carrotstien

thanks Mr Skeptic. I understood that, but for some reason after you said it it all began to make sense. The speed gets changed by the tangential force, while the perpendicular force later takes this increases speed and changes its direction.

I understand that from the laws of conservation of momentum and energy the velocity must increase. That, however, doesn't answer my question. My question is of a lower level than that. Why is the speed of an oject moving in a circular orbit always constant, or why does the speed of a charged particle moving in a magnetic field always constant (not counting radiation losses), because the force is always perpindicular to velocity, so that it can only change the direction but not the magnitude. In the elliptical case, the force is always perpindicular the perpindicular componant of the velocity, perp to the r vector, so I don't see why by the same logic does the perp velocity change. Once again I'd like to point out that I understand that it must in order for conservation to work, but that doesn't explain the source of the force. Maybe i'm just thinking this in a wrong way.

Take earth orbiting the sun. The path that earth takes is an ellipse where the sun is at one of the foci. At one time, earth is the closest to the sun and moving the fastest, while at another time, earth is farther from the sun, and travels slower. My question is thus: Lets say you take the velocity at any moment and you seperate it into two components, one parallel to the line connecting earth and the sun (the r vector), and on perpindicular to the r vector. Since the force between earth and the sun is always in the direction parallel to the r vector, and always perpindicular to the perpindicular component of velocity, how does that component of velocity change from the min to the max and so on? I understand the need for it to happen due to conservation laws, but I don't see the forces the cause the effect.

I understand that that the outside are accelerating faster than the inside. But, why would anyone of these be invalid (when the mu's are high enough to sustain them) ~sum of forces from outside tires = mv^2/R and the other tires don't do anything. where mass of car is M and radius of center of mass' motion is R ~vice versa ~each tire applies the same force as long as the sum of all the forces is mv^2/R and torques add to 0 I am not sure about the last one, but the first two are perfectly feasible since they are describing a 2 wheeled motorcycle with a center of mass off the line connecting the tires - which is algebraically solvable. The reason i'm asking if one set of tires worked to its max first before the other in some way is because i was thinking of the following cases: If you have block [A] and touching horizontally on a table like [A]; ~you apply a force on block A horizontally to the right. What is the force of friction that excerts on the table? - well, that depends if the force of max friction of [A] has been brought to its limit. Only when [A] starts to try to move, then starts helping along. ~what about if in the same case, you have a rod connecting the two blocks together through their centers; then you apply a rightward force on the rod. You know that if its not slipping, then the sum of frictional forces have to be equal to your force, but that doesn't tell you the distribution. Would it be 50-50 until one can't add anymore? Or would it be something else entirely such as the increase of force of friction is a certain percent of the max of each simultaneously. So if block [A] has a max static friction of 100 newtons, and has a max of 10, then when [A] resists with 10 newtons, resists with 1, and when [A] resists with 20, resists with 2, and so on.

When the car is moving in a circle at a constant velocity, how would you figure out the forces that come from each wheel (in the case that the max friction of each tire is much greater than anything encountered). For a motorcycle i figured it out easily - it comes out to simple solving two equations: sum of torques around center of mass = 0 sum of forces on body = centripetal acceleration = mv^2/R = mRw^2 This can even be solved for a two wheeled car, where instead of the other set of wheels, you have frictionless pegs. Is there a way to solve it, or does it work in a way that the inside tires are put up to their extreme, and the outside tires try to make up anything left? Or vice versa? But either way, how would you figure out which tires starts to slip when if the car is turning with sand and debri lowering the friction of any chosen tire? Roman

There is a thin ring of mass M radius R. At each direction, north, south, east, and west, you have a rocket that pushes with a constant F newtons. Each rocket push vector is Nx,Ny, Ex,Ey, Sx,Sy, and Wx,Wy. The ring's center of mass is moving at V so that Vx and Vy are the components of velocity in the x and y direction respectively. The ring is also spinning with an angular velocity of Z radians per second clockwise. The rockets are much lighter than the ring so that they don't really affect any calculation due to their relatively small mass. What are the linear and angular accelerations of the ring?

nice, i would have loved to try that, but i don't have any dominoes. I did something like that with heavy backgammon pieces, but there aren't that many of them, and they obviously weren't standing on their smaller sides

I was under the impression that 'universe' meant everything everywhere, which is made up of, matter floating around in space. Space, is just a container for matter. So the question is how large is this container. (atleast i think thats the question), because if the question is about the size of the volume whose boundaries are defined by actual energy/matter being there, then the question isn't whether space ends, but whether there is a limited amount of matter in the universe spread over a finite volume at any specific moment (so that volume is expanding.) Otherwise, if space is only where energy exists, that results in the paradox of motion - can something move in such a way that the next place its at, is only available to be at, because it will be there; sort of like building a bridge while crossing it.

