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Calculating the final velocity of a simple electric train

  1. Nov 29, 2018 #1
    • Moved from a technical forum, so homework template missing
    I am currently in grade 12, and for a physics project (a huge project, which gets assigned to you at the start of the semester and needs to be completed just before exams. You think up your project, make a proposal for it and you prove your hypothesis to be right after a presentation and lab report.) I need help with calculating the velocity of a simple electric train. Currently, we are learning gravitational fields and have not learned anything about magnetic fields and what not (we will be in about a week) , so many of the equations and especially variables seem foreign to me.

    Here is the video of the simple electric train:
    (I need to re-do this but with different variables such as different types of batteries, different gauges of copper wire, more mass etc etc.)

    I went through my textbook and had seen where they had made qvb equal to centripetal acceleration and had solved for velocity which resulted in v=qbr/m. Although I am certain that this is incorrect.

    I was thinking something along the lines of using w=fd, subbing the force of the magnetic force into f (I do not know what that equation is, to solve for the magnetic force) and then taking the result in joules and subbing it into (result) = mv^2/2 and solving for v. But once again I am not sure if this is right or not.

    If anyone can help me with this it would be greatly appreciated, thank you.

    Edit: I had calculated the velocity using v=qbr/m using test values (except b, I had measured the mt earlier today)
  2. jcsd
  3. Nov 29, 2018 #2
    So I have found this equation to calculate an electromagnetic force.
    FPull= ( n x I ) 2 μ0(A/(2g)^2)
    F : Force.
    n : Number of turns.
    I : Current.
    μ0 : permeability of air.
    A: Area in m2
    g : the gap that is separating the electromagnet and the object.
    Once again, if someone can help me with my process to finding the final velocity, it would be very helpful.
    Ok, here goes:
    So, assuming that I know how to calculate this (or somehow calculate the electromagnetic force), my plan is to (with the current knowledge I know) multiply this force by 2 (since there is one force attracting and the other force repelling) which causes a net force to be directed in one direction (am I wrong here?). Once this is done, I will plug this force into w=fd. The distance would be the total distance that the battery will travel (0.3m-0.6m, i am still thinking how long my "track" would be) and get the work done in joules. After this subtract the value I got in joules by thermal energy (still need to know how to calculate this, as I do not know the coefficient of friction between my two materials). Once I get this net energy, I will substitute it into the kinetic energy equation (mv^2/2). The mass would be the total mass of the battery and I will solve for v. Does this make sense at all, and will it work? Or do I have to take another approach to this? If anyone could help me with this it would be very helpful, as I am stumped and am having a very difficult time trying to solve for the final velocity. Thank you.

    I have also noticed that I do not have any B (magnetic field) value within my plan to calculate the final velocity, and I am guessing that I need one.

    If anyone can help out it would be greatly appreciated, thank you once again.
  4. Nov 30, 2018 #3


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    But what d would you use? The problem is that the electricity continues to do work on the train. Why does it not just go faster and faster?
  5. Nov 30, 2018 #4
    The d would be the distance of the entire solenoid from one end to the other
  6. Nov 30, 2018 #5
    Although it seems as if the speed of the battery seemed to remain constant, don’t resistive forces cancel it out?
  7. Nov 30, 2018 #6
  8. Nov 30, 2018 #7


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    Yes. If the velocity is constant the acceleration is zero so the net force is zero. That means the propulsion force equals the friction force.

    The problem will be calculating the friction force in this set up with any hope of accuracy. The train wont be sliding smoothly but rattling off individual turns of wire.
  9. Nov 30, 2018 #8


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    Then what you calculate would be the KE gained in one pass through the solenoid. I thought you wanted the steady state speed.
    Yes, that was my point, and as CWatters writes that means you need to know what the frictional force is.
  10. Nov 30, 2018 #9
    Hm, say that I calculate this without any friction, I get the value of the actual train using v =d/t during the experiment, and I use both velocities to calculate the force of friction itself.

    Also I used this equation : v = qBr/m to calculate for the velocity (this was given to me by my teacher) and when I plugged all the value's in (q constant) (8.355 mt) (0.075)/(0.35) -> (the mass was a guess, whereas the B value was measured, and the radius is an approximate value, not exact). I ended up getting 2.68m/s. Although when I actually constructed the project and had seen it travel across a very short distance, it seemed to be going much much slower (somewhere around 0.2 m/s to 0.4 m/s, I am assuming this is due to the frictional force correct?) Although I was not using the exact mass or radius. (mass of battery + magnets and the radius of the solenoid).

