problems.

Yeah, i understand that it would make it a lot easier, but the example i have makes Vi = 2.4ms-1

 

 

Edit: By the way, if you need real Physics, I have bad news for you. This doesn't even begin to scratch the surface.

Good. Thank god i am only 16 so i have time ahead of me to learn it all.

 

 

because it can save you a lot of time when solving simple projectile motion problems.

We're kind of doing a mixture of angular momentum and relative velocity at the moment. Im just hoping i can teach myself this sort of stuff so i can excell in the class. Our teacher is hopeless.

[K^2]

Do you have the basic Newtonian Mechanics covered? F=ma, conservation of linear momentum, Kinetic/Potential Energy, etc?

 

Typical progression is like this:

 

Newtonian Mechanics

Electricity and Magnetism

Optics

Classical Mechanics

Electrodynamics

Special Relativity

Quantum Mechanics

Statistical Mechanics

Solid State Physics

Particle Physics

Relativistic Electrodynamics

Quantum Field Theory

Condensed Matter Physics

Relativistic Quantum Field Theory

General Relativity

Quantum Gravity

 

Needless to say, few people get through the whole list. I'm somewhere in RQFT/GR area right now, and I doubt I'll get to Quantum Gravity. Dirac's Equation in curved spacetime is entirely too silly.

[!!GC!!]

 

Do you have the basic Newtonian Mechanics covered? F=ma, conservation of linear momentum, Kinetic/Potential Energy, etc?

Well, most of that was covered last year, but we went more into it this year and finished that a few weeks ago.

 

 

Typical progression is like this:

 

Newtonian Mechanics

Electricity and Magnetism

Optics

Classical Mechanics

Electrodynamics

Special Relativity

Quantum Mechanics

Statistical Mechanics

Solid State Physics

Particle Physics

Relativistic Electrodynamics

Quantum Field Theory

Condensed Matter Physics

Relativistic Quantum Field Theory

General Relativity

Quantum Gravity

Yeah, that would be hard to get through completely.

We aren't doing that many things, but it'll get carried through to next year where we will probably do it.

 

Our year so far:

Optics

Wave Phenomena (basic, easy as)

Linear Motion

Newtonian Mechanics

Electricity and Magnestism (half of it to come yet)

 

And to come:

Classic Mechanics

Stat and Quantum Mechanics

Quantum Field Theory

A few others that i cant remember and dont recognise from that list.

 

What level are you learning at?

(Might be different for other countries, though)

[K^2]

I'm finishing up coursework for the Ph.D. I really don't think you'll be doing QFT next year. Even basic QM is difficult without good background in partial differential equations. For QFT you need some serious math.

[asimov]

I see you 16 years old, so your in year 11 yeah? You won't be touching on anything close to quantum field theory in high school dude, you'll just do the basics -energy in everday life, movement and electricity-. You won't do anything close to K^2's level of work until your well and truly started a university physics course of some sort. if your interested there are heaps of books written for a people not as accustomed to the topic that are very interesting though.

 

 

[Rob.]

Hi, don't suppose you mind if I use this topic to ask another physics problem?

 

Topic: moments of inertia

 

 

Consider a uniform, thin rod of length L and mas M

 

(a) Find the moment of inertia of the rod about an axis that is perpendicular to the rod and through one end. [5 marks]

 

(b) The rod is held vertically with one end on the floor and is then allowed to fall. use energy conservation to find the speed of the other end just before it hits the floor, assuming the end on the floor does not slip. [8 marks]

 

© You have an additional point mass m that you have to attach to the rod. Where do you have to attach it, in order to make sure that the speed of the falling end is not altered if the experiment in (b) is repeated? [7 marks]

 

My main problem is with part ©;

 

Part (a); I = M(L^2)/3

Part (b); omega = root*(3g/L)

Thus speed = omega*r = L*root*(3g/L) = root*(3gL)

 

Part ©; My reasoning is that the point mass must be added to the pivot, at a distance r=0. As it is only then that the moment of inertia of just the point mass can then be zero, thus unaffecting the resultant moment of inertia of the entire rod, and by consequence maintaining the value of I calculated in part (b). However, this is worth seven marks, and I can't see whether or not i'm supposed to do more.

 

Cheers to anyone who can help me out.

