A block is gently placed on a conveyor belt moving...

A block is gently placed on a conveyor belt moving horizontally with constant speed. After 4 s the velocity of the block becomes equal to the velocity of belt. If the coefficient of friction between the block and the belt is 0.2, then velocity of the conveyor belt is (a) $2 \mathrm{~ms}^{-1}$ (b) $4 \mathrm{~ms}^{-1}$ (c) $6 \mathrm{~ms}^{-1}$ (d) $8 \mathrm{~ms}^{-1}$

A block is gently placed on a conveyor belt moving horizontally with constant speed. After 4 s the velocity of the block becomes equal to the velocity of belt. If the coefficient of friction between the block and the belt is 0.2, then velocity of the conveyor belt is
(a) $2 \mathrm{~ms}^{-1}$
(b) $4 \mathrm{~ms}^{-1}$
(c) $6 \mathrm{~ms}^{-1}$
(d) $8 \mathrm{~ms}^{-1}$

Key Concepts

Newton's Second Law

This principle states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In the context of the problem, it explains how the frictional force between the block and the belt produces an acceleration that changes the block's velocity until it matches the belt's speed.

Friction Force

Friction is the resistive force that opposes relative motion between two surfaces in contact. In this scenario, friction acts as the driving force that accelerates the block from rest to the speed of the moving conveyor belt. Its magnitude is determined by the coefficient of friction and the normal force.

Coefficient of Friction

This is a dimensionless value that quantifies the frictional resistance between two surfaces. For the block and the conveyor belt, it determines how strong the frictional force is and, consequently, how quickly the block will accelerate to match the belt's velocity.

Kinematics of Constant Acceleration

This concept involves using equations of motion when an object experiences a constant acceleration. In the problem, it is used to relate the acceleration (caused by friction) over a given time period to determine the final velocity of the block, which becomes equal to the belt's speed.

Relative Motion

Relative motion refers to the motion of an object as observed from a particular frame of reference. In the case of a block on a moving conveyor belt, the block initially has a different velocity from the belt, and friction works to reduce this velocity difference until the block moves in unison with the belt.

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