A block of mass m=0.1 kg is released from a height of 4 m on a curved smooth surface. On the h

step 1 In this question we have given a block which is released from a height of 4 meter on a curved sm

A block of mass m=0.1 kg is released from a height of 4 m...

A block of mass $m=0.1 \mathrm{~kg}$ is released from a height of $4 \mathrm{~m}$ on a curved smooth surface. On the horizontal surface, path $A B$ is smooth and path $B C$ offers coefficient of friction $\mu=0.1$. If the impact of block with the vertical wall at $C$ be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be: (take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ ) (A) $29 \mathrm{~m}$ (B) $49 \mathrm{~m}$ (C) $59 \mathrm{~m}$ (D) $109 \mathrm{~m}$

A block of mass $m=0.1 \mathrm{~kg}$ is released from a height of $4 \mathrm{~m}$ on a curved smooth surface. On the horizontal surface, path $A B$ is smooth and path $B C$ offers coefficient of friction $\mu=0.1$. If the impact of block with the vertical wall at $C$ be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be: (take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
(A) $29 \mathrm{~m}$
(B) $49 \mathrm{~m}$
(C) $59 \mathrm{~m}$
(D) $109 \mathrm{~m}$

Key Concepts

Conservation of Mechanical Energy

This concept states that in an isolated system without non-conservative forces, the total mechanical energy (potential plus kinetic) remains constant. In problems involving the conversion of gravitational potential energy into kinetic energy, energy conservation is used to compute velocities and energy available for subsequent motion.

Gravitational Potential Energy to Kinetic Energy Conversion

When an object is released from a height, its gravitational potential energy is converted into kinetic energy as it descends. This conversion process is central in determining the speed of the object at the bottom of the descent before other effects, such as friction or collisions, come into play.

Work Done by Friction

Friction is a non-conservative force that converts mechanical energy into thermal energy, reducing the kinetic energy of a moving object. The work done by friction can be calculated by multiplying the frictional force by the distance over which it acts, and is crucial to determine how far the object will travel before coming to rest.

Elastic Collision

In a perfectly elastic collision, both kinetic energy and momentum are conserved. This means that when an object collides with a surface and rebounds, there is no loss of kinetic energy during the collision, although the direction of the velocity may change. This principle is essential when analyzing motion after collisions.

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