[!!GC!!]

 

I see you 16 years old, so your in year 11 yeah? You won't be touching on anything close to quantum field theory in high school dude, you'll just do the basics -energy in everday life, movement and electricity-. You won't do anything close to K^2's level of work until your well and truly started a university physics course of some sort. if your interested there are heaps of books written for a people not as accustomed to the topic that are very interesting though.

No, 16 years old is Year 12 over here, which is what im in. But, i am doing University Entrance Yr 13 Physics work.

I know that we wont be taught down to the details of QFT, but our teacher said that if we have a spare 1 or 2 weeks towards the end of the year, then he'll just give us some notation on it that we can do before we head to uni.

That's why i put it last on the list, because we might scratch the surface of it.

 

@Rob: Sorry, i cant help you. Im not familiar enough with those terms and i've been taught I = Impulse and i cant get it into my head that im trying to work out inertia.

These other guys are sure to help you out, though.

[K^2]

 

Hi, don't suppose you mind if I use this topic to ask another physics problem?

 

Topic: moments of inertia

 

 

Consider a uniform, thin rod of length L and mas M

 

(a) Find the moment of inertia of the rod about an axis that is perpendicular to the rod and through one end. [5 marks]

 

(b) The rod is held vertically with one end on the floor and is then allowed to fall. use energy conservation to find the speed of the other end just before it hits the floor, assuming the end on the floor does not slip. [8 marks]

 

© You have an additional point mass m that you have to attach to the rod. Where do you have to attach it, in order to make sure that the speed of the falling end is not altered if the experiment in (b) is repeated? [7 marks]

 

My main problem is with part ©;

 

Part (a); I = M(L^2)/3

Part (b); omega = root*(3g/L)

Thus speed = omega*r = L*root*(3g/L) = root*(3gL)

 

Part ©; My reasoning is that the point mass must be added to the pivot, at a distance r=0. As it is only then that the moment of inertia of just the point mass can then be zero, thus unaffecting the resultant moment of inertia of the entire rod, and by consequence maintaining the value of I calculated in part (b). However, this is worth seven marks, and I can't see whether or not i'm supposed to do more.

 

Cheers to anyone who can help me out.

Pivot works, but that's not what the problem is asking for. Use the conservation of energy again. For the rod you had:

 

omega²*M*L²*/6 = M*g*L/2

 

That's what you use to get answer to b). Now, you also have a point mass m at distance R away. You get:

 

omega²*M*L²/6 + omega²*m*R²/2 = M*g*L/2 + m*g*R

 

You already know omega, so it simplifies things a little:

 

M*g*L/2 + m*g*R²/L*3/2 = M*g*L/2 + m*g*R

 

R*3/2 = L

 

R = 2*L/3

 

Edit: Note that I divided through by R while solving this. That's where you can put in your other solution: R = 0. If your teacher is anal about it, you might want to show both solutions. But do use conservation of energy for reasoning for both positions. That's the proper way to address the problem. Not that there is anything wrong with your reasoning.

[Rob.]

Hi, don't suppose you mind if I use this topic to ask another physics problem?

 

Topic: moments of inertia

 

 

Consider a uniform, thin rod of length L and mas M

 

(a) Find the moment of inertia of the rod about an axis that is perpendicular to the rod and through one end. [5 marks]

 

(b) The rod is held vertically with one end on the floor and is then allowed to fall. use energy conservation to find the speed of the other end just before it hits the floor, assuming the end on the floor does not slip. [8 marks]

 

© You have an additional point mass m that you have to attach to the rod. Where do you have to attach it, in order to make sure that the speed of the falling end is not altered if the experiment in (b) is repeated? [7 marks]

 

My main problem is with part ©;

 

Part (a); I = M(L^2)/3

Part (b); omega = root*(3g/L)

Thus speed = omega*r = L*root*(3g/L) = root*(3gL)

 

Part ©; My reasoning is that the point mass must be added to the pivot, at a distance r=0. As it is only then that the moment of inertia of just the point mass can then be zero, thus unaffecting the resultant moment of inertia of the entire rod, and by consequence maintaining the value of I calculated in part (b). However, this is worth seven marks, and I can't see whether or not i'm supposed to do more.

 

Cheers to anyone who can help me out.

