# Newton's Third Law of Motion and Gravity

I have another question about the third law of Newton (if you can check the last one that I posted) :

Why is it that the gravity that pushes me on the Earth is so powerful, but the reaction force (normal force) is so weak (I feel a force only on my foot, but even if I jump, gravity keeps me on the Earth). Newton says that for every action, there is an equal and opposite reaction, so why is it that the gravity is so powerful that it keeps me on the surface, but the reaction force is so weak, or is only my imagination?

Sorry for the editing, but I have another question:

If the normal force acts upward, why don't I accelerate?

... the reaction force so weak or is only my imagination?

The normal force is exactly as strong as the gravity force:

If the normal force acting on some part of your body (e.g. your head) was not exactly the same as the gravity force acting on that part of your body, that part of the body would be accelerated, fall down and sink into the ground.

Why if the normal force acts upward I don't accelerate?

Some body is accelerated if the sum of all forces acting on the body is not zero.

Because the gravity force and the normal force are equal (but have opposite directions), the sum of both forces is zero.

You could also argue: When you are standing on the ground, the gravity force accelerates you downwards and the normal force accelerates you upwards the same time. The sum of both accelerations is zero.

When you don't touch the ground, there is no normal force. For this reason you are accelerated downwards.

EDIT

Newton's Third Law of Motion

It seems to me that you are mixing up the Second and the Third Law:

• The Third Law says that the force dragging the earth into the direction of your body is as strong as the force dragging your body into the direction of the earth.

Needless to say that a certain force acting on a very light body (for example your body) has a completely different impact than the same force applied to a very large body (for example a huge ship or even a hole planet).

• What you are talking about is the Second law if I understood your question correctly:

This law implies that the normal force is as strong as the gravity force IF (and that is important) you are not accelerated (and no other forces act on your body).

• The normal force and gravity do not need to balance, as they do not constitute and action-reaction pair. – Sandejo Aug 15 at 14:07
• @Sandejo I did not claim that. However, as far as I understood the question correctly, the user asking the question misunderstood the Newton's laws. I'll edit my answer... – Martin Rosenau Aug 15 at 17:58
• @Sandejo Please see my "Edit" section. – Martin Rosenau Aug 15 at 18:13
• In a question about jumping it is wrong to claim “ The normal force is exactly as strong as the gravity force”. While pushing upwards the normal force is much higher than the gravity force. While in the air the normal force is zero but gravity is not. – Dale Aug 16 at 11:58

The gravity and normal force acting on you do not constitute an action-reaction pair for the purposes of Newton's Third Law. Newton's Third Law generally refers to pairs of forces originating from the same source, but acting on different objects, and does not require that the net force on either of the objects be balanced.

In your example, your normal force is briefly stronger than gravity (while you are jumping), causing you to accelerate upwards away from the surface when you jump. The reaction to the Earth's gravity on you is your gravity on the Earth; likewise, the reaction to the Earth's normal force on you is your normal force on the Earth. While you are just standing, these forces balance out, and when you jump, the Earth's mass is much greater than yours so that only your motion is noticeable.

Why the gravity that pushes me on the Earth is so powerful . . . . ..

There is no pushing that you feel, indeed you do not “feel” the force of gravity directly.

When you are standing on the ground all you can feel is the normal force of the ground acting on you.
For example if you are in free fall there is no upwards push on you due to the ground and you cannot “feel” the force of attraction of the Earth, indeed you “feel” weightless.

. . . . . so why gravity is so powerful that keeps me on the surface but the reaction force so weak or is only my imagination?

The normal contact force on you due to the ground can feel “enormous”.
Just imagine what what you might feel if you fall and that results in a broken limb.

So when you stand still in the ground there are two equal magnitude and opposite direction forces on you which are not a Newton third law pair; the upward force on you due to the ground which you “feel” the effect of and the downward force on you due to the gravitational attraction of the Earth which you do not “feel” but “observe” the effect of.

Why if the normal force acts upward I don't accelerate?

The downward force on you due to the gravitational attraction of the Earth has the same magnitude, so the net force on you is zero.

Here are the forces:

$$f_1$$ and $$f_4$$ are owing to gravity; they are of equal size and opposite direction.

$$f_2$$ and $$f_3$$ are owing to electrostatic repulsion; they are of equal size and opposite direction.

Here $$f_2$$ is just balancing with $$f_1$$ so the man is not accelerating. Gravity is not especially strong or weak compared to the electrostatic force here. They both have the same size.

This picture shows a man who has just started to make a leap; his centre of gravity is accelerating upwards. Now the force on his feet ($$f_2$$) is larger than his weight ($$f_1$$). This is because the chemistry in the muscles have caused the muscles to expand, so he both pushes the Earth away and his centre of mass begins to accelerate upwards. The Earth also accelerates but since it is so heavy this acceleration is negligible.

And here he is in freefall.

Newton's third law says the forces come in equal and opposite pairs, as indeed they do, but note that the partners in each pair act on different objects, and the parts of each pair are owing to the same interaction. They are two parts of one interaction, whether gravitational, or electrostatic, or whatever. It is fairly easy to jump off the ground, so gravity is not all that strong. The reason it is hard to jump right into orbit is that gravity keeps acting on you all the way up, whereas the force you can apply with your feet against the ground only acts for a short moment at the beginning of the jump. If you had a rocket pack offering just a little more force than your weight then you would keep on accelerating up and away. You will need a lot of fuel though.

Think about it this way: earth's gravity is exeeting a force on you and you are also exerting a force on the earth. Though, since the earth is so massive, it hardly shows any change.

Forces are equal, but masses are very different

For your second question: stand still relative to the ground. Are you accelerating? No. This is due to the normal force cancelling out the gravitational force since it is in equal magnitude. This is the heart of newton's third law

Also, see kartikey's comment to better understand the forces in play while you are standing

• @Kartikey, I was referring to after they stood up-- not while in the act of standing. Were you talking about that as well? If you did, would you please elaborate as I'm not sure I totally understand how once can be accelerating upwards while they are stationary relative to the ground. – Sceptual Aug 15 at 15:04
• My downvote is locked, I can undo it only if you edit your answer – Kartikey Aug 15 at 16:40
• @Kartikey I made my answer more clear and said that you are not accelerating when you stand still on the ground – Sceptual Aug 15 at 16:44
• Yes, I referred to the act of standing. Elaboration-> The motion of extended bodies is described in terms of motion of it's centre of mass, which depends on the geometry of a body. I process of standing you are stationary to the ground but your body's geometry changes so the the centres of mass accelerates as it moves. It is more nearer to the ground while sitting and farther after standing. – Kartikey Aug 15 at 16:47

I think you are messed up with the cause of normal force and gravitational force .

Cause of the Normal force is explained here :

How can I stand on the ground? EM or/and Pauli?

while gravitational force is the force due to mass. And two completely different types of forces can't form an action- reaction pair in Newtonian mechanics. The gravitational force with which earth pulls you and the gravitational force with which you pull the earth forms an action- reaction pair.

Normal force which acts upon you is completely balanced by the gravitational pull of the earth (or you can say it the other way) as they have the same magnitude. So you can't accelerate upward with the normal force.

The reaction force is the same but the mass of the earth is so big it barely accelerates up and due to air friction it practically doesn't move at all?.