# Sum of the Normal Force

1. Sep 8, 2015

### Kenshinz

1. The problem statement, all variables and given/known data
Hi all! I have been blindly drawing normal forces till today and i stumbled on this question.

2. Relevant equations

3. The attempt at a solution
I have drawn 3 normal forces,
- Hand
- Leg
- Center of mass

Is there a normal force at the center of mass and is it the sum of the normal force at the hand and the leg?

Thank you!

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2. Sep 8, 2015

### BvU

Hello Ken, welcome to PF !

There is no normal force at the center of mass.
In fact the mg at the center of mass isn't there either: the force of gravity is spread out over the whole of his body. But for convenience we add up all these small contributions to one force, that then equivalently acts at the center of mass (basically that's a definition that locates the center of mass)

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3. Sep 8, 2015

### Kenshinz

Hi BvU!

Thank you for the prompt and intuitive response! But how would I indicate the weight of the man then?

4. Sep 8, 2015

### BvU

You are doing just fine indicating the weight this way. And your total FN is also correctly located (*) (and the arrow should be just as long as the mg arrow: if the guy is in a stable position, the sum of FN plus mg has to be zero). But the total FN is not a new force acting on the man; instead it is the sum of the two others at hands and feet.

(*) Correctly located, because not only the sum of the forces has to be zero (that would still allow FN at the toes to be the whole of mg) but also the sum of the torques (the leverages). Which means that the line of action of the sum of the two FN coincides with the line of action of mg (c.q. the sum of all gravity force onall parts of the guys body)

5. Sep 8, 2015

### SteamKing

Staff Emeritus
A normal force is a contact force. If there is no contact, there is no normal force.

6. Sep 9, 2015

### Kenshinz

Thanks guys! And since normal force is an opposing force, would the normal forces in the picture be drawn correctly? I drew it in red.

The question is *Draw the normal forces that the legs of the skateboarder and the metal rail exert on the skateboard.*

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• ###### Untitled.png
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7. Sep 10, 2015

### BvU

I don't like the question (don't know why not - intuition (*)?) but yes, that's what was asked.

(*) skater exercises a force on the board, and I suppose you can consider that a normal force.

8. Sep 10, 2015

### Kenshinz

Thank you for the reply BvU.

I am still unable to get hold of why the normal forces are pointing downwards for the legs instead of upwards as the force 'weight' would be pulled by gravity hence facing downwards.