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Math Help - Floating object on the Earth and the Moon.

  1. #1
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    Floating object on the Earth and the Moon.

    The question is: The standard unit of measurement of force is the newton (N). It is the force needed to accelerate a mass of 1kg at 1 m/s^2 . On Earth's surface, a mass of 1 kg requires a force of 9.8 N to counteract the acceleration due to gravity of 9.8 m/s^2 downward. Multiplying the mass by this acceleration gives the weight. On the moon, the acceleration due to gravity is 1.63 m/s^2.

    part c) When a certain object is floating in water on Earth, 75% of it is submerged. If water were found on the moon, and the same object were floating in i, how much of it would be submerged?

    What I did was a ratio between the acceleration due to gravity of earth and the acceleration due to gravity of the moon and multiplied what was given to get an answer. However, the answer is 75% and I am not sure why. Can someone help explain? Any help would be appreciated.
    Last edited by mr fantastic; March 17th 2011 at 07:13 PM.
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  2. #2
    MHF Contributor

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    Yes, 75% is correct. In fact, if you were to put this object into water on any planet (where there was sufficient water!) it would submerge to 75%. An object that has less density than water will submerge in water until it displaces water whose weight is equal to its own weight. On the moon, or any other planet, the change in weight of the object and water will be multiplied by exactly the same fraction. That is why the formula for submergence, Archimede's law, is usually stated in terms of mass, not weight. Objects, and water, have the same mass no matter what the gravity is.
    Last edited by HallsofIvy; March 19th 2011 at 11:11 AM.
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