A block of mass 100 g is moved with a speed of 5 ·0 m / s at the highest point in a closed cir

step 1 Okay, in this question, a block of mass that is 100 gram, okay, that is 0 .1 KG, is moved with a

A block of mass 100 g is moved with a speed of 5 ·0 m / s...

A block of mass $100 \mathrm{~g}$ is moved with a speed of $5 \cdot 0 \mathrm{~m} / \mathrm{s}$ at the highest point in a closed circular tube of radius $10 \mathrm{~cm}$ kept in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.

Key Concepts

Work

Work is defined as the scalar product of a force and the displacement through which it acts. It quantitatively measures the energy transferred to or from an object by the force as it moves along its path.

Work?Energy Theorem

The work?energy theorem states that the net work done on an object is equal to the change in its kinetic energy. This concept allows one to relate forces acting over distances to the resulting variations in an object’s speed and energy.

Conservative versus Non-Conservative Forces

Conservative forces, such as gravity, depend only on the initial and final positions and have associated potential energies, while non-conservative forces, like friction, dissipate energy and depend on the path taken. This distinction is essential when accounting for energy losses in mechanical systems.

Constraint Forces

Constraint forces, which arise from the geometrical restrictions imposed on a system (for example, the forces from a tube guiding an object’s motion), typically do no work when they are perpendicular to the displacement. However, if friction or other dissipative effects are present, these forces can perform work that alters the system’s mechanical energy.

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