Chapter 6, Problem 1Q

Does an apple exert a gravitational force on the Earth? If so, how large a force? Consider an apple (a) attached to a tree and (b) falling.

To determine

Whether an apple exerts force on the Earth, if yes the magnitude of the force while considering an apple attached to a tree.

Answer to Problem 1Q

The apple exerts a force on the Earth in which magnitude is equal to the force at which Earth exerts on apple.

Explanation of Solution

According to newton’s third law of motion, for every action there will be equal and opposite reaction and the action and reaction are acting on different bodies. The Earth attracts every object towards its center. The force is equal gravitational attractional force.

According to universal theory of gravitation, Earth attracts apple with magnitude equal to $F_{\text{apple}}=\frac{G{M}_E{m}_{\text{apple}}}{r^2}$ where, $G$ is the universal gravitational constant, $M_E$ is the mass of the Earth, $m_{\text{apple}}$ is the mass of the apple and $r$ is the distance between center of Earth and apple. Newton’s third law implies that force acting on Earth by apple is equal to force that Earth exerts on apple.

Conclusion:

Therefore, the apple exerts a force on the Earth in which magnitude is equal to the force at which Earth exerts on apple.

To determine

Whether an apple exerts force on the Earth, if yes the magnitude of the force while considering the apple is falling.

Answer to Problem 1Q

The apple which is free fall exerts a force on the Earth in which magnitude is equal to the force at which Earth exerts on apple.

Explanation of Solution

Universal gravitational law states that every object in the universe attracts every other object with a force which is equal to product of their masses and square of the distance between them.

At each point of motion the gravitational force of attraction increases due to decreasing separation. The Earth attracts the apple which is falling at each time of motion. Then according to Newton’s third law of motion, the apple exerts equal force on the Earth.

Conclusion:

Therefore, the apple which is free fall exerts a force on the Earth in which magnitude is equal to the force at which Earth exerts on apple.