    FPull= ( n x I )^ 2 * μ0(A/(2g)^2)

    Also I have a few doubts about the variables of this equation:
    n, are these the total amount of coils done, or just the amount of coils from one end of the battery the other.
    I, how would this be measured, just with the battery alone or with the battery IN the solenoid
    A , Would this be the cross sectional area for the neodyium magnets?
    g, the gap that is separating the electromagnet and the object. <-- although as you can tell that there is NO gap whatsoever separating the electromagnet from the solenoid. (would the gap be the distance between the two magnets, or the width of them?)

    Again, thank you so much for the responses, it helps me greatly.
  11. Nov 30, 2018 #10


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    Can you quote the source for that equation? Its probably intended to calculate the max spring tension in a relay? In your application g=0 so that's not going to work.

    Regarding the equation for the velocity your teacher gave you. I don't recognise that equation but what is r? You appear to have set it to 75mm?
  12. Nov 30, 2018 #11


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    Thinking aloud here....

    Basically what you have is a motor. Normally simple DC motors accelerate until the back emf is roughly the same as the applied voltage. _If_ that works for this circuit then we could look to equations like this for the back emf...


    Vemf= -N dBA/dt

    Where N is the number of turns between the magnets. B the magnetic field, A the cross sectional area of the coil.

    I'm thinking that N/dt is related to the velocity eg number of turns passed per second?

    What do others think of this approach?

    Edit: It suggests that spacing out the turns would speed it up and bunching them up would slow it down?

    Edit2: The voltage may well not be anything like 1.5V as the battery is virtually shorted.
  13. Dec 1, 2018 #12


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    Speed from the video with the long coil is [/i]about[/i] 3.5sec for one revolution. It will probably be faster if the coil is in a straight line.

    For finding the coil current you don't need it to be coiled, you just need the same electrical length as when it is coiled. If you have access to an Ammeter that should be easy. Without an Ammeter you will need to measure the battery voltage with it connected to the wire. Then you can either measure the resistance if you have an Ohmmeter that reads that low (remember to acocunt for the resistance of the meter leads), or knowing the wire diameter, look up the resistance in a wire table. Hint it is less than 10 Ohms per 1000 ft (305m).

  14. Dec 1, 2018 #13

    Here is where I had gotten that equation from, as well as a few other posts for forums had mentioned this.

    This is one

    Also, what is the d supposed to be, and for N/dt I am assuming that I have to physically see it and calculate it when the experiment is on-going?
    Vemf= -N dBA/dt (is that d before the variable B a typo?)

    And I had asked this question on another forum, they had mentioned that the gap would be approximately the width of one magnet ( or the distance separating the electromagnet from the two other magnets).

    Here is the link to that:

    To get the equation my teacher gave me, all we did was take f = qvb and the centripetal force eqn and made them equal to each other. the v's canceled out (leaving only one) and we just isolated for v.

    qvb = mv^2/r
    v = qbr/m

    Thank you for your reply
    Last edited: Dec 1, 2018
  15. Dec 1, 2018 #14
    So, I would just attach the copper wire (the length being the amount used in the coil) and connect both sides to the ends of a 1.5 v battery, essentially making a circuit and then cutting in between that circuit and then taking an ammeter to measure the current yes?

    like this video.

    Thank you for your reply.
  16. Dec 1, 2018 #15
    I just scanned through this - but where is the energy coming from? It is an unlimited source? What determines the current "I" in the equations above.

    Also - the "train" is not on a frictionless track - correct? How could you experimentally estimate the friction it sees?
  17. Dec 1, 2018 #16
    The energy being calculated it coming from the equation FPull= ( n x I )^ 2 * μ0(A/(2g)^2). (Which I still need to know how to use) The Energy is coming from the electromagnet.

    The current would be the current flowing through the solenoid.

    I am aware the train is not on a frictionless track and I do not know how to calculate it, I will just calculate the actual velocity when the experiment is done (using v = d/t) and then I will just compare the velocity calculated and work backwards to find the thermal energy.
  18. Dec 1, 2018 #17
    Really ? The electromagnet is the source of the ENERGY?
  19. Dec 1, 2018 #18
    Another question, I am assuming that the circuit for the experiment would be a series circuit. Doesn't current stay the same throughout the circuit? Or am I wrong here and will have to measure it by using the amount of copper wire used?
  20. Dec 1, 2018 #19
    As far as I know, yes. I've never really worked with energy in this situation (have only worked with kinetic, potential, elastic etc.) , so I am assuming it is because of the equation I found.
  21. Dec 1, 2018 #20
    Make a diagram of the system... show the coil, magnets, etc.... what does each element do. Other than a magnet / electromagnet - what else is going on?
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