How to calculate the force needed to get out of bed?

[CWatters]

.. intuition tells me it can't just be that, because if the bed were flat, sitting up the torso from a flat 0 degrees to 90 and then 20 degrees more towards the feet, is not as hard.

Your intuition is wrong. These two situations are not the same.

In the first the "extra" 20 degrees is from -20 to 0 (horizontal). The centre of mass of the torso is being raised so you are doing work against gravity.

In the second the "extra" 20 degrees is from 90 (vertical) to 110. The centre of mass of the torso ends up lower as you bend forward so you are doing no work against gravity. (aside: It still takes some effort because you have to compress your stomach etc.)

It's not just the extra angle that matters. It's where that extra angle occurs.

One problem with analysing situations involving the human body is that the human body is inefficient. For example...Suppose you do a partial sit up to the 45 degree position and hold in that position. After awhile it will get harder and harder to remain in that position until your stomach will be screaming at you to stop. It feels like you are doing lots of work but you aren't. On the way up to 45 degrees you are doing work against gravity. Once you reach the 45 degree position and stop you are no longer raising your centre of mass so you are doing no work against gravity. The pain you feel while holding in that position is entirely due to the inefficiency of the human body.

 

[CWatters]

Ok here is my last attempt to explain it in terms of the work done against gravity..

 

[marciokoko]

Thanks CWatters. So you would say that in the first scenario you make 90 degrees against gravity but in the second you make in 110 degrees against gravity?

 

[sophiecentaur]

In addition to CW's mechanical explanation (which is, of course, sufficient), there is the psychological factor. As you raise your body from horizontal, the required force / torque gets less from the start. (Cos(θ) drops from 1 towards zero). When pulling up from below the horizontal, the required force actually increases as you approach horizontal. That can make the process appear to take more effort.
The Forces and the Energy involved in this process are all relevant to how 'hard' the action feels. It is easy to mix the two up. Also, the angles and heights involved are governed by trigonometry - adding possible confusion. Thus, moving from -45° to +45° involves a different change of height than from 0° to 90° and hence a different amount of Work needed.

 

[CWatters]

Thanks CWatters. So you would say that in the first scenario you make 90 degrees against gravity but in the second you make in 110 degrees against gravity?

Looks like I am confusing you.

There are two ways to calculate the work done...

1) Work = force * displacement

In this case "displacement" is the vertical displacement of the centre of mass. It's different for the 90 and 110 cases due to basic geometry. Force is the weight of the upper torso which is a constant depending on your mass.

2) Work = torque * angular displacement

In this case "angular displacement" is (the radian equivalent of) 90 or 110 degrees. The problem is that Torque is not constant, it's also dependant on the weight of the upper torso but it also varies with the angle making the maths harder.

The two methods give the same answer but 1) is probably easier to understand and calculate.

With the above you can calculate the work done against gravity and that should account for most of the difference between 110 and 90 degrees.

It's interesting to note that if you do a sit up and then lay back down the net displacement is zero as your torso is back where it started. So the net work done is zero. However it sure doesn't feel like you have done no work. What happened is that you do work against gravity on the way up and gravity does work on you on the way back down. It's just hard luck that humans have no way to collect and store the energy that gravity does on you. It ends up being wasted.

 

[marciokoko]

Im sure pretty soon we will when IoT continues invading the health industry.

Anyway, back to my question. Let's say I don't want to calculate anything.

Is there a way to answer the question:

"Why does it feel harder to do a situp from -20 to 90 then from 0 to 90?". Is it really harder? Is it just the fact that more work is being done?

It may seem unbelievable that after 55 posts I am still not clear, but I have gotten sidetracked by some other comments.