Final answer:
Work done by nonconservative forces such as friction results in the conversion of mechanical energy into other forms of energy, with more work required when the force of friction is larger.
Step-by-step explanation:
When considering the work done by nonconservative forces like air resistance or friction, we need to understand that it changes the mechanical energy of a system into other forms, such as heat or sound. For instance, pushing a heavy box across a rug with a larger friction force compared to a smooth concrete floor will result in more work done against friction. This is because friction is a nonconservative force that does work on an object, depending on the path taken.
Specifically, in the scenario provided, we calculate the work done against friction by multiplying the friction force by the distance over which it acts. The larger friction force on the rug will result in more energy being dissipated as thermal energy compared to the smooth concrete floor. Hence, more work is done when going across the rug than going around the floor, which can be quantified by the extra work needed.