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3 simple problems

  1. Nov 20, 2004 #1
    I have 3 ideas that i am stuck on,

    1. If you have water displaced in newtons by a floating object, is the newtons displaced of oil or any other liquid, what is the equation to find this. I tried many equations with densities and bouyant forces, but i can't seem to get the right answer, i was maybe thinking since it is newtons of water replaced and oil replaced, not mass, that maybe the newtons of water replaced equals newtons of anything replaced. meaning if 100 N of water is displaced, 100 N of oil will be displaced by the same object, Am i correct in thinking this?

    2. If you have a pendlum swinging from an elevator accelerating upwards, in taking the equation of pendlum's being period = 2 * pi * sqrt( L / g ), would you just add the acceleration to g by changing the part in the equation where g is to
    (g + a)?

    3. I am trying to find the difference in periods of 2 planets with different masses, and different eccentricity, i have been hunting through my book for an hour, and another hour or 2 on the internet, and cannot find an equation that can give me these differences in periods. I was wondering what the impact of eccentricity is on a period. Is a bigger eccentricity going to cause a longer period? I cannot find this property anywhere.

    Last edited: Nov 20, 2004
  2. jcsd
  3. Nov 20, 2004 #2
    1. I am not sure whether I am correct. I haven't learnt that but just had a look at them.
    Buoyant force= volume displaced x density.
    The V of 100N of water is not equal to V of.100 N of oil
  4. Nov 20, 2004 #3


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    Staff: Mentor

    1. A newton is a measure of force, such that 1 Nt = 1 kg * 1 m/sec^2.

    Bouyancy works on the displacement of volume. A material denser than water will sink, lighter than water will float.

    A ship made of steel will float because it surrounds a volume of air (void) and displaces that volume of water.

    The bouyant force = density (of liquid) * volume (displaced) * g (accel. of gravity), just like F = mg.

    2. Yes. In the elevator accelerating with a in a gravity field g, the effective g becomes g+a.

    3. http://scienceworld.wolfram.com/physics/KeplersLaws.html

    Good site for physics
  5. Nov 20, 2004 #4
    the question for the first one is really , 16,000 N of water are displaced by a boat, how many newtons of saltwater is displaced with a specific gravity of 1.17

    and for the second one, are you absolutely positive it's g + a, beause on another post i found in the K - 12 section they had it at g - a, does it add or subtract from gravity
    Last edited: Nov 20, 2004
  6. Nov 21, 2004 #5
    It depends on how you define direction. The elevator is accelerated upward. If you define that as positive, then g is negative, since the gravitational force points downward. If define up as negative (which is kinda weird in this case, but you can do it), then g is positive. Think about what the variables a and g represent and you should be able to assign signs to them.

    EDIT: More complications: you can also say g indicates a negative force, so a+g actually indicates a minus the magnitude of g...getting confused? Basically, however you choose to define things, make sure you are consistent throughout your work on the question, and look at things to see if they make sense. In this case, you know the acceleration of gravity must be taken away from the acceleration a.
    Last edited: Nov 21, 2004
  7. Nov 21, 2004 #6
    When an object falls into a liquid with a speed, there are two forces acting against the weight, right?
    Buoyant force and fluid resistance.
    Is fluid resistance a force? like friction is called frictional force and is a frictional force.
  8. Nov 21, 2004 #7

    Doc Al

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    Staff: Mentor

    Archimedes's principle

    Assuming you are talking about the amount of liquid displaced by a floating object, then you are correct: An object floating in a liquid displaces a volume of liquid whose weight equals the weight of the object. Of course, this is equivalent to saying that the mass of displaced liquid equals the mass of the object, since mass and weight are proportional. The same object floating in different liquids will displace the same weight or mass of liquid, but different volumes.
  9. Nov 21, 2004 #8


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    Staff: Mentor

    1. Doc Al provided a better and direct answer.

    Weight is a force, which is given by mass x acceleration of gravity. A 20,000 ton ship (its weight) will displace 20,000 tons of water, and 20,000 tons of oil, but the volumes of water and oil would be different.

    2. Yes, I am sure. The acceleration of the pivot of the pendulum is up, so the reaction on the pendulum mass is down in the direction of gravity. Since the pendulum is not accelerating (changing velocity) with respect to pivot, the net force is zero - this is a statics problem.

    However, g is decreasing as distance from the center of the g-field increases, so if the a is constant, g will decrease on the acceleration effect will just become 'a'.
  10. Nov 21, 2004 #9
    So the answer best answer would be 2 pi sqrt ( L / a )?

    Another similar problem is a bucket of a incompressible fluid of density, sitting on the bottom of an elevator accelerating downward with magnitude a, what is the pressure difference between the two points, seperated by delta H

    i think it's density (g + a)delta h, anyone explain these forces of gravity with resepect to accelerations
    Last edited: Nov 21, 2004
  11. Nov 21, 2004 #10

    Doc Al

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    Staff: Mentor

    That post in K-12 is incorrect. See my response in that thread.
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