Final answer:
The standard metric unit for both work and energy is the joule (J), which is equivalent to one newton-meter or 1 kg·m²/s².
Step-by-step explanation:
In the context of work and energy, the standard metric unit is the joule (J). This unit is derived from the calculation of work, which is the product of force and distance. The name 'joule' honors the British physicist James Prescott Joule. It is defined as the amount of work done when a force of one newton displaces an object by one meter in the direction of the force, equating to one newton-meter (1 N·m). Further, in the International System of Units (SI), 1 joule is equivalent to 1 kilogram meter squared per second squared (1 kg·m²/s²). This fundamental unit showcases the correlation between work and energy, signifying that they can be interconverted and expressing that different forms of energy can be measured with the same unit.
Work and energy have the same units, which are measured in newton-meters (Nm) in the SI system. One joule is defined as the amount of work done when a force of 1 newton acts on an object and moves it through a distance of 1 meter.
For example, if you push a box with a force of 1 newton and it moves a distance of 1 meter, the work done on the box is 1 joule.