Chapter 7, Problem 30A

If you step off a ledge, you accelerate noticeably toward Earth. Does Earth accelerate toward you as well? Explain.

To determine

To identify:Whether the Earth will accelerates towards the person when the person steps off the ledge.

Answer to Problem 30A

Yes, the Earth also accelerates towards the person with negligible acceleration and motion of the Earth cannot be noticed by the person.

Explanation of Solution

Introduction:

Newton’s second law of motion:

The force $\left(F\right)$ acting on an object is the product of the mass $\left(m\right)$ of the object and the acceleration $\left(a\right)$ of the object.

  $\begin{array}{l}F=ma\\ a=\frac{F}{m}\end{array}$

From the above expression, it is observed that mass and acceleration are inversely proportional to each other, if the force applied on an object is constant.

Newton’s third law of motion:

When an object $P$ applies a force on another object $Q$ , then the object $Q$ will also apply equal and opposite force on object $P$ .

Consider a person steps off the ledge.The Earth exerts a gravitation force on the person and pulls the person towards the Earth.According to the Newton’s Third Law of Motion, the person will also exert an equal and opposite force on the Earth and tries to pull the Earth towards himself.Consider the force exerted by the Earth on the person and the person on the Earth is a constant $\left(F\right)$ .According to the Newton’s Second Law of Motion, the Earth’s acceleration towards the person is inversely proportional to Earth’s mass.As the Earth’s mass is too large, the Earth’s acceleration towards the person is negligible (but not equal to zero).Hence, the Earth’s acceleration towards the person is negligible and motion of the Earth cannot be noticed by the person.

Conclusion:

Thus, the acceleration of the Earth’s acceleration towards the person is negligible and motion of the Earth cannot be noticed by the person.