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If I have two rubber bands and two cylinders, one smaller in circumference than the other in each case. What circumference does the smaller rubber band need to be in order to apply the equal force in the case of the larger band/cylinder?

Assuming you know the circumference of the two cylinders as well as the larger rubber band. How does the force applied by the smaller rubber band onto the smaller cylinder relate to the bands un-displaced circumference?

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  • $\begingroup$ This is an ill-posed problem. How are the elastic coefficients related? $\endgroup$
    – Bill N
    Commented Jun 21, 2018 at 20:02
  • $\begingroup$ Or, how about friction. Can it be ignored? $\endgroup$
    – John Alexiou
    Commented Jun 21, 2018 at 20:07
  • $\begingroup$ The elastic coefficient's should be the same assuming the same material properties and cross sectional areas. $\endgroup$
    – inputchip
    Commented Jun 22, 2018 at 4:26

1 Answer 1

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You will need to deform both rubber bands by the same factor. For example, if you put the big rubber band around a cylinder that is 3 times its diameter, you will need to look for a cylinder that is 3 times the diameter of the small rubber band in order for them to apply the same force per unit area.

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  • $\begingroup$ You are assuming that the elastic coefficient of each rubber band is the same. That's not necessarily true, especially if the rubber bands are of different circumferences. $\endgroup$
    – Bill N
    Commented Jun 21, 2018 at 19:59
  • $\begingroup$ The elastic coefficient of each rubber band is exactly the same if the material is the same, regardless of how much they stretch. $\endgroup$
    – user3408085
    Commented Jun 21, 2018 at 20:20
  • $\begingroup$ I disagree. Two rubber bands of exactly the same material but one is half the circumference. Hang 500 g from each. The smaller will stretch half as much as the larger. Therefore, the total elastic coefficient of the smaller is twice as large. $\endgroup$
    – Bill N
    Commented Jun 21, 2018 at 20:24
  • $\begingroup$ You are mistaking the linear displacement of the elastic bands with their STRAIN, which i s a "percentage of deformation" if you want to see it that way. The Force applied by the bands is related with the stress in the band, and the stress in the band is related with their strain: [researchgate.net/profile/Ilhan_Ozan_Tuncoez/publication/… So if they have the same strain value, they will apply the same force. $\endgroup$
    – user3408085
    Commented Jun 21, 2018 at 20:28
  • $\begingroup$ The slope of the curve in the graph is the elastic coefficient, and it is only material defendant. $\endgroup$
    – user3408085
    Commented Jun 21, 2018 at 20:31

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