A block of mass 30 ·0 kg is being brought down by a chain....

A block of mass $30 \cdot 0 \mathrm{~kg}$ is being brought down by a chain. If the block acquires a speed of $40 \cdot 0 \mathrm{~cm} / \mathrm{s}$ in dropping down $2 \cdot 00 \mathrm{~m}$, find the work done by the chain during the process.

Key Concepts

Work-Energy Theorem

The work-energy theorem states that the net work done on an object by all forces is equal to the change in its kinetic energy. This theorem provides a fundamental link between forces applied to an object and its motion, making it possible to calculate energy changes resulting from various work contributions, such as those from gravity and other forces.

Gravitational Potential Energy

Gravitational potential energy is the energy held by an object because of its position relative to a gravitational source. When an object is lowered, the decrease in gravitational potential energy is determined by the product of its mass, the gravitational acceleration, and the change in height, playing a crucial role in energy balance calculations.

Kinetic Energy

Kinetic energy is the energy of motion of an object, calculated using the formula 0.5 times the mass times the velocity squared. Understanding kinetic energy is essential when using the work-energy theorem because it quantifies how much energy the system has gained or lost due to changes in speed.

Work Done by a Force

Work done by a force represents the energy transferred to or from an object when a force causes displacement. In problems involving multiple forces, determining the work done by a specific agent requires isolating its contribution from other energy changes, such as those due to gravity, to fully understand its impact on the system’s energy.

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