# Force with zero acceleration [duplicate]

If I apply a force on a body which is kept against a wall, then the body will not move. The body is not moving means that its velocity is zero, and hence its acceleration is also zero. According to Newton's second law of motion, $$\ F = ma$$ If the acceleration is $0$, then $F = 0\ \text N$. It means that I'm not applying any force on the body, but how can it be if I'm pushing my hands against the body?

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## marked as duplicate by Waffle's Crazy Peanut, dmckee♦Mar 25 '13 at 19:03

Possibly, You don't need an object between you and the wall. But simply, the same thing happens if you push the wall. – Waffle's Crazy Peanut Mar 25 '13 at 14:38

It means that the ball is pushing to the wall. And, due to Newton's third law, the wall also on the ball. The forces on the ball are then equal and opposite.

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According to Newton's third law of motion, to every action there is an equal and opposite reaction. When I'm applying the force on the body which is kept against the wall, so I'm not just applying that force over the body but also on the wall, as a result it reacts by applying opposite force on me which is equal in magnitude to that of my force. Therefore, both the forces cancel each other out and the net force is 0. However, if I apply a force on the wall directly then the wall will exert an equal amount of force over me. These forces are not cancelling each other out. The reaction force is acting on me, whereas the action force is acting on the wall. Inertia is the property of an object which tends to keep the state unchanged, and mass is the measure of inertia of an object. Therefore, I'm more likely to be pushed by the wall backward and accelerate because my mass is very much less than the wall, whereas the wall wouldn't move from its place because it has a greater mass and hence greater inertia.

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Acceleration appears if the resulting force is not zero. Your probe body experiences two forces: yours and the wall's that are in the opposite directions. They in sum give zero.

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