# Normal reaction - force without acceleration

When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.

However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?

• It is assumed that forces can be added and decomposed. Diverse effects cause different forces on the same body (e.g., weight or elastic force of the table). These forces on the same body have to be added to a resultant force. Only the resultant force is relevant for the acceleration of the body. Jun 3 '14 at 13:53

When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.

Correct

However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?

But you do have an acceleration, $g$, which you stated in the first paragraph (the force on the body due to gravity...). And this force is equal and opposite to the normal force: $$\mathbf F_{g} = -\mathbf F_N \\ mg\left(-\hat{z}\right) = -mg\hat{z}$$ That the net force is zero only means that the object is not accelerating, not that there are no forces acting on it.

• may I ask how you settled that if body is lying on the Earth's surface then it is in the state of Equilibrium under its Weight and Normal Force. The Equilibrium exists when the two opposite and equal forces are applied on a single or same body. In the boy's case the action force is acting on the ground and reaction force is acting on the body. The question stays unanswered yet. That say's that if body was applied an equal force in reaction by Earth then it must be experiencing some acceleration viz., it must move away a little bit from earth in the direction of reaction force.
– user73555
Feb 27 '15 at 10:47
• I settled it because the person isn't accelerating relative to earth, so there must not be any net force acting on them (the gravitational force and normal force are equal and opposite). Feb 27 '15 at 13:29
• Newton's second law says that $\sum \mathbf =m\mathbf a$ (the sum of the forces is mass times acceleration). In the case of a non-accelerating body, $\mathbf a=0$, thus we require $\sum\mathbf F=0$. Since we have two forces, gravity & normal, then $\mathbf F_g+\mathbf F_N=0\to\mathbf F_g=-\mathbf F_N$ as I've written. Feb 27 '15 at 13:31
• It's actually really simple to conclude this. If you were accelerating, then your velocity is necessarily changing in time. If you are stationary (not moving), then you have no velocity. Thus, stationary objects have no acceleration. Even if your acceleration were "small," over time you'd have a noticeably non-zero velocity, but you don't. Feb 27 '15 at 18:46
• So you are quoting yourself & your entirely flawed understanding of Newton's 2nd law? Good luck with that. Feb 27 '15 at 20:53

Newton's second law of motion states this (verify on Wikipedia): $$\vec F_{net} = m\vec a$$ Here, $\vec F_{net}$ is zero, so $\vec a$ is zero too. Going back in reverse (what you did in question), $\vec a = \frac{\vec F_{net}}{m}$ can only deduce that the body is experiencing no net force. That's it.

Feel free to use Law of Gravitation, Coulumb's Law etc when the force in question isn't the sole cause of the effect. Newton's second law of motion can't help here.

how can the body exert a force on the ground when it does not have any acceleration?

The body has acceleration relative to the earth $$F_{earth} = F_{object} \\ m_{earth} * a_{earth} = m_{object} * a_{object}$$

Since force equals mass times acceleration (magnitude-wise) how does a body without acceleration experience a force?

The sum of forces in the body equals the external force acted on it.

The reaction force of a body can not exist without the action force,this is precisely why the body experiences a press on it, the reason it doesnt accelerate is because the forces balance,but that doesnt mean the gravity would seize to act thus the reaction felt by the object

When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.

Correct

However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?

But you do have an acceleration, g , which you stated in the first paragraph (the force on the body due to

• You seem to have submitted this before finishing your thoughts. Could you update with the completed thoughts? Nov 5 '14 at 14:26