# Can force be applied without accelerating?

When I push against a wall, I am applying force on the wall and the wall applies an equal force against mine therefore the wall doesn't move and neither does my hand. But isn't acceleration required to apply force? My hand is not accelerating when I am applyin the force. Still let's assume that the muscle fibres are accelerating, but how is the wall accelerating to apply an opposite force. So are the atoms accelerating somehow?

• It might seem intuitive that force and acceleration must be tied together. But that's unfortunately not the case. No law ties force to acceleration. There is only a law tying the total force to acceleration, not individual forces. – Steeven Aug 10 '19 at 15:47
• It depends how hard you push and whether the wall gives way or not. – Michael Walsby Aug 10 '19 at 15:47
• Related Question: With Newton's third law, why are things capable of moving? – BioPhysicist Aug 10 '19 at 15:48
• You might be interested in Statics: Statics is the branch of mechanics that is concerned with the analysis of loads (force and torque, or "moment") acting on physical systems that do not experience an acceleration (a=0), but rather, are in static equilibrium with their environment. – Alfred Centauri Aug 10 '19 at 22:35

Acceleration happens when the net force on an object is not zero.

You can apply as much force as you like to an object and it won't accelerate if something else is applying an equal and opposite force.

When I push against a wall, I am applying force on the wall and the wall applies an equal force against mine therefore the wall doesn't move and neither does my hand.

Your reasoning is flawed. The reason your hand and the wall do not move is not because the two forces you mention are equal in magnitude and opposite in direction. The two forces are acting on different objects (one being your hand, the other being the wall), so you can't use both forces to analyze the motion of each object separately. The correct reasoning will follow from explaining the rest of your question.

But isn't acceleration required to apply force?

The best way to phrase this is "net forces cause accelerations". If there is no acceleration, then there must be no net force.

Your hand is not moving. Therefore, there is no net force acting on your hand. Therefore, there is/are some other force/forces counteracting the force the wall applies on your hand. What is this force? Well, it is most likely the force from your arm, wrist, muscles, etc. that prevents your hand from snapping too far backwards.

The wall is not moving. Therefore, there is no net force acting on the wall. Therefore, there is/are some other force/forces counteracting the force your hand applies to the wall. What is this force? Well, it is most likely the force the ground, building structure, etc. that prevents walls from moving and makes buildings fairly safe to be in.

Ultimately Newton's third law just tells us that forces arise from interactions. It doesn't tell us anything about how these forces then cause objects to move around, accelerate, etc. That is up to Newton's second law to do. Don't try to use N3L to explain something it does not explain.

Well my question was how is my hand able to apply force without accelerating becuase f = ma and force can't be apple without acceleration right?

Newton's second law of $$F_{\text {net}}=ma$$ does not mean that in order to apply a force an object needs to be accelerating. What is means is that when a net force is applied to an object then that object will experience an acceleration. You have to understand what equations mean. In physics: equality does not mean any physical interpretation is allowed. Net forces produce accelerations is the correct interpretation. Objects do not need to be accelerating to produce forces.

• Well my question was how is my hand able to apply force without accelerating becuase f = ma and force can't be apple without acceleration right? – user662650 Aug 10 '19 at 16:20
• @user662650 oh ok I think I get what you are saying – BioPhysicist Aug 10 '19 at 16:47
• @user662650 See my edit – BioPhysicist Aug 10 '19 at 16:51

But isn't acceleration required to apply force?

In fact, there's a branch of mechanics concerned with (static) applied forces that (vector) sum to zero so that there's no net force and, thus, no acceleration.

For example, consider the analysis of a truss in a steady state condition.

Image credit

Note that there are applied forces and yet the truss is static.

Well aside what other users said, actually a part of wall does move, you can't just see it with naked eyes. The point you are trying to push "deforms" very slightly. If you want to see it yourself, instead of pushing, punch it as hard as you can. I did it my self and this is the result:

My hand hurts a little though. Anyway the force exerted on your hands also pushs your flesh inside, so your flesh accelerates too (for a moment at least), you can't see it (but you can still feel it). If you were in space, and there was a floating wall in front of you, by pushing it you would accelerate in opposite direction, in the Earth however, it doesn't happen because other forces go against it.

Well my question was how is my hand able to apply force without accelerating becuase f = ma and force can't be apple without acceleration right?

No no, your hand does accelerate the wall. Let's say wall is rigid (well it's not really possible, but let's assume it anyway) and you are on skateboard, if you push the wall away, you will accelerate on opposite direction, what about wall? Well wall is connected to ground, so what you are trying to push is actually earth itself! I mean just think about it, the mass of earth is about $$10^{24}kg$$ it means the acceleration will be $$F/10^{24}=a$$ now compute the acceleration yourself based on the value of force.

First of all, F =ma doesn't mean that to apply force you have to have acceleration. F =ma means force F applied on mass m produces an acceleration a and this product of m and a gives the force which was applied. How much force can you apply can only be known when you set some mass on motion, your acceleration doesn't have to do anything with applied force. I can explain you with an example, let's imagine that a cricket ball hits the ground (ground is still) and bounces off, since their is change in velocity(direction has changed) that means there must be some acceleration behind that change and to produce acceleration there need to be a force, force came from ground but ground was initially at rest (ball didn't set the ground in motion but due to action-reaction it got bounced off).
You may have moved but there is friction between your feet and the ground and the center of mass also plays some role. Wall didn't move because of the friction, higher the mass more the friction. Every force develops an acceleration but friction nullifies it.
Hope it helps! If not then let me know through comments.