# Why there is an extra componet of force in this Equilibrium state?

I have a question about the forces on a body at equilibrium. Look to this image:

here i draw a man standing with a pen on earth. And I think that I draw all possible forces on it. They are as follows:

1) Force $F_1$ due to the weight of pen.

2) Force $F_2$ acting on earth by pen accourding to newton's third law.

3) Force $F_3$ due to friction between hand and pen to hold it.

4) Force $F_4$ equal and opposite to $F_3$ acting on man.

(Note that magnitude of $F_1=F_2=F_3=F_4$ ).

5) weight of man $W$ acting downward.

6) Since $F_4$ acting on the man downward, the normal reaction is $W+F_4$ acting upward.

I think that I mention every forces here. Due to the fact that the body in equilibrium, all forces must cancel each other. But there comes an extra component equal to the weight of pen. Where is my mistake?

• physicsclassroom.com/class/newtlaws/Lesson-2/…
– user83548
Dec 20, 2015 at 16:43
• Your mistake is that you're not consistent in your definition of 'W'. In the first use of 'W' in your picture the 'W' represents the weight of the man AND the pen. In the second use of 'W' where you show "$F_{4}+W$, the 'W' now represents the weight of the man only.
– user93237
Dec 20, 2015 at 21:59

Due to the fact that the body in equilibrium, all forces must cancel each other.

Which forces must cancel each other when a body is in equilibrium?

When a body is in equilibrium, resultant of forces acting on it must be zero. In current question, we have three bodies those are in equilibrium (man, pen and the earth). So, net force exerted on each of them must be zero.

For this purpose, you should draw free body diagram for each body. For example, free body diagram for man is like figure below: (Let's assume that man has held the pen on his palm because if you want to consider to friction, you should consider to the normal forces between hand and pen also) The forces are as follows:

1. $F_1$ due to the weight of the man.

2. $F_2$ due to the normal reaction of pen.

3. $F_3$ due to the normal reaction of the earth.

First of all, you should at first learn to decompose all forces for all objects and after to put the interaction between objects/bodies/etc.Here you have three object:earth, pen, human. You also have some Normal Forces on earth used in the friction. For details here

"In mechanics, the normal force $F_{n}$ is the component, perpendicular to the surface (surface being a plane) of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from falling. Here "normal" refers to the geometry terminology for being perpendicular, as opposed the common language use of "normal" meaning common or expected. "

• ok but it seems you does'nt answer my question. What you mean by saying the concept of 'normal' here? Dec 20, 2015 at 17:18