# Where is this external force coming from? Center of Mass [closed]

When I lift my hands above my head, my center of mass moves upwards. What force causes my center of mass to move upwards?

We know that $$\vec{F}_{\text{net external over all particles}} = M\ddot{\vec{R}}_{cm} \tag{1}$$ where $M$ is the total mass and $\vec{R}_{cm}$ is the center of mass of the system. This is the equation of motion for the center of mass. It says that only external forces determine the trajectory of a center of mass.

Thoughts :

When I lift my arms above my head, this force could be an external force. If so, my question disappears. However, a new question arises which is: where is this external force coming from? It's source/location? (One would think the food that we eat... However I'm still confused how an external force can reside within our bodies/midochondria).

Now equation $(1)$ assumes that all internal forces are equal and opposite. If we assume this is not the case, equation $(1)$ becomes

$$\sum_{\alpha}\sum_{\beta\neq\alpha}\vec{F}_{\alpha\beta} + \sum_{n} \vec{F}_{\text{n}}\;^{\text{external}} = M \ddot{\vec{R}}_{cm}$$

where the double sum takes care of internal forces and runs over all particles (the force on particle $\alpha$ due to all other $\beta$). So maybe it's the internal forces which allow my center of mass to shift upwards when I raise my arms. However, I'm still confused what this would even mean.

With play-doh if you deform the shape, it's easy to see why the center of mass would move. You are applying an external force to the play-doh. The human body is much more complicated, but I was wondering if I'm missing something in my above logic. (there is also a subtlety between a discrete and continuous mass distribution - but I think the equations still apply - or maybe they dont)

## closed as unclear what you're asking by ja72, sammy gerbil, Chris♦, Bill N, Jon CusterFeb 9 '18 at 13:58

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• Is this biology question of a physics one? If the latter: bringing the human body into a problem never makes the physics clearer. Model this with a big mass (your body), and compressed spring (muscles), and a little mass (your arms) on top: what happens when to the CM when the spring relaxes to equilibrium? What's the force on the ground? How is energy balanced. When you have that dialed, increase the complexity of your model. – JEB Feb 4 '18 at 16:58
• -1 Not clear. Are you asking about a situation where you are floating in space, or when you are standing on the Earth? – sammy gerbil Feb 5 '18 at 13:14
• Stand on a scale and raise your hands. You will see where the force is coming from. – ja72 Feb 5 '18 at 16:32
• Possible duplicate of Measuring weight with weighing scale doing dumbbells – Bill N Feb 8 '18 at 22:32
• It's the reaction from the ground. – valerio Feb 9 '18 at 7:46