A block m slides with a speed of v0=6 m / s along a track from one level to a higher level as s

step 1 In this question we have given a block M that slides with a speed of 6 meter per second along a

A block m slides with a speed of v0=6 m / s along a track...

A block $m$ slides with a speed of $v_{0}=6 \mathrm{~m} / \mathrm{s}$ along a track from one level to a higher level as shown. The track is frictionless until the block reaches the higher level, where co-efficient of friction is $0.6$. The distance $d$ travelled by block on higher level before stopping is $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (A) $\frac{7}{6} \mathrm{~m}$ (B) $\frac{5}{6} \mathrm{~m}$ (C) $\frac{29}{6} \mathrm{~m}$ (D) $3 \mathrm{~m}$

A block $m$ slides with a speed of $v_{0}=6 \mathrm{~m} / \mathrm{s}$ along a track from one level to a higher level as shown. The track is frictionless until the block reaches the higher level, where co-efficient of friction is $0.6$. The distance $d$ travelled by block on higher level before stopping is $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $\frac{7}{6} \mathrm{~m}$
(B) $\frac{5}{6} \mathrm{~m}$
(C) $\frac{29}{6} \mathrm{~m}$
(D) $3 \mathrm{~m}$

Key Concepts

Conservation of Energy

This concept deals with the idea that the total mechanical energy (kinetic plus potential) of an isolated system remains constant in the absence of non?conservative forces. When a block moves without friction, its kinetic energy can be converted to potential energy and vice versa, setting the stage for understanding energy transformations along different segments of a path.

Work-Energy Principle

This principle states that the work done by all forces acting on an object equals the change in its kinetic energy. In the presence of non-conservative forces like friction, the work done by friction is taken into account, as it leads to a decrease in the mechanical energy of the system.

Kinetic Friction

Kinetic friction is the resistive force that acts opposite to the direction of motion when two surfaces slide against each other. It is calculated as the product of the coefficient of kinetic friction and the normal force, and it plays a critical role in determining how far an object will travel before coming to rest when friction is present.

Potential Energy

Potential energy, often gravitational in nature, represents the energy stored within an object due to its position in a force field, such as gravity. When an object moves to a higher level, its kinetic energy is converted into gravitational potential energy, affecting the subsequent dynamics, especially in systems where energy conservation is analyzed before friction comes into play.

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