Final answer:
The macroscopic work done on a block lifted at a constant speed through a height h is given by W = mgh, which also represents the gravitational potential energy gained by the block.
Step-by-step explanation:
The macroscopic work done on a block lifted at a constant speed through a height \( h \) is a fundamental concept in physics, particularly in the context of gravitational forces. When lifting a block against gravity, the work done (\( W \)) is calculated using the formula \( W = mgh \), where \( m \) is the mass of the block, \( g \) is the acceleration due to gravity, and \( h \) is the height through which the block is lifted.
This expression stems from the relationship between force, distance, and work. In lifting the block against gravity, a force equal to its weight (\( mg \)) is applied, and the block is moved vertically through a height \( h \). The work done is the product of the force and the distance over which it is applied. Hence, \( W = mgh \) quantifies the energy expended to lift the block against the gravitational force.
The energy added to the block during this process is identified as gravitational potential energy (\( PE_g \)). Gravitational potential energy is a form of stored energy associated with an object's position in a gravitational field. In this scenario, the work done to lift the block is converted into gravitational potential energy, and this potential energy can be subsequently transformed into kinetic energy if the block is allowed to fall.
Understanding the relationship between work, gravitational potential energy, and the forces acting on objects provides a foundation for comprehending the dynamics of mechanical systems and energy transformations in various physical phenomena.