Building a strong lower back, strong stomach muscles

What is it with some machines at the gym, say the ones for the stomach and lower back where you say push back for the back or push up with the chest for the stomach, it seems real easy to practically do a whole lot of the weights, most of them in the machine!

Below the first picture is of the lower back machine, the second picture shows a kind of crunch, slightly different but basically the same exercise.





In the second photo, the difference in the machine I use is I believe one pushes forward on a bar with the chest but I believe this is the same concept.

Now, sometimes one can see people exercise where I believe it is something like, if I am apt in my description, a person runs ahead of another with an elastic exercise cord or band around their midsection, kind of reminiscent to someone in a coach guiding a horse. Maybe I've even seen it where a variation of this is for the person to actually tug someone on one of those little roller things one can use for abdominal excercises, rolling it forward and back.

What I think is similar and what I have done it a lot is to carry things on a bicycle, if one rides a bike and the back of the bike has a rear rack that is loaded up with a lot of weight, that must be good for the stomach muscles and the back.