When you say that the universe is expanding, do you mean the volume taken up by mass, or the actual region that mass could theoretically take up space in. If you are saying that space itself is expanding, how fast is it expanding. If the size of space depends on mass, then i guess the rate of expansion of space can't be the speed of light. So what would happen if you travel faster than the rate of expansion till this ever expanding edge? I imagine a cup of honey. You pour all of it onto a table. At first, you get a thick bulging circle of honey. As time progresses the radius of this circle gets larger and larger and the height if the circle/bulge gets smaller and smaller. In that case you can easily get to the edge and beyond, since it is traveling slower then you finger could easily move. Whats beyond it...the table - so the honey, while being the 'space' in the sense that it is the region that could be occupied by honey bubbles, anagolous to stars, it still exists in a larger region that can be occupied by honey univererses, just as my #4 suggests, the table, which exists in my house, which exists on earth and so forth and so forth. Unless when you mean that space is expanding, you mean to say something else.

If after the explosion all the mass makes a circular distribution as you would expect from an explosion, then the gravity starting from the boundary of the distribution acts as though all the mass is at the center of the distrubtion. So, as the radius of distribution gets larger, each piece of matter gets further and further away from the center. If at any time all the matter forms a circular distribution, then the center of the circle along the surface of the sphere is at two points at all times. So, in a sense, a point at one pole, is a circle of a radius equal to half the circumference of the sphere with respect to the other pole. What is energy lose, friction, heat, em radiation. Besides mechanical energy loss, all other energy loss is due to em radiation, which you could imagine tries to spread itself out all over the sphere. (maybe we call this background radiation, sorry that i don't know enough about this to really be certain) Other than that, there is no energy loss from the system, if you define the system to be the whole surface of the sphere. All things being equal, entropy isn't really related to energy and work, its just a measure of pattern-ness. There are infinit more unpatterned setups then patterned setups, so that it would mean that to make order, it is likely that some non random action is applied to change it from the more likely disorder. Imagine if I take a bunch of nuetral particles and position them to form my name. This is a very level of order you may say, but that doesn't mean that it took energy for me to make it, since if all the particles started motionless in a bag, and i moved them to their final motionless positions (relative to me as the observer) i did no work, and yet created an obviously un-entropic (?) situation. So, the fact that entropy tends to increase is just an logical observation that comes from the fact that an overwhelming majority of random actions, push a system away from order then toward order. I don't like the idea of black matter, because it is something that our formulas predicts but something that has never actually been verified. Black holes make sense, and i'm pretty sure that we have observed enough stars at enough stages in their lives to see how a creation of one is very likely. Black matter - ok our formulas predict it, but do we have any other reason to say that its there? What if our formula so far accurately predict everything we have observed, but fail to accurately predict other cases (which we attribute to black matter) Just as there is a unique polynomial of Nth degree that fits to a statistical data plot of N+1 points, and there are infinite polynomials of higher degree that fit to the same plot. If our formulas are analogous to a polynomial of slightly higher degree then the minimum, then we could be predicting something that isn't there.

i attached a Word document, maybe its easier to read with the sub and super scripts and *'s math.doc

