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Newton's third law and surface area of paddles

  1. Apr 1, 2012 #1
    why do paddles/oars have a large surface area? I thought that it does not really matter as i would just apply a force on the water so as to attain a action-reaction force on the boat thus pushing me forward. but if i look at the free body diagram of the paddle 1 force will be me pushing and the other (opposing) is water resistance. But ultimately i will have a greater pushing force to push the paddle back so the reaction force will push the boat forward. but that is the net force of the paddle, i don't think action and reaction pairs are based on the net force of object rather they are based on the integral forces in the particular system. So, i'm confused about this newton's third law and also how the larger surface area will give more force to push the boat forward.

    Thanks for the help! :smile:
  2. jcsd
  3. Apr 1, 2012 #2
    Your action is pushing the water backward. The force equal to amount of water and how fast the water accelerate as you push.

    The reaction is the force that makes you and the boat forward.
  4. Apr 1, 2012 #3
    So how does having a larger surface area help? Since you can apply the same force on the small surface area too...
  5. Apr 1, 2012 #4


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    You can, but it will result in the paddle traveling more quickly through the water. To maintain the same force, you will therefore need to have more paddle strokes, and it will involve more effort on your part (since you are imparting the same force, but over a greater distance). Basically, the more resistance the paddle has with the water, the less the paddle will move, allowing each stroke to last longer.
  6. Apr 1, 2012 #5


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    You can't just apply a greater force on the paddle and expect to get an equal force back on the paddle from the water. Think about what happens when you wave the paddle in the air. A very small part of the force acts on the air molecules, the rest goes to accelerate the paddle.

    The water will apply a force on the paddle equal to the water pressure times the area of the paddle. Any additional force will just go to increase the speed of the paddle. That's why a greater area allows a greater force to be applied to the water.
  7. Apr 2, 2012 #6
    But I thought there are two bodies involved right now? One is the paddle and the other is the water. So when I apply a force on the paddle it is to overcome the water resistance acting on the paddle so as to love back. Then how do I push the boat forward? Does thus mean not all the water resistance acts paddle while some acts on the boat to give a forward motion?
    Also, when dealing with newton third law, is the action reaction pair based on the net force acting on something or the individual forces acting? Lastly, going back to what you said, if I exert a force on the water won't I get an equal and opposite force acting on me? I don't see the connection besides the difference in pressure of the two paddles. One just has more pressure. But won't the forces be the same still? Thanks for the help!
  8. Apr 4, 2012 #7
    Yea, but when I look at the free body diagrams, looking at the paddle with large surface area: I exert 10N water resistance exerts 5N so I have a net force of 5N. Looking at the paddle with small surface area: I apply 10N water resistance exerts 2N so I have a net force of 8N. But aren't these the fbd of the paddle and not the water? Thanks
  9. Apr 4, 2012 #8


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    Think about what happens to the water. If your strokes make a small mass of water, W1, move quickly, speed V1, then you've expended energy W1*V1^2/2 to gain forward momentum W1*V1. If you make twice the mass move half as fast you've gained the same momentum for half the energy.
    In the limit, the water being sufficiently shallow, you do best by punting, not rowing.

    [Funny thing... I'm new to this forum. I see a vast breadth and depth of understanding of physics here, but it often doesn't extend to the importance of momentum]
  10. Apr 5, 2012 #9

    Ken G

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    The way I'd put it is, the larger the paddle, the less its velocity needs to be in the frame of the water to get the water to return the force you are capable of exerting. The less the velocity in the water, the less energy is imparted to the water. That's good-- you want the work you are doing, in the boat frame, to all go into kinetic energy of the boat (and its dissipation into turbulence by the prow of the boat). You don't want much to go into motion of the water being moved by the paddle. Think of a giant paddle that just sticks into the water and pushes the boat along without moving the water at all-- that would be ideal, except for dealing with the weight of the giant paddle! So a wide paddle is more efficient. However, actual rowboats use a different principle-- they use a long oar, so you can use leverage to scale down the actual force of the oar in the water compared to the force you are exerting, but that force applies over a larger distance. That means the oar is moving through the water, so there's a lot of lost energy efficiency, but somehow the leveraging effect still makes that a useful tradeoff. I'm not sure why, it seems very lossy, but I guess the point is that the energy dissipated by the motion of the boat itself is always a lot more than what is dissipated by the motion of the oars through the water.
    Last edited: Apr 5, 2012
  11. Apr 5, 2012 #10
    Adding my two cents to this :P

    The main point is that you are pushing against water. If you were to push against a solid the area would not matter. 50N applied to the Oar will give a 50N force against the solid.

    In the case of water having saying a thin oar, the water will pass around the oar. The molecules of water the oar does hit however, will be affected by the force, but will also move back. (As with a solid, it will in a sense keep its position and push back on the oar).

    And so having a larger area oar allows for a greater area of water molecules to which you apply your, say 50N force too. The more molecules you push back the greater return on the force you applied on the top of the oar perhaps ??

    (Im sorry if my answer is wrong, and if so, please tell me why as im interested in this question too :P.)
  12. Apr 5, 2012 #11


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    This problem is really not as complicated as all the words seem to make it. Just think that you rowing can have either 2 effects (actually a combination of both). Either it moves the paddle, or it moves the boat. You want to move the boat, not the paddle.

    Ideally, you would have something very rigid to push off of (e.g. the shore), and in that case you only move the boat (and not really the paddle). On the other end of the spectrum, you could push off of something extremely not rigid (e.g. air) and mostly move the paddle and not the boat.

    A larger oar is increasing drag in the water, and is basically like giving you something more rigid to push off of.

    A pencil oar would be useless because only the pencil would move and you would not go anywhere.
  13. Apr 5, 2012 #12


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    Ken G, Matterwave and valleysheep are all correct in a hand-waving sort of way, but the physics underpinning it in each case is what I said - momentum versus energy.
    To go forward you have to move water backwards; momentum is conserved, and that's mass * velocity. (See e.g. http://www.atm.ox.ac.uk/rowing/physics/basics.html)
    For a given momentum, you can propel a small mass of water at high speed or a larger one at lower speed. Since kinetic energy is mass * speed^2, the smaller mass costs more energy.

    Wrt oar length:
    Ken G is right that the principle of catching a large mass of water should favour a short broad oar. But it's diminishing returns; a standard oar already has a sufficiently broad blade that it's not going to make that much difference. Meanwhile, other effects cost you.

    Using oars that are too short would be like cycling in a gear that's too low. You'd waste a lot of energy on moving your own body back and forth.
    A long oar with a very broad blade would be cumbersome.
    What might work would be a mechanical arrangement that sweeps a broad blade along the length of the boat, close in, while the rower makes a fairly conventional movement.
    Getting it to return smoothly, balancing the craft at the same time, would be the challenge.
  14. Apr 6, 2012 #13

    Ken G

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    Yes, that is certainly the crux of it, and it shows that the main issue is to have the speed of the oar, relative to the water, be significantly less than the speed of the boat. That insures that the energy dissipation is happening mainly due to the boat, not the oars (because in steady state the force of the oars on the water has the same strength as the force of the boat on the water), as this maximizes efficiency. Thus I was wondering why they didn't make the paddles larger, but you must be right that they are plenty large enough without being unwieldy. I was also wondering why they make the oars so long, when that would seem to mean the oar would be moving through the water at a faster speed (losing efficiency), but I forgot how fast those boats go-- no doubt the oars are long simply to match the speed of the boat to the comfortable rowing speed of a human, such that the oars have the minimum relative speed in the water. It's interesting that good physics can give you an edge in boat racing!
    Last edited: Apr 6, 2012
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