# 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. – Wojciech Mar 10 '14 at 13:26

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.
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 – aukxn Mar 10 '14 at 13:37