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91Ó°ÊÓ

Two planks \(A\) and \(B\) are sliding in the same direction on smooth horizontal surface such that \(A\) is faster than \(B\). Packets of equal weight are transferred from \(A\) to \(B\). Due to this: (1) \(A\) will be accelerated and \(B\) will be retarded (2) \(B\) will be accelerated and \(A\) will be retarded (3) There will be no change in \(A\) but \(B\) will be accelerated (4) There will be no change in \(B\) but \(A\) will be accelerated

Short Answer

Expert verified
(2) B will be accelerated and A will be retarded.

Step by step solution

01

Understand Initial Motion

A and B are moving on a smooth horizontal surface with no external forces causing resistance. Plank A is moving faster than plank B.
02

Analyze Packet Transfer Effect

When packets are transferred from A to B, momentum is transferred from A to B. This means a force acts on A to reduce its velocity (retardation) and on B to increase its velocity (acceleration).
03

Apply Conservation of Momentum

According to the law of conservation of momentum, the total momentum of the system must remain constant if no external forces are acting. Therefore, the gain in momentum of B must equal the loss in momentum of A.
04

Conclude the Outcome

Since packets are transferred and momentum is conserved, transferring mass from faster-moving A to slower-moving B results in B getting accelerated and A getting retarded.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Momentum Transfer in Physics
Momentum transfer is a core concept in physics that describes how momentum is moved from one object to another. This can happen in everyday scenarios, like playing pool or in the case of two planks on a smooth surface. Imagine plank A, which is faster, transferring packets to plank B, which is slower. This transfer process involves momentum. The momentum of an object is the product of its mass and velocity ( \( p = mv \) ). Plank A loses some of its momentum when it transfers packets, as mass moving from a fast object to a slow one results in speed adjustments. B gains momentum and A loses it, adhering to momentum conservation principles and equations.
  • Momentum is a vector quantity, involving direction as well as magnitude.
  • The transfer is isolated to the internal system of two planks without external forces influencing them.
  • Changes in velocity due to momentum transfer heavily rely on the masses of the packets being identical and the smoothness of the surface.
Understanding momentum transfer offers insight into how systems change internally, keeping the total energy within isolated systems stable.
Newton's Laws and Their Role
Newton's laws of motion are frameworks for understanding how objects interact in the world. In this context, primarily Newton's third law is at play. According to this law, for every action, there is an equal and opposite reaction.
  • When plank A transfers packets to plank B, the interaction slows down A and speeds up B.
  • This is because as A pushes the packets toward B, an opposite force acts on A.
  • Action and reaction forces act on different objects, showing how interaction leads to motion modification.
Moreover, Newton's second law, \( F = ma \), tells us how much acceleration is involved based on the force exerted and the mass of an object. In momentum transfer, it helps predict how plank B speeds up and A slows down due to the changes in force distributions. Integrating Newton's laws allows for a detailed understanding of why the internal mechanics of the plank system behave as they do during mass transfer.
Mechanics Problems in Physics
Tackling mechanics problems requires applying theoretical principles to real-world scenarios. These problems, like the one with planks A and B, help clarify concepts such as momentum transfer and Newton's laws.
  • Mechanics problems often focus on isolated systems, ignoring external forces like friction.
  • Simplifications are made to understand core behaviors like acceleration and momentum shifts.
  • By breaking down problems into simpler steps (e.g., initial conditions, forces involved, results), students build a systematic approach to physics challenges.
In teaching and understanding mechanics, students learn how to deduce outcomes based on initial conditions and understand the bridge between theory and practical applications.
As in this exercise, identifying key factors like mass transfer clarifies how physics operates in simplified systems and everyday life dynamics. Embracing mechanics problems fosters critical thinking and deepens intuition regarding physical interactions.

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Most popular questions from this chapter

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