Question

How does weight (in terms of w=mg) affect a wide and narrow grip pull ups? does velocity, acceleration, displacement have something to do with it?

Answer 1

Grip determines what muscles will be the main drivers of the movement, which is also determined by hand orientation. As you probably know, pull-ups and chin-ups are almost the same exercise. The (main) difference is that the grip is supinated in the chin-up, while being pronated in the pull-up. Close grip pull-ups are hands down way easier than shoulder width and wide grip pull-ups. Why? This is due to the fact that you are utilizing both arms and back muscles, with the emphasis on arms to pull you up. In doing shoulder width or even wide grip pull-ups, you’re isolating most of the work done on the upper back (lats) alone. This is why shoulder width and wide grip pull-ups are generally much tougher than close grip pull-ups.

With your hands in a close-grip position, you place the shoulders and elbows in a more mechanically advantageous position. Hence, you'll be able to complete more repetitions of close-grip pull-ups than wide grip. The difference in hand placement between the close- and wide-grip pull-ups influences how your shoulder joints move as you perform the exercise. The velocity, acceleration, displacement of the movement depends on the grip position.