Question

You drop a piece of paper, and observe that it eventually falls at a constant speed. Which of the following statements about this situation is based on a fundamental physics principle? (a) Because the paper is moving downward, we know that it experiences a nonzero net downward force. (b) Since the momentum of the paper does not change from one instant to the next, ${\overrightarrow{\mathbf{P}}}_{\mathbf{f}\mathbf{u}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{e}}\mathbf{}\mathbf{=}{\overrightarrow{\mathbf{P}}}_{\mathbf{n}\mathbf{o}\mathbf{w}}$, and therefore the net force on the paper must be zero. (2) You give a push to a toy car, which rolls away smoothly on a wooden floor. Why does the car keep moving after your hand is no longer touching it? (a) The momentum of the car just after it leaves your hand reflects the total impulse given to the car by your hand. (b) Your hand continues to exert a force on the car even after the car and hand no longer touch.

Short answer

(1) (b) is the correct statement.

(2) (a) is the correct statement.

Step-by-step solution

Understanding Newton’s first law

Newton's first law asserts that if any particular body is at a rest position or moving in a straight path at a constant speed, it will remain at a rest position or continue to move in the same straight line at a constant speed until acted upon a particular force.

The interactions between particles and physical things are governed by the physical laws of matter, energy, and the fundamental forces of nature, according to physics.

(1) Using Newton’s first law in option (b)

The paper has a constant velocity which means it has a constant speed and constantly travels downhill.

The momentum is constant and does not vary. So, the net interaction of this paper with its surroundings is zero as per according to Newton's first law.

Thus, option (b) is the correct option.

Explanation for option (a)

Zero interaction of paper with its surroundings does not imply that there must be motion.

It implies that the object's status of motion will change due to the contact between the paper with its surroundings.

Thus, statement (a) is incorrect.

(2) Understanding the role of the momentum in option (a)

The momentum has been maintained throughout interactions between the automobile and its surroundings. So, the car keeps moving after the hand is no longer touching it.

Thus, the correct statement is (a).

Explanation for option (b)

The hand no longer exerts force, and there is no contact between the hand and the automobile once the car has departed. The hand cannot continue to exert a force on the car even after the car and hand are no longer in touch.

Thus, the statement (b) is wrong.