Every action is equal to each and opposite reaction. Then why when we stand on mud or sand does our foot sink? Is this following Newton's Third Law?

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valentin68 | College Teacher | (Level 3) Associate Educator

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Suppose you are standing on firm ground, just one step in front of mud. Newton first law is saying that as long as there is no force acting on you, because of your inertia you will keep your moving state (in this case not moving on the vertical axis). Hence on firm ground the resultant force on you (your weight+ground reaction) is zero.

`G +N =0`

Now you take one step ahead and feel that you begin sinking in mud. Because (on the vertical axis) you were not moving just before and now you sink (you are now moving down), there need to be a resultant force directed downwards that pulls you down. Thus on mud or sand there is a resultant force downwards.

`F =G +N > 0`

However this does not contradict the Newton third law. In this case there will be a third force (your body inertia -`m*a` ) which added to the previous two forces will make a total of zero.

`G+N+m*a =0`

In this case (body sinking in mud or sand) the third principle can be written as:

The reaction to the resultant (`F`) of body weight (`G`) plus ground normal force on you (`N` ) (the sum of these two forces is the action) is equal to the body inertia (the body inertia is the reaction).

`F+m*a =0`

If you want to say it a bit different:

Action force = Reaction Force for a body that is in keeping its moving state (for example standing), i.e. it has zero acceleration.

Resultant of all forces (action) = body inertia (reaction) for a body that has an non negative acceleration.

Thus Newton third law is in all cases valid.

Sources:

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