This is by far the most philosophical question of physics. Possibilities: 1: The shape/size/geometry of the universe is something that we cannot actually mentally grasp so that we cannot say anything absolutely true about it. 2: Space is infinite in a way that you can, if you lived forever and space didn't blink out of existence for any unknown reason, travel in a perfectly straight line (somehow garanteeing that is perfect) and go on for an infinite amount of time without ever seeing anything perfectly repeat or every reaching a limit/boundary. 3: Space is something that is bent/warped in such a way that traveling in a straight line would make you eventually come back to the place you started. 4: Or space as we know is, is a piece of other space(s) which are inturn smaller pieces of other space(s) and so forth and so forth until one of the prior possiblities become correct (unless they never do in which case the box in a box in a box goes forever which is kind of like #2). If its #1, then we can't even try to talk about it since by definition its something we can't even begin to imagine. If its #2 then we get to a rather interesting peculiaraty mentioned earlier that makes the mass in the universe be a small speck/dot of volume of the whole infinite thing. (unless there are infinite packets of mass extending forever in this infinite universe. If there are an infinite # of packets then each packet would stay where it is because the gravity from other packets would be equal in all directions.) Other than the small oddities #2 cannot ever be prooved since we or a light beam we shine can't ever get to the other end (which doesn't exist) and bounce back to let us know that its there (which it isn't) #3 is my favorite since it, IMO fits perfectly which why the mass in our universe is expanding now. I will explain this at the end of this post. A problem that arrises from #3, or rather a couple of problems that arise are: a. If it is bent, what causes the bending? b. If it is bent in the nth dimension, what if we learn to travel in the n or n+1th dimension, can we go past the bend? (this of course is a byproduct of my mental cartesian thinking so it might not even make sense) #4 is just as unprovable as #2 except now, you can say for certain that there is an infinit amount of energy in the whole universe of universes of universes of.... I don't like infinit energy cases of anything since they would allow perpetual work causing motion if we figure out how to harness energy from this infinit sink. ------------------ my theory on how #3 is beautiful Lets say that the universe is warped in such a way, that if you were to subtract 1 dimension from all the geometries the universe would be shaped like a sphere. So that our 3d universe becomes the surface of the sphere. Some time ago, all the matter, for one reason or another was at a point. Now, for some reason or another, it went BOOM! And all the matter started moving away from this point. Lets say, that this sphere has a north pole and a south pole. Let the north pole be the start of the explosion. As all the matter moves away from the pole, its gravity tries to slow down expansion, and at the same time, gravity gets weaker and weaker. When all the matter is at the equator of this sphere, and if it still has kinetic energy, it will overshoot and keep going. When all the matter is at the equator, the gravititation force pulling all the matter towards the center of the expansion (the north pole) becomes very weak, and at the same time, equal to the gravitation force towards the south pole. Now, as the matter keeps moving the northgravity gets weaker, and the south gravity gets stronger, and the matter accelerates towards the south pole. Eventually all the matter will reach the south pole, be all at one small, or very small point/area, and then, for the same reason that it all went BOOM the first time around (or the last time around) it goes BOOM again and starts the process all over again. Now, i don't have a phD in physics and i'm only going into my 4th term of college, but I have to say that this seems pretty logical for me. It doesn't require any weird black matter, or anti gravity and explains why our universe is accelerating its expansion, since this idea, if it was true, would mean simply that the mass in our universe as past the equator. I guess this can be verified (since no experiment could actually prove anything) by comparing the rate of change of acceleration (which my math text book calls jerk ), to the rate predicted by this model. - Roman R.

Kinetic energy is something which is actually relative. If I am moving along a straight road at 1m/s and i have a mass of 60kg, what is my kinetic energy? Could you say that it is 60kg * (1m/s)^2, what about that velocity, to some viewers I could be seen moving at .5c in one way or .6c the other way or not moving at all. About the ball: You are doing work to the ball by slowing it down, this work is equal to F dot X which ends up to be -FX. So you are doing negative work. If you count the kinetic energy of the ball before hand add (-FX) you will get 0 which explains why you see the ball stop. The fan situation is similiar to if you were to take a ball and wiggle it back and forth. Each time you accelerate the ball, you apply a force over a distance so you are doing work. This work could be negative or positive depending on the direction, but that is just bookkeeping. The only reason you get tired is because your arm isn't 100% effecient. Imagine if your arm was, or if the ball was bouncing on a perfect spring with no air resistance attached to an unmovable object (lets say the earth, since the balls affect on the earth is negligable). The ball will bouce forever. So energy is not being lost at any time. It get converted between kinetic energy, potential energy of the spring and potential energy of gravity. The sum of all those energies is always equal to the energy put into the system to begin with. This is easier to think about then the motor and the fan because the potential energy is different. There, even if you were to use superconducting wire, you would still need to do work to accelerate the fan and decelerate the fan due to the lorentz force and the eddie currents that arise. Because the work is negative when u slow it down and positive when u speed it up, it all adds up to 0. I would imagine that if u did use perfect wires than the battery would not do any work to decelerate the fan, because the fan would send a voltage back through the battery causing the total voltage around the circuit to be 0. If you used a perfect rechargable battery, or even a very large capacitor instead, than you would have the same case as with the perfect spring and ball.

