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dlucaswood

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I hope I'm posting in the correct section! I’m trying to work out the force required to stretch resistance training bands for two particular set ups shown in the pictures. I’m not a physics student or anything like that (I'm many years out of school!), however I am pretty good at maths. I’m just not quite sure of the equations I need to work these problems out, so any help much appreciated!

**Set up 1:**

With the first set up, I would be standing in the same position, with my feet anchoring the band a certain distance apart, and my hands holding the band a certain distance up, as shown.

I’m guessing the force required on each side is based on the length of exposed band from my left hand to left foot, and the same on the right. Is that correct? What I’m confused about is that the smaller that distance, the more force required to pull the band. So, pulling the band 5 inches when there is a lot of band exposed is easier than pulling it 5 inches when only a small amount of band is exposed. Why is this?

How might I put this into an equation that relates the three variables of force, length of required elongation and exposed band length for each band in question (I have 5 bands, all with different cross-sectional areas, all made of latex rubber)?

**Set up 2:**

With the next set up, the band is now anchored and pulled at a certain angle:

In this instance, the band is anchored on a vertical surface, and the is held a certain distance from that anchor, leaving a certain length of band exposed.

How might I put this scenario into an equation that relates the four variables of force, angle of pull, length of required elongation and exposed band length for each band in question?

The bands are loop bands as shown below:

I’m guessing that using them doubled over vs. just one side means that the force required in the above scenarios is just multiplied by 2?

Really appreciate your help, apologies if this all seems very basic! It’s been a few decades since school!!

Darren