Pivot works, but that's not what the problem is asking for. Use the conservation of energy again. For the rod you had:

 

omega²*M*L²*/6 = M*g*L/2

 

That's what you use to get answer to b). Now, you also have a point mass m at distance R away. You get:

 

omega²*M*L²/6 + omega²*m*R²/2 = M*g*L/2 + m*g*R

 

You already know omega, so it simplifies things a little:

 

M*g*L/2 + m*g*R²/L*3/2 = M*g*L/2 + m*g*R

 

R*3/2 = L

 

R = 2*L/3

 

Edit: Note that I divided through by R while solving this. That's where you can put in your other solution: R = 0. If your teacher is anal about it, you might want to show both solutions. But do use conservation of energy for reasoning for both positions. That's the proper way to address the problem. Not that there is anything wrong with your reasoning.

Cheers thank you K^2. My main failures seem to be on obscurities like these, but you've cleared it up for me now.

 

I'm currently in my first year of doing joint honours in Maths and Physics at University. I really enjoy it but it can be hard work. This year is the first i've seen of Quantumn mechanics, the shrodinger equation I find particularly interesting, well, allbeit in one dimension.

 

 

[Breaking Bohan]

How did the test go?

 

 

We all hope you got the correct answer - and we hope you will share that with us.

 

Many thanks!

[K^2]

This year is the first i've seen of Quantumn mechanics, the shrodinger equation I find particularly interesting, well, allbeit in one dimension.

It's exactly the same in 3 dimensions.

 

In general, for pretty much any QM equation.

 

H * Psy = E * Psy

 

E = i*ħ*d/dt

 

Specifically for Schroedinger Equation:

 

H = p²/2m + V

 

In 3D the momentum operator is given by:

 

p = ħ* ∇/i

 

∇ is the nabla operator. It is the vector consisting of partial derivatives in each direction. In 3D:

 

∇ = <∂/∂x, ∂/∂y, ∂/∂z>

 

And so the time-dependent Schroedinger Equation takes form:

 

- (ħ²/2m) * (∂²/∂x² Psy + ∂²/∂y² Psy + ∂²/∂z² Psy) + V = - i*ħ*d/dt Psy

 

If V is equal to zero, the solution is a set of plane waves:

 

phi(k,r) = exp(i*(k·r-omega*t))

 

With wave vector k = p/ħ, at position r, and with frequency omega = p²/2mħ

 

As you can see, it's almost identical to one dimension.

[mr_bungle]

Damn, how do you people understand this stuff? I don't even get quadratics in maths

[K^2]

Damn, how do you people understand this stuff? I don't even get quadratics in maths

It's actually no harder than quadratics. The Schroedinger Equation is just a simple quadratic in p. The only trick is that p is an operator. There is a whole algebra that deals with operators instead of numbers. It has rules very similar to normal algebra, plus a few additional caveats. Like A*B ≠ B*A. So basically, it's just a matter of learning a whole new algebra, and after that, these equations are pretty straight forward. And learning algebra the second time is a lot quicker.

[Swarz]

Hey K^2, can I make you one of my 'Phone a friends' when I get on a TV show?

[Icarus]

Typical progression is like this:

 

Newtonian Mechanics

Electricity and Magnetism

Optics

Classical Mechanics

Electrodynamics

Special Relativity

Quantum Mechanics

Statistical Mechanics

Solid State Physics

Particle Physics

Relativistic Electrodynamics

Quantum Field Theory

Condensed Matter Physics

Relativistic Quantum Field Theory

General Relativity

Quantum Gravity

I need to take an optics course next year and I'm also doing a course in condensed matter, so that should take care of two more on the list.

 

In my SR class, we actually touched base on the surface of relativistic electrodynamics (mostly line charges on infinitely long wires or two infinitely large plates separated by a distance d), but most of us were confused as hell as the professor sucked and our electricity and magnetism course from the previous year was no help (we didn't learn a thing) and our electromagnetic theory course was the following semester.

 

I also know I will not see a GR course; SR was not my strong-point, so I believe I will be avoiding GR like the plague, which is kind of a shame, because my stat mech prof last term said his greatest failure of his undergraduate career was never learning about GR.

 

Schroedinger's Equation in 3D is beautiful.