Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 decade ago

Which will go down the ramp faster the can that is full or the empty can? Why?

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  • 1 decade ago
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    The can that is full will go faster -ultimately. The empty can will start quicker because it does not have the weight of the contents holding it still. The full can will ultimately go faster as it builds momentum down the ramp.

    Edit: Depending on the height, they will NOT drop at the same speed. If the cans are the same size, the full can will go faster as the momentum builds. Gravity is funny that way.

  • 1 decade ago

    I assume that you're rolling the cans down a ramp. We note in advance that if the can rolls without slipping, v = r ω.

    mgh = 1/2 m v² + 1/2 I ω²

    where m = mass of can, g = local acceleration of gravity, h = height of the ramp, v = final translational velocity, I = moment of inertia of the can, and ω = final angular velocity.

    empty can: I = mr² (approximately)

    full can: I = 1/2 m r² (approximately)

    Empty:

    mgh = 1/2 m v² + 1/2 (mr²) ω²

    gh = 1/2 v² + 1/2 (r²) ω²

    gh = 1/2 v² + 1/2 v²

    gh = v²

    v = sqrt ( gh )

    Full:

    mgh = 1/2 m v² + 1/2 ( 1/2 mr²) ω²

    gh = 1/2 v² + 1/2 ( 1/2 r²) ω²

    gh = 1/2 v² + 1/4 v²

    gh = 3/4 v²

    v = sqrt (( 4 / 3 ) gh )

    The full can has the larger final velocity and makes it down the ramp in less time than the empty can. It doesn't matter if the cans are of different weights; it's the distribution of mass (that is, moment of inertia), not the mass itself, that affects the final velocity.

    One notes that some of the other responders to this question have a somewhat...ah, Aristotelean view of motion.

  • Anonymous
    1 decade ago

    When you roll them in a vacuum... they will go down at the same time...

    but, if you roll them down in an ordinary ramp/situation.. the heavier can will roll faster because IT HAS MORE MASS.. therefor it has greater force against wind resistance...

  • 1 decade ago

    You really haven't given enough information. We need to know what the can is filled with, what the ramp is made of, is the can completely full?

    If you drop them from an equal height, they will hit the ground at the same time though.

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  • 1 decade ago

    If one of the can's is filled up with anything except air, the filled can will move faster as the force of gravity will help it move faster and also because it has more mass.

  • 1 decade ago

    a car with a full can because there is more force pushing downward. And when there is an incline, the downward force gets broken into horizontal and vertical components. Then with more downward force, there will be more horizontal force. With more force, there is more acceleration, and with more acceleration there is more speed.

    Source(s): me
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