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Discussion in 'Electronic Basics' started by [email protected], Mar 8, 2005.

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  1. Guest

    Biking is much more fun than electronics, especially as summer is
    icumen in, but do you youngsters *know* about it?

    E.g. you know that its a lot more fun discharging a small 370V
    capacitor than a *huge* 5V one because energy is proportional to the
    voltage *squared* (because if you double voltage then the current
    doubles too and energy is their product)because
    Energy = CV^2

    | |
    | |
    V | Energy |
    | |
    | |
    | |

    The same thing applied to speed. If you double the speed you quaduple
    the energy because Energy = MV^2

    So if you hit a massive artic' while doing 1 mph (the lorry is
    stationary) on yer bike then (assuming you weight "one" unit) you will
    dissipate one unit of energy.

    If you hit the same vehicle at 101 mph when it is doing 100 mph then,
    ignoring the lorry's slight speed increase, you will dissipate the
    difference between you doing 101 and 100 i.e.

    101*101 - 100*100 == ~200

    That's nearly 200 hundred times more dangerous.

    Wazzat? ya don't believe it? (The local boy racer is reading this over
    my shoulder, he is snorting disbelief). Well if you prefer a belief
    system to a mathematical system then look at it this way: How much
    energy do you have to put it to get ya bike up to 1 mph? Not much, you
    just start pushing it and after a couple of strides both of you are up
    to 1 mph but what about 100 to 101? First of all you have to *be*
    running at 100 *before* you start pushing and *then* you must push and
    get it to 101. The ground you have to cover *while* pushing is
    evidently a hellofalot more. Does that not seem like a *lot* more
    stored energy to you?


    Robin Pain (ouch)
  2. How much
    Yeah, and since the Earth is moving at 30km/s around the Sun, we have so
    much energy stored in us that on every step we explode like a nuclear
    bomb. I can't imagine what should happen if we take the speed of our
    solar system into account, not to mention the galaxy...
  3. Bob Masta

    Bob Masta Guest

    The relative speed difference is all that matters.
    Consider that both of you are zipping along at
    over 1000 mph on the surface of the Earth,
    and the Earth is whizzing along at 19 miles
    per second, etc, etc, none of which matters here.

    Best regards,

    Bob Masta

    D A Q A R T A
    Data AcQuisition And Real-Time Analysis
  4. James Beck

    James Beck Guest

    I think the rest of the universe might not go along with your theory.

  5. John Larkin

    John Larkin Guest

    You have just disproven the theory of relativity and thus destroyed
    the entire foundation of modern physics. Bad boy!

  6. No, as I recall, kinetic energy is 1/2 * m * v^2.
    No, it's 200 times less dangerous if you hit something stationary.
    However, you haven't yet hit anything stationary.

    The dissipation can also be measured from the lorry's reference frame.
    From that frame, the system has only your kinetic energy measured in
    relation to it's own velocity (1/2 m * 1^2). When you hit the lorry, the
    system has a tiny bit of kinetic energy (it's now moving slightly in the
    pre-collision reference frame), and a tiny bit of energy from the
    collision (probably in heat, or in radiation). It isn't possible to
    determine the relative percentages in general.

    From the road's reference frame, the difference in energy you perceived
    is translated into that small amount of heat, plus a change in the
    kinetic energy of the lorry + you system. You only dissipated a tiny bit
    of the energy into heat (which is what hurts); you transferred the rest
    of it to the kinetic energy of the lorry + you system.
    No. It's the same amount of energy. Assume you are on a train travelling
    at 100 mph. Now, accelerate 1 mph in the direction the train is
    travelling. How much energy do you need to expend?
    Robert Monsen

    "Your Highness, I have no need of this hypothesis."
    - Pierre Laplace (1749-1827), to Napoleon,
    on why his works on celestial mechanics make no mention of God.

  7. I recall seeing that claim from a high school physics teacher when
    I was a smart-ass twerp. I posed the following puzzle to him:
    A rocket car starts at rest, accellerating at a constant rate
    because its thrust is constant. It is burning fuel at a constant
    rate to produce that constant thrust. The kinetic energy of
    the rocket car is allegedly M * V^2 / 2, so it is increasing
    quadratically versus time. But the fuel consumed increases
    only linearly with time. How can this be?

