This seems like a simple yes, but here is my confusion.

A band snaps back faster than an object would free fall.

So even if a stretched band was 20 pounds of force, it is pulling at a higher velocity than a twenty pound weight.

For example if you do an arm curl with a 20 pounds weight, it applies 20 pounds of force pulling down by gravity, but if you do an arm curl against a stretched band the 20 pounds of force is pulling your arm down at a greater potential velocity, but with the same poundage...

Can a physics person help me clarify this?

The acceleration that your forearm experiences when you let it fall to your side under gravity with no resistance by your muscles is equal to the acceleration due to gravity: g = 9.8 m/s^2 (N.B. it[s actually a bit more complicated than this, given that your forearm rotates about your elbow as opposed to falling straight down, but this is good enough to get the idea across). And if you are holding a 20 pound weight in your hand, the acceleration of your forearm plus the weight when you let them both fall is also that same acceleration, . Mathematically, the controlling equation is :

Case A: Arm with no weight:


Case B: Arm plus weight:


In both cases the acceleration is the same. Note it doesn't matter what the mass of your arm or the weight is.

But it's different with the elastic band, because its force is not dependent on its mass:



If you assume that the mass of the band is 0, this becomes:



So you see the acceleration downward in this case is greater than .

Bottom line: if you apply the same force to a system with less mass, you get greater acceleration.

Yeah...

Gravity pulls per pound... meaning 2 lbs will have twice the force as 1 lb. Thus when gravity accelerates 1lb or 1000lbs, it is going to move at the same time.

An elastic band only applies that amount of force at which it is rated. So, an empty band will pull far faster than a weighted one. Furthermore each point you have it stretched will have a different poundage.

How does this work in exercise equipment...

To move a set of weights up and down at a constant speed, you have to apply the same amount of force through the entire cycle. With a band system, you will usually go past the point where the force is equal to the weights, so now you are trying to apply the same force and it is kicking harder.

Let me illustrate this in a real world view.

Lets say there are two bars set up for squatting. One with a band system, and the other with weights. The guy first uses the weights, say 200 kilos. In order for him to squat down, and then return up he would have to apply the same force during the entire down motion to prevent gravity from taking it down faster... and then extra on the way up to cancel out gravity and then move it upward.

In the band system, say, the band was stretched to 200 kilos while he was stand perfectly upright, as he got lower, the amount of force he needs to keep it at the same pace lessens, and on the way up the same thing happens in reverse.

After watching this you go use the banded one thinking it will be easier... but you forget that you are a couple of inches taller than he. When you get under the bar and the band tightens, you have around 220 kilos on your shoulders instead. You can't really handle 220 so you start to buckle. By the time you reach the point where the band is only putting 200 kilos on your shoulder you are going faster than you would if you had had 200 kilos on your shoulder. The amount of force to stop you now is greater, and as you go down the band seems lighter, but you have continued to go faster because momentum takes over.

Conclusion... bands aren't exact.

If you have 20 lb test band, test it against 20 lbs to compare it to gravity (It will fail)

I hope this makes some sense...