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It's important that you don't miss the verb used in the first sentence: "If non-conservative forces (i.e., external forces) are "acting upon". Describing a force as simply acting upon an object is considerably different than describing a force as doing work upon an object. For instance, as you sit in your seat and read this page (it's assumed that you do homework while sitting), there is a normal force acting upon your body. This force is not doing work upon you (it's assumed you are sitting and not bouncing). If the normal force were doing work upon you, then you would be changing your speed or your height. Non-conservative forces (such as normal forces) do that to a person when they do work - they change the person's total mechanical energy by changing speed or height. But you are likely not changing your speed or your height. The normal force is indeed acting upon your body, but not doing work upon it. There is a big difference between a force acting upon an object and a force doing work upon an object.
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Many students get confused by this question. Either because of ignorance (they don't know any better) or negligence (they don't read carefully enough), this question causes much frustration. As discussed in the A Very Fine Detail section, there is great importance in the phrase acting upon an object. Whether a force acts upon an object or not has little importance in this unit on work and energy. What is of utmost importance in every analysis is whether a force does work upon an object or not. The total mechanical energy of an object is only changed if non-conservative forces do net work upon an object. See Dictionary section.
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Definition of Non-conservative Force:
All the different types of forces that could do work upon an object can be categorized as either conservative or non-conservative forces. A non-conservative force is a type of force that changes the total amount of mechanical energy possessed by an object. When non-conservative forces do work upon an object, the total amount of mechanical energy changes.
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