# Do we stand on the earth because of Newton's third law?

This is the question I encountered and I'm not sure I understand. The Newton's third law say that, when a body 1 exerts a force on the body 2, then the body 2 will exert the same force on body 1, but in opposite direction. Here, the answer say that 2 force apply on the same object. Both gravitational force and the upward contact force all apply on the car. So, if Newton's third law is true, there must be a force that exert to Earth surface so that there will be the reaction force. What force is this?

Also, I don't understand the part of answer which is after the first sentence.

• I'm not sure if I understood You correctly, but when the earth exerts a gravitational force on the car, at the same time the car exerts a gravitational force on the earth, their values are equal, but they have opposite directions. Mar 10 '14 at 13:26

## 1 Answer

You posed two questions: First, Earth exerts a gravitational force on the car. The car, in turn, exerts a gravitational force on Earth. These are equal and opposite. This can be seen from the fact that the formula for magnitude of the (Newtonian) gravitational force: $$F_g=\frac{GM_1M_2}{r^2}$$ remains of exactly the same form if the masses are switched. The fact that they are acting in opposite directions is obvious.

Furthermore, one could say that the car exerts a fore upon the ground. This force is just because of the attraction between Earth and the car. Then, the reaction force is the contact force that the ground exerts on the car, keeping it in its place.

About the answer you found, I can say the following things. You probably know that $\vec{F}_{\text{net}}=m\vec{a}$. But we can write $\vec{a}=\frac{d\vec{v}}{dt}$ where $\vec{v}$ is the velocity. Since $m$ is constant, we can say $$\vec{F}=m\vec{a}=m\frac{d\vec{v}}{dt}=\frac{d(m\vec{v})}{dt}=\frac{d\vec{p}}{dt}$$ So, you see that the force is the time derivative of the momentum $\vec{p}=m\vec{v}$. If the momentum is constant, the time derivative, and therefore the net force, is zero. Therefore, all forces acting on the car must cancel out. Since there are only $2$ forces, they must be equal and opposite in order to cancel out, so we arrive at the conclusion.

• So, since the car exert gravitational force on the Earth and vice versa, they are true to Newton's third law right? I mean, the gravitational force the car exert on Earth can be considered the reaction force of the gravitational force which the earth exert on the car. The reason I asked is because I don't know if it is the reaction force or not according to the newton $3^rd$ law that I learned in class Mar 10 '14 at 13:37
• Both gravitational forces occur as a result of masses proximity and each of them is a reaction to the other one. They comply with 3rd law. Mar 10 '14 at 13:40
• @aukxn You should also keep in mind that the name "reaction force" is only a label (and not a very useful one, really). Don't attach too much value to it.
– Danu
Mar 10 '14 at 13:46