In an ideal simple machine, what is the relationship between input and output work?

The correct relationship in an ideal simple machine is that input work equals output work. This principle stems from the conservation of energy, which states that in a perfect system, energy cannot be created or destroyed, only transformed. In the context of simple machines, this means that whatever amount of energy (or work) is put into the machine as input is entirely converted into output work, with no energy lost to friction or other inefficiencies.

In real-world scenarios, simple machines are not perfectly efficient due to friction, heat loss, and other factors, which is where the other options speak to practical limitations. However, in an ideal situation, these losses do not occur, providing a scenario where the input and output work are identical. This concept is foundational in understanding how machines operate and is essential for analyzing their efficiency in practical applications.