The co-efficient of friction between the block and plank is μand its value is such that block be

step 1 For this question, a block sliding on plank friction will be at opposite to velocity of block. S

The co-efficient of friction between the block and plank is...

The co-efficient of friction between the block and plank is $\mu$ and its value is such that block becomes stationary with respect to plank before it reaches the other end. Then (A) the work done by friction on the block is negative. (B) the work done by friction on the plank is positive. (C) the net work done by friction is negative. (D) net work done by the friction is zero.

The co-efficient of friction between the block and plank is $\mu$ and its value is such that block becomes stationary with respect to plank before it reaches the other end. Then
(A) the work done by friction on the block is negative.
(B) the work done by friction on the plank is positive.
(C) the net work done by friction is negative.
(D) net work done by the friction is zero.

Key Concepts

Energy Dissipation and Conversion

Friction is a non-conservative force that typically converts mechanical energy into thermal energy (heat), leading to an overall reduction in the system’s mechanical energy. In problems where friction acts between parts of a system, some objects may gain kinetic energy while others lose it, with the net change reflecting the energy dissipated into heat. Recognizing how friction dissipates energy is key to solving problems involving work and energy balance.

Work–Energy Theorem

The work–energy theorem states that the net work done on an object is equal to its change in kinetic energy. When forces perform work (either positive or negative), they alter the speed of the object, and thus its kinetic energy. This principle is widely used to relate the forces acting on a moving object to the resulting changes in its motion.

Internal Versus External Forces

When analyzing a system composed of multiple interacting bodies, forces between the bodies are classified as internal forces. Although they act in equal and opposite pairs, the work done by these forces on individual bodies can be different even though, when considering the whole system, their contributions may partly cancel or lead to energy redistribution. This distinction is important for understanding energy transformations and momentum conservation in isolated systems.

Kinetic Friction

Kinetic friction is the resistive force that acts between surfaces in relative motion. It always opposes the relative sliding motion between the surfaces and is characterized by a coefficient (usually denoted ?) multiplied by the normal force. In dynamics problems, kinetic friction influences the acceleration and energy changes of the objects involved, often converting some of the system’s kinetic energy into heat.

Work Done by Forces

Work is defined as the product of the force applied and the displacement of the point of application in the direction of the force. The sign of the work depends on whether the force acts in the same direction as the displacement (positive work) or in the opposite direction (negative work). This concept is crucial when analyzing energy changes in a system, as positive work increases kinetic energy while negative work decreases it.

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