Investigating Drag with Paper Cones

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Discussion Overview

The discussion revolves around an experiment investigating how the angle of a paper cone affects the time it takes to fall a distance of 2 meters. Participants explore the relationship between the cone's angle, drag force, and cross-sectional area, while considering the implications of various constants in their experimental setup.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant observes an inverse relationship between the angle of the cone and the time taken to fall, but questions whether they are inversely proportional.
  • Another participant asks what variables are being held constant while changing the angle of the cone.
  • A participant mentions holding velocity and air density constant, but expresses uncertainty about whether changing the angle affects the drag force, drag coefficient, or both.
  • There is a discussion about whether the area of the base of the cone remains constant, with one participant clarifying that it does not, as the cone is dropped upside down to prevent tumbling.
  • Some participants suggest that the frontal area is also changing with the angle and propose making cones with the same frontal area and weight.
  • One participant questions how to change the angle while keeping the base diameter constant, leading to a discussion about modifying the height of the cone.
  • Another participant explains that the size of the wedge cut from the paper affects the height and circumference of the cone, impacting the angle.
  • There is a suggestion to keep the base area fixed while varying the angle, which would require adjustments to the diameter of the paper circle used to construct the cone.
  • One participant argues that the angle may not significantly affect the velocities and suggests focusing on changing the base area instead.

Areas of Agreement / Disagreement

Participants express differing views on the significance of the cone's angle in relation to drag force and terminal velocity. There is no consensus on whether the angle should be a primary variable of interest or if the focus should shift to the base area.

Contextual Notes

Participants note the complexity of controlling variables in the experiment, including the relationship between angle, base area, and mass. There is an acknowledgment that changing one variable may inadvertently affect others, complicating the experimental design.

  • #31
There are some drag coefficients here..

https://en.wikipedia.org/wiki/Drag_coefficient
The Cd of a cone point first is given in the top right hand table as 0.5.
The Cd of a flat plate is given in the lower table as = 1.28

Note these are only a rough guide. The angle of the cone isn't specified.
 
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  • #32
CWatters said:
Yes I would expect a cone with a wider angle to fall more slowly than a cone with a narrow angle because Cd is higher.

Would a reasonable scientific explanation of this be to discuss how the rate in change of momentum of air particles changes between the flat circle and cone. Looking at the flat circle, air particles will undergo a change in momentum of 2mv when they strike the surface. The force would be the rate of change of momentum which would be dictated by the velocity of the object. If we look at the cone then the air particles strike the surface of the cone which is now at some angle compared to the normal of the cone. Therefore the momentum will go down by the sine of the angle between the air particle striking the surface and the normal. Is this ok to explain why a cone falls faster through the air?
 
  • #33
Perhaps but its not that simple. The shape behind the point of maximum cross sectional area also matters, perhaps not in this case (the back of a disk and the back of a cone are similar) but certainly for wing sections.
 
  • #34
You might also consider adding a short string ( ~ 10 CM?) with a little weight on one end, and the other pulled through the tip of the cone, and attached on the inside. This would help keep the cone pointed down, and the weight would be more consistent cone-to-cone, as small variations in cone weight would not affect total weight very much (%-wise).
 
  • #35
There seems to be a lot more floundering around than necessary in this discussion. You want to know how drag depends on the angle of your cone. It sounds like all your cones are constructed of the same amount of paper so their masses are equal. The area A is the orthographic projection which, simply put, is the area presented to the onrushing wind and that is the area of the base. The area of the base is A=πR2 where R=rsinθ and r is the radius of the paper circle (6" for you) and θ is the angle of the cone. Therefore A=π(rsinθ )2. You should therefore expect the measured drag to be proportional to the square of the sine of θ, FD∝sin2θ.
 
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