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This is a question I've had for several years but never had the knowledge to calculate myself. Please keep in mind I don't have much background in physics (learned some on middle school I guess...), but I'd still love a thorough answer and I'll do the research further needed to understand it.

Years ago, I was told that the force applied on my back while brushing my teeth leaning is about a 2000kg, and putting a hand down on the sink would make this force become 0. I found this very weird but lately I started doing some work with motors and found the force of torque, so this feels a little more possible but still kinda wrong.

So let's get to it. Assuming I lean forward while brushing, my weight would have some force on the pivot point of my back.

Let's assume that pivot point is 95cm above the ground, and the top of my head is 171cm above the ground. This gives us a total of 76cm from the top to the pivot point.

Let's also assume that the weight above the pivot point is 55kg and that it's spread equally throughout the height.

We'll also assume that the leaning angle is 25° from the position where I'm standing straight.

How can I calculate the torque (or whatever units of measurement would be appropriate here) applied on that pivot point?

Bonus: How can I calculate the torque applied when putting a hand down? You are welcome to assume anything here since I don't even know what variables would be needed for such a calculation.

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  • $\begingroup$ Brushing your teeth will be totally fine. It is when you are lifting a heavy box from the ground where being bent over will very extremely serious. But because you do not yet understand the torques = moments involved, your recollection has a lot of unit mistakes that make comparing computed results very difficult. For example, rather than 2000 kg, I got 883 kg cm worth of torque on the pivot point by your numbers. This result spikes really quickly with angle and weight, so the general concept they are trying to tell you is correct. $\endgroup$
    – naturallyInconsistent
    Commented Feb 25 at 23:12
  • $\begingroup$ @naturallyInconsistent thanks for the comment! I'd love to see your calculations so I could also play around with some of the numbers and understand the concepts better. $\endgroup$
    – Yoda
    Commented Feb 26 at 0:18

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The vertebrae column is a wonderous contraption full of balances, tensegrity, and organics. As such, it is a daunting challenge to predict its behaviors, even at a PhD level of physics, much less middle school. Fortunately for us, that means all of the PhDs do a bunch of measurements for us! I found this page which has the following picture in it:

Increased Pressure due to posture

As we can see here, you absolutely do increase pressure on your spinal disks when leaning over. And it's a lot: 275kg rather than 100kg for an upright individual, but its a far cry from 2000kg.

Now I do note that you're using masses to represent forces here. To turn this into a force, we multiply by the acceleration of gravity, 9.8 m/s2. That 275kg is 2695N. That number is close enough to your original 2000 that I'm wondering if the original statement had a units issue.

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