Why does a sit-up on vertical plane expend more energy than a sit-up on a horizontal plane? If the work done against gravity by the upper body is represented by the formula mgh, where m = (mass of upper body) and h = (distance from the hip to the centre of mass of the upper body), the h distance travelled is equal for both vertical and horizontal planes, and there should be no difference in the work done against gravity by the upper body for both cases (horizontal and vertical planes). Yet a vertical sit-up is indeed more difficult than a horizontal one. Why is this so?
 A: Yet a vertical sit-up is indeed more difficult than a horizontal one. Why is this so?
It is because there is a difference between physical effort and the mechanical work done. I can’t explain the details on why there is greater  physical effort in a vertical sit-up than a horizontal one (it might have to do with different muscle emphasis), but to demonstrate that physical effort does not necessarily equate to work done, consider the following.
You are standing  still and holding a heavy box in your hands. You are not lifting the box, so the work you do on the box is zero. However, it will certainly require physical effort to hold the box. 
To give another example. Suppose you are doing sit-ups on a horizontal plane and  instead of completing each sit up in one continuous motion you stop mid way, hold that position for a while, and then complete the sit-up. You will do the same amount of mechanical work for each sit-up, but it will certainly feel more difficult stopping mid way each time.  Maybe even more difficult than the sit-ups on a vertical plane.
Hope this helps.
A: I think a major reason is that when you do a sit-up on the floor, you get a "break" at both ends of the movement (you can release the muscle tension): at the top, your torso is basically balanced over your hips, so there is no gravitational torque to overcome; and at the bottom, the torso is supported by the floor.  This doesn't change the amount of work, but it gives the muscles a chance to rest.  When doing sit-ups hanging upside down, there is only one chance per cycle to rest: at the bottom.
You can verify this by doing sit-ups in a horizontal position, but without the floor support.  Try doing horizontal sit-ups on an elevated platform which supports only the bottom half of your body (sitting on the edge of the platform facing inward).  You still lower your torso to fully horizontal, but you have to stop it there using muscle tension.  This type of sit-up is much harder than a normal one, and maybe almost as hard as a vertical one.
