Chapter 4, Problem 11Q

To determine

Does the Earth move when we exert a force on it.

Answer to Problem 11Q

Solution:

Earth doesn’t move even though we exert a force on it.

Explanation of Solution

Let us find the acceleration of the Earth and the object assuming the mass of the freely falling object to be m = 1 kg. If the mass of the Earth is M, then the acceleration of the Earth would be found using Newton’s laws of motion.

Acceleration of free falling object will be mg= 9.8m/s²

From Newton’s third law of motion that every action has an equal and opposite reaction, Force on the Earth is:

$\begin{array}{l}{F}_{Earth}=F_{object}\\ M\times a_{Earth}=mg\\ a_{Earth}=mg/M\end{array}$

Since the Earth has a mass that is on the order of 10²⁵ kg, then the acceleration of the Earth is on the order of 10^-24 g

$\begin{array}{l}{a}_{earth}=mg/5.7\times {10}^{24}\\ a_{earth}={10}^{-24}mg\end{array}$

This value is very very small and this tiny acceleration is undetectable. So Earth doesn’t move.