If you have a rod, or more simply 2 very small masses connected by a massless rod of length L (each mass being equal; M kgs.) You then connect a massless rocket thruster an x distance to the right of the center of the rod so that the thrust is always F newtons perpendicular to the rod. How would the system behave? O, and before people start saying how massless things don't work, then say that the mass of the rod is .0000000001 * M and the material behind ejected out of an equally light rocket is lighter a million times lighter than that, but is going at a very very large velocity close to the speed of light so that its dP/dt = F This is how I tried to solve it: α - angular accel α1 - angular accel of mass 1 α2 - angular accel of mass 2 τ - torque a - linear accel a1 - lin accel of mass 1 a2 - lin accel of mass 2 M - mass M1 - mass1 M2 - mass2 L - length of rod R1 - distance that the center of mass 1's (left mass) motion is to the left of 1 along the line of the rod where mass 2 is always relatively to the right of mass 1 by distance of L meters R2 - '' '' '' for mass 2 (right mass) Rf = distance to the point left of the thurster that the thurster creates a torque around F - force from rocket I - moment of inertia of system I = (M1)*(R1^2) + (M2)*(R2^2) M1 = M2 = M R2 = R1 + L let R = R1 I = MR^2 + M(R+L)^2 I = M*(R^2 + R^2 + 2RL + L^2) I = M*(2R^2 + 2RL + L^2) τ = F*Rf τ = F*(x+L/2 + R) assumption: α2 = α1 let α2 and α1 = α (in the case that assumption above is correct) α = τ/I α = [F*(x+L/2 + R)] / [M*(2R^2 + 2RL + L^2)] right from the starting point where nothing is moving or spinning or anything F = (a1)*(M1) + (a2)*(M2) (conservation of momentum) a1 = α1*R1 a1 = α*R a2 = α2*R2 a2 = α*(R+L) F = (α*R)*(M) + (α*(R+L))*(M) F = Mα(2R + L) α = [F*(x+L/2 + R)] / [M*(2R^2 + 2RL + L^2)] F = M*[F*(x+L/2 + R)] / [M*(2R^2 + 2RL + L^2)]*(2R + L) M's cancel, F's cancel 1 = [(x+L/2 + R)] / [(2R^2 + 2RL + L^2)]*(2R + L) 2R^2 + 2RL + L^2 = (x+L/2 + R) * (2R + L) 2R^2 + 2RL + L^2 = 2Rx + RL + 2R^2 + Lx + L^2/2 + LR L^2 = 2Rx + Lx + L^2/2 L^2 - Lx - L^2/2 = 2Rx L^2/2 - Lx= 2Rx (L^2/2 - Lx)/2x = R R = (L^2 - 2Lx)/4x So far, this works for when X = 0, because you would expect the system to travel straight (or equavilently saying that it would travel a circular path of radius infiniti). Also, the further you get from the center (or as X approaches + or - infiniti, R becomes -.5L (which would mean that the center of rotation becomes the center of the system) -> also expected. However, i have some difficulty expected that any force far enough from the center would add nothing to the linear momentum of the system (for the short time that it is going more or less straight (the first dθ). This would be true, if, for a similiar case, if the center of the rod was attached to a pivot - if the force that the pivot applies onto the rod when a torque/force is applies reduces to 0 as the distance of the application of the force approaches infiniti. Even if I made no incorrect calculations or assumption, I can't imagine how to even apply this to the case after the first dtime where there is already and angular and linear motion because the formula F = (α*R)*(M) + (α*(R+L))*(M) is only true if both masses are traveling around the same center point and this seems to only be true for the very first moment. So...um...how would I do this