    I would be interested in your take on this. My physics teacher
    could not resolve it, (but, to his credit, that bothered him).
  8. I have resolved it. Consider the kinetic energy of the rocket exhaust
    along with that of the car. Assuming none of the exhaust loses kinetic
    energy due to turbulent mixing with air that converts kinetic energy to
    heat, the combined sum of kinetic energies of the car and exhaust will
    increase linearly with respect to time during the time period that rocket
    exhaust is being generated.


    Back to the original: If a car moving 1 MPH hits a stationary one, or a
    car moving 101 MPH rear-ends one doing 100, the amount of kinetic energy
    loss from causing a tiny dent or a "bump" noise from the bumper or slight
    heating of any cushioning in the bumper is the same. But if the cars
    doing 101 and 100 go out of control, their remaining kinetic energy is a
    big problem if they hit enything else. If their wheels lock, the
    remaining kinetic energy can abrade a lot of rubber from the tires.
    Although I doubt a car doing 101 tapping the rear bumper of one doing 100
    will result in any catostrophe unless at least one driver is incompetent
    in ways besides one tapping another at high speeds.

    - Don Klipstein ()
  9. Rich Grise

    Rich Grise Guest

    I like the one where he asks, "if you're going 100 MPH, and you meet
    another car head-on that's coming the other way at 100 MPH, how much
    energy is expended?" the point being that hitting a 100 MPH car isn't
    like a 200 MPH crash at all - it's exactly the same as hitting a brick
    wall, assuming all the standard assumptions. :)

  10. Jon Hoyle

    Jon Hoyle Guest


    Just wanna add a couple of my thoughts after reading this one. Please feel
    free to correct things, lol.

    'Accelerating at a constant rate because its thrust is constant' True or
    I think false. Does drag increase with speed up until terminal velocity
    is reached?
    If thrust is constant, will drag eventually equal the thrust once a
    certain speed is reached?
    Therefore does the thrust need to increase to match the increase in

    'The kinetic energy of the rocket car is allegedly M * V^2 / 2, so it is
    increasing quadratically versus time' True or false?
    Does 'M' get smaller as the rocket car uses fuel?
    What shape would the graph be if it does?

    'But the fuel consumed increases only linearly with time' True or false?
    As pressure and temperature builds inside a combustion chamber, does the
    fuel burn rate (thrust) also increase?

    Well that was fun. Please tell me my understanding of physics is phlawed ;)

  11. You've put that behind you then. ;)
    Beats me. May have something to do with the exhaust, as Don says. Might
    also have to do with the heat generated in the rocket. Probably
    something to do with reference frames, and the velocity of the fuel
    exhaust changing with regards to a stationary observer. That is all it
    really can be, since the closed system is rocket, fuel, exhaust. Inside
    the system, the energy is constant. However, working it out is another
    Energy is a funny thing. You have to be careful about how you count it up.

    The classic riddle here on s.e.b is 'given a capacitor charged up to V
    volts, the energy is 1/2 * C * V^2. If you connect an equal uncharged
    cap in parallel, the charge will equalize such that the voltage is 1/2
    what it was. Thus, the energy is now 2 * (1/2 * C * (V/2)^2) = 1/2 what
    it was before. Where did the energy go?'

    Robert Monsen

    "Your Highness, I have no need of this hypothesis."
    - Pierre Laplace (1749-1827), to Napoleon,
    on why his works on celestial mechanics make no mention of God.
  12. John Larkin

    John Larkin Guest

    At low velocities, a rocket is a very inefficient source of
    propulsion; at near-zero velocity, it's using its usual amount of fuel
    but hardly delivering any kinetic energy to the vehicle. As velocity
    increases, efficiency improves (or rather becomes less terrible) and
    vehicle energy accumulates faster. That trend continues until you run
    out of fuel.

