It is difficult to drive a nail into a freely suspended wooden frame with a hammer. Which law of mechanics best explains this observation?

Introduction / Context:
Hammering a nail into wood is a familiar everyday activity that illustrates basic principles of mechanics. When the wooden support is rigid and fixed, the nail enters easily. When the wooden frame is freely suspended and can move, it becomes difficult to drive the nail in. This observation is often linked to Newton's third law of motion, which describes the action and reaction forces between interacting bodies such as the hammer, nail, and frame.

Given Data / Assumptions:
• A wooden frame is freely suspended and not rigidly fixed to a massive support. • A hammer is used to strike a nail placed against the frame. • The hammer exerts a force on the nail, and the nail interacts with the wooden frame. • We compare this case with the situation where the frame is rigidly fixed to a wall or heavy support.

Concept / Approach:
Newton's third law states that for every action, there is an equal and opposite reaction. When the hammer strikes the nail, the nail exerts an equal and opposite force on the hammer. Similarly, the nail exerts a force on the wood, and the wood exerts an equal and opposite reaction on the nail. If the wood is rigidly supported, this reaction force has a solid backing and helps the nail penetrate into the wood. However, when the frame is freely suspended, the reaction causes the frame to move away instead of providing a strong opposing force on the nail. In this way, action reaction pairs and the resulting motion explain why the nail does not go in easily.

Step-by-Step Solution:
Step 1: When the hammer hits the nail, the hammer exerts a force on the nail (action). Step 2: According to Newton's third law, the nail exerts an equal and opposite force on the hammer (reaction). Step 3: The nail also pushes on the wooden frame, trying to penetrate. Step 4: The wooden frame exerts an equal and opposite reaction on the nail. If the frame is rigid and supported, this reaction helps redirect the hammer's impulse into driving the nail inward. Step 5: When the frame is freely suspended, the reaction force causes the entire frame to move backward instead of effectively resisting and helping push the nail into the wood. Step 6: As a result, much of the hammer's energy goes into moving the frame rather than forcing the nail inside, making it difficult to fix the nail.

Verification / Alternative check:
You can easily verify this by practical experience. Trying to hammer a nail into a loose wooden plank that you are holding in the air is much harder than hammering the same nail when the plank is firmly placed on the ground or against a wall. In the firmly supported case, the support provides an additional reaction force that helps keep the wood from moving away, making the nail enter more effectively. This emphasises the role of action reaction pairs as stated in Newton's third law and how they influence the motion of interacting bodies.

Why Other Options Are Wrong:
Option a (Law of inertia): Inertia (Newton's first law) deals with the tendency to maintain state of rest or uniform motion but does not directly explain the equal and opposite forces during the hammer nail interaction. Option b (Newton's second law): Newton's second law relates net force and acceleration (F = m * a) but the key idea here is the pair of forces between bodies, which is better captured by the third law. Option d (Pascal's law): This applies to pressure transmission in fluids and is not relevant to hammering a nail in solid wood. Option e (Archimedes' principle): This deals with buoyant force in fluids and has no connection to the situation described.

Common Pitfalls:
Students sometimes confuse which Newton's law to apply in everyday examples. If the focus is on pairs of forces between two objects (action and reaction), think Newton's third law. If the focus is on how force produces acceleration, think Newton's second law. If the focus is on a body remaining at rest or uniform motion unless disturbed, think Newton's first law. In this nail example, the essential point is the equal and opposite reaction of the frame and support, making Newton's third law the best answer.

Final Answer:
The difficulty in fixing a nail into a freely suspended frame is best explained by Newton's third law of motion.