attachments...are attached, lol

I really dont see what the problem is. If the question isnt perfectly stated, fine, im sorry - but that doesnt mean that you should, perfectly understanding the situation, choose to avoid answering. This remind of my physics professor. I gave him this problem, before I included the rails under the incline - and instead of solving it, he showed me a screenshot of his physics simulator showing that the wedge tips over. Sheesh, thats obviously not what Im going for. Now, the solution for people that care about it, and dont spend time writing paragraphs of excuses for not answer the question at hand. Every force in the universe has to exist with a reaction force. That means, that the horizontal force applied onto the incline must equal the total reverse horizontal force from the system. In this case, the only source of this force is the blocks normal force upon the plane, which acts at an angle. So, if N is the normal force, Nsin@ = F. If E is the acceleration of the block (not the incline) than EMsin@ = F. E = F/(Msin@) That deals with the physics of it, now the geometry. There is no friction - that means that the only way that the wedge could push the block is perpendicularly to the surface no matter the motion of the wedge. (See attatchment [edit, oops its in the next comment]). So, for every dx is an small movement of the wedge, and db is a small movement of the block, then dxSin@ = db. Taking the double time derivative gives u that the acceleration of the Block is Sin@ * the acceleartion of the incline. So you are left with --> E = Asin@ = F/(Msin@) So, A = F/(Msin@sin@) Was that so hard that everyone had to make such a fuss over it? I dont mean to sound mean at anyone who actually tried. The purpose of this was to test your understanding of physics and intuition, not to test you problem solving skills or your skills of higher level physics (for those of you who think this way, why didnt you include the bending of space time and all the mini black holes located in the Nth dimension?) Interestingly enough, complicating the problem with more realistic stuff will get you answers that, when simplified by 0ing a variable, get you back to where to started. If A is the mass of the incline, and B is the mass of the block then Acceleration of incline = F/(A + Bsin@sin@) If the above situation, but with friction between the blocks (and the blocks are slipping) Acceleration of incline = F/(A + Bsin@sin@ + B[mu]cos@sin@) If the above but with gravity Accel = (F-GBcos@sin@ - [mu]GBcos@cos@)/(A + Bsin@sin@ + B[mu]cos@sin@) If you even add friction to the rails Accel = (F-GBcos@sin@ - [mu]GBcos@cos@ - GA[muRAIL] - GB[muRAIL]cos@cos@)/(A + Bsin@sin@ + B[mu]cos@sin@ + B[muRAIL]cos@sin@) ------------------ A final note, physics is the science which tries to predict and explain stuff that happens in nature. When doing physics problems, you cant expect to deal with real things, since we still dont know for sure, what exactly is going on everywhere, and we probably never will. Physics is a study where every law and the such is built up upon everything before. Not counting relativity, how come I have never heard anyone question why F = MA. This is a relationship gotten through common sense, intuition, and empirical data - however there is still no concrete reason why mass has inertia. So people, relax a little, and when shown a problem, solve it, then question its validity - or else you are nothing better than a good arguer.

What are you talking about? Why cant I have a massless object apply a force - ropes and pullies apply forces even when they are considered massless. Like I said, if it bothers some weird part of you that this problem isnt very realistic one way or another, give both things mass and volume, add wind resistence - the more stuff you add, the more complicated the problem gets. Trying doing to simpler way first, if you cant, ill understand.

First of all, you cant have a massless object in reality whose shape is an incline. But this isnt reality, its an ideal situation. Maybe I should include that the incline, even though is massless, does not permit other object to go through it, just like normal objects have surface normal forces when pushed by other objects. If you want to more realistic problem, imagine the incline having a mass, and do the same problem. You will get a solution, that when you set the variable of the mass of the incline to be 0, you get the solution to my original problem.

Ok, maybe nothing is super about this, but I created this problem when studying for a mechanics test (first year of college) and none of my friends can do it. I gave the problem to my professor, and never got a reply, hmm... Anyway, I am just really interested to see how many people could actually solve it besides me. Just a challenge. You have an massless frictionless inclined plane that is attached to a frictionless rail so that it can only move left and right - no rotation or vertical movement. It has an angle of theta, where theta isnt 0 and is equal to or less than 90. On this incline is a block of mass M. You apply a force of F on the vertical part of the incline so as to make it move along the direction of the rail (so the the force is acting parallel to the rail). There is no gravity or friction anywhere in the problem. What is the acceleration of the incline? If you could solve this, then solve the same situation but with friction coefficients, static and kinetic (so you have to solve for the set up that would make the block slip and the set up that wouldnt), and a mass of the incline N. Still no gravity, or friction at the rail. Good luck!