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It sounds like you are hung up on the most fundamental bit, that a force applied at a velocity is power. (in scalar terms). It is a bit hard to rectify the first principle, but doesnt it follow your intuition?
If you are push a box along a floor that has 10lb friction force, doesn't it make sense that your rate of doing work (power) would be 2x as much at 10mph as it would be at 5mph for example? Or imagine riding a bike up hill, it seems intuitive that it takes a bunch more power to ride at a constant 100mph, vs say a 1 mph walking pace.
Your friends bicycle cheating device would work as hypothesized, but you will require more and more power for you mechanism to keep it at the required angle as the speed increases.
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