Question

In the examples given below, which of Newton's Law of Motion will apply? Justify your answer.
(a) When a Swimmer pushes the water backwards.
(b) When a cricket and tennis ball are thrown with the same force, the tennis ball moves with greater acceleration.

Hint:

Always remember: Third Law is about pairs of forces, while the Second Law is about the result of force on a specific mass.

Answer 1

Step 1: Understanding the Concept:
Newton’s Laws explain the relationship between a body and the forces acting upon it. We must identify which specific principle (Inertia, Acceleration, or Action-Reaction) governs the movement.
Step 2: Detailed Explanation:

1. (a) Swimmer pushing water backwards: This applies Newton's Third Law of Motion (Law of Action and Reaction). - Justification: The swimmer exerts a force on the water (Action), and the water exerts an equal and opposite force on the swimmer (Reaction), pushing them forward.
2. (b) Cricket vs. Tennis ball: This applies Newton's Second Law of Motion (Law of Acceleration). - Justification: The law states $F = ma$ (Force = mass $\times$ acceleration). If Force ($F$) is constant, acceleration is inversely proportional to mass ($a \propto 1/m$). Since a tennis ball has less mass than a cricket ball, it achieves greater acceleration.
Step 3: Final Answer:
(a) Third Law (Action-Reaction). (b) Second Law (Force and Acceleration).

Answer 2

Each part of this question involves a different one of Newton's three laws, and looking at the forces and their effects in each scenario separately identifies which law applies and why.

(a) Swimmer pushing water backwards: Here two separate objects are involved, the swimmer's hands and the surrounding water, and each exerts a force on the other. The swimmer pushes the water backward, and simultaneously the water pushes the swimmer forward with an equal magnitude but opposite direction, a second, separate force acting on a different body. Because this scenario involves a pair of equal, opposite forces acting on two different objects at the same instant, it is a direct case of Newton's Third Law of Motion.
(b) Cricket ball versus tennis ball: Here only one force is being compared across two different masses. Newton's Second Law states \( F = ma \), which rearranges to \( a = \dfrac{F}{m} \). Suppose the same force \( F \) is applied to both balls; since a tennis ball has a much smaller mass \( m \) than a cricket ball, dividing the same \( F \) by a smaller \( m \) produces a larger value of \( a \). This is why the lighter tennis ball accelerates more than the heavier cricket ball under the same applied force, a direct outcome of the Second Law.

So the swimmer example involves two bodies exerting equal and opposite forces on each other, Third Law, while the ball example involves one force producing different accelerations depending on mass, Second Law.