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Thread: Calculate friction for falling object

  1. #1 Calculate friction for falling object 
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    For school, I have to build a device that can move bottles of beer around. These bottles fall from a certain hight into a case. However, the hight from which they fall, 0.75 meters, is too much for the bottles and they will break. I need to slow them down in the tubes that they travel through. I was thinking of using brushes to do this, but first I need to calculate a certain kinetic friction co-efficient, but I don't know how to do this. Can someone help me with this?

    Thanks


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  3. #2  
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    Is your tube sloped or do the bottles fall straight down? If the tube is sloped, you could use conservation of energy. You would calculate the final velocity you want the bottles to have. It won't be zero because you dont want the bottles to hang up before they fall into the carton. The initial potential energy is mgh and the initial kinetic energy, if any depends on the velocity when it enters the tube. The energy lost due to friction is the frictional force multiplied by the length of the tube. The frictional force is the normal force (mg cos theta) multiplied by the coefficient of friction between the bottle and the surface of the tube. Theta is the angle the tube is sloped relative to horizontal.

    If you are using brushes in a vertical tube then (cos theta) is zero and the normal force has to be provided by adjusting the brush against the bottle. It will depend on things like the stiffness of the brushes, number of bristles, how they are adjusted, and so forth which you will need to know in addition to the coefficient of friction between the bottle and the bristles of the brush. You would probably be better off just to adjust it experimentally.


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  4. #3  
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    Hi Harrold,

    Thanks for your reply.

    The bottles have a mass of 0.553 kg
    The tubes are placed vertically. The bottles break when they fall from 0.65 meters, but the setup has the bottles fall from 0.75 meters. When the bottles fall from 0.65 meters, they have 3.52 Joules of energy at the point of impact and a speed of 3.57m/s

    When they fall from 0.75 meters they have 4.05 Joules of energy at impact and a speed of 3.86m/s

    I need to slow the bottles to 3.06m/s, this will give them 2.5 Joules of energy at impact and they will survive the fall.

    How the friction is applied is not important for the calculations, just that a certain friction factor is applied so that they slow to the desired speed. I don't know how to calculate this, can you help me with this?

    Thanks again
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  5. #4  
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    No. Like I said, it's not a simple calculation. Why can't you just play around with different brushes until you have it adjusted properly?
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  6. #5  
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    We will experiment with brushes until we have the desired results, but I can't do that in the calculations. If the calcs are no easy fix then that's that I guess. Thanks for your help.
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  7. #6  
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    At first I thought, "hmm... this is easy, it's high school level problem." But then I learned that this question was quite difficult because it's dealing with a frictional force in vertical situation, not horizontal surface. Now, this is how I got the magnitude of the frictional force. Assuming the frictional force is constant, I calculated the ideal acceleration of an object so it does not crack. You said you need to slow it down to 3.06m/s, so using the equation, Vf2-Vi2=2a*d, it's 3.06^2-0^2=2*a*.75. Therefore, a = 6.24m/s2 Since our gravitational acceleration is 9.8, it should be slowed down to that number. Using another equation, ∑F=Fg-Ff=m*a where Fg is mg or .553*9.8=5.42N, and a (or ideal accelation) is 6.24m/s2, ∑F=5.42-Ff=.553*6.24, so the frictional force (Ff) will be 1.97N. Now, here's where the difficult part comes from. If the beer was moving horizontally on the surface, the frictional force is just mgu (u=frictonal coefficient) so you just need to divide the frictional force by mg to get the coefficient. However, the beer is now falling vertically, which means you can only use mgu if the beer is exerting the force on the wall. In summary, if you really want to find the coefficient, I think you need to find something that makes the beer exert the force on the wall. Unforunately, I don't think the brush really does that. Otherwise, just do what other people told you: try different brushes.
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