    In a system that goes from extremely inefficient to only rather
    inefficient, it's not hard to shape the efficiency curve into a
    quadratic. A cog railway can be nearly 100% efficient, so it will need
    increasing amounts of fuel if it accelerates at constant gees, but
    anywhere on the path it will be a lot more efficient than a rocket.

    That make sense?

  13. Here is a web page written by somebody who has been driven insane by
    this problem:

    His solution is that kinetic energy is really mv, not 1/2 mv^2. He has
    equations and everything. Pretty wierd stuff. Who knows?

    Robert Monsen

    "Your Highness, I have no need of this hypothesis."
    - Pierre Laplace (1749-1827), to Napoleon,
    on why his works on celestial mechanics make no mention of God.
  14. sergiometra

    sergiometra Guest

    if there is not resistance in circuit and cap, circuit will oscillate
    otherwise energy dissipate in heat and oscillation eventually end
  15. sergiometra

    sergiometra Guest

    I think he demonstrate the exact opposite;
    if you jump from 2nd floor, speed at arrival is not double that a jumping
    from 1st floor as it take less time from floor 1 to 0 than from 2 to 1 , but
    energy is double as you need double energy to go up 2 floor than 1 , so
    energy increase more rapidly than speed i/e Energy>mv;
  16. Rich Grise

    Rich Grise Guest

    How about a thought experiment - for each plate, use two plates that
    slide over each other, and that can move, so that you can widen the
    plates to twice their size, causing the capacitance to double? Does
    the voltage change? And what happens to the energy? (the plates are
    very thin, so the thickness difference between overlapping plates
    is negligible)

    And what if you have just a movable plate so that you can change
    the spacing?


  17. Yes. I should have known this little puzzle would
    not take you folks long to sort out. The key is to
    consider that starting condition. All the energy ends
    up in the exhaust at the limit of zero rocket speed.
    The problem gets a little easier to see if it involves
    chucking cannonballs from a railway car.
  18. You have assumed something into the problem
    that complicates it without affecting its nature.
    The "terminal velocity" concept requires some
    kind of liquid or gaseous medium. No such
    medium was postulated in the original problem.
    This is a reasonable point, but again a complication
    that does not change the nature of the problem.
    One can imagine an ion engine whose mass usage
    is so low that it can be neglected for a limited time
    that still fully exposes the quadratic/linear "dilemma".
    Another complication. The original problem is not
    about startup characteristics of rocket motors.
    I'm not ready to say "flawed", but I wonder if you
    plan to go into engineering. If so, you will have to
    learn how to neglect certain phenomena and how
    to decide that such neglect is appropriate.
  19. The voltage changes, and you do mechanical work on the system to change
    it. Electrostatics causes a force to be exerted, and you need to move
    against or with that force, thus doing work.
    Same thing.

    Robert Monsen

    "Your Highness, I have no need of this hypothesis."
    - Pierre Laplace (1749-1827), to Napoleon,
    on why his works on celestial mechanics make no mention of God.
  20. Where is the oscillation coming from again? I know that an LC circuit
    near absolute zero will oscillate, but I didn't say anything about an

    But you are right, the transfer of energy requires some dissipation.
    That is the answer, the extra energy is dissipated. It's easier to see
    if you put in resistors instead of wires between the caps (but wires are
    just resistors with lower values, right?). Then, the integral of power
    through the resistor from 0 to infinity gives the solution, which is 1/2
    the original energy.

    Start with cap A charged to V, connected to an uncharged cap B through
    one terminal. The other terminal has a switch and a resistor. B is
    uncharged. To the circuit, the two resistors are simply series caps, so
    the total is 1/2 C. Thus, the voltage across the resistor at t is

    V(t) = V * exp (-t*2/RC)

    Thus, instantaneous power through the resistor is

    P(t) = V(t)^2/R

    The integral of this from 0 to infinity is

    C*V^2/4 = 1/2 * (1/2 C * V^2)

    Robert Monsen

    "Your Highness, I have no need of this hypothesis."
    - Pierre Laplace (1749-1827), to Napoleon,
    on why his works on celestial mechanics make